What is corporate social responsibility? How does that play into risk and funding?

What is corporate social responsibility? How does that play into risk and funding?

Essential Activities:

Reading Chapter 9 and 10 in the text will assist you in writing this discussion forum.

Watching the videos The man who figured out Madoff’s Ponzi Scheme and Internal Control Basics will assist you in writing this discussion forum.

Notes:

Please refer to the discussion forum rubric on the start here tab for this assignment.

Initial discussion forum is due by Wednesday and responses to two of your classmates are due by Saturday.

Each week to earn full points on the discussion forums, make sure to include outside sources to support your discussion.

Ensure that you are citing and referencing your work in APA format.

You should respond to at least two fellow students on two separate days.

Requirements: in-depth example

296cor91411_ch09_296-329.indd 296 01/20/17 04:22 PMIs there such a thing as a high-reward, zero-risk investment?Characterizing Risk and Return9PART FIVEviewpointsBusiness ApplicationManagers from the production and marketing departments have proposed some risky new business projects for your firm. These new ideas appear to be riskier than the firmÕs current business operations.You know that diversifying the firmÕs product offerings could reduce the firmÕs overall risk. However, you are concerned that taking on these new projects will make the firmÕs stock too risky. How can you determine whether these project ideas would make the firmÕs stock riskier or less risky? (See the solution at the end of the chapter.)Personal ApplicationSuppose an investor owns a portfolio invested 100 percent in long-term Treasury bonds because the owner prefers low risk. The investor has avoided owning stocks because of their high volatility.The investorÕs stockbroker claims that putting 10 percent of the portfolio in stocks would actually reduce total risk and increase the portfolioÕs expected return. The investor knows that stocks are riskier than bonds. How can adding the risky stocks to the bond portfolio reduce the risk level? (See the solution at the end of the chapter.)Final PDF to printer

297cor91411_ch09_296-329.indd 297 01/20/17 04:22 PMYou can invest your money very safely by opening a savings account at a bank or by buying Treasury bills. So why would you invest your money in risky stocks and bonds if you can take advantage of low-risk oppor-tunities? The answer: Very low risk investments also provide a very low return. Investors take on higher risk investments in expectation of earning higher returns. Likewise, businesses also take on risky capital invest-ments only if they expect to earn higher returns that at least cover their costs, including investorsÕ required return. Both investor and business sentiments create a positive rela-tionship between risk and expected return. Of course, taking risk means that you get no guarantee that you will recoup your investment. In the short run, higher risk investments often significantly underperform lower risk investments. In addition, not all forms of risk are rewarded. In © Brand X Pictures/Superstock LG9-1 Compute an investmentÕs dollar and percentage return. LG9-2 Find information about the historical returns and volatil-ity for the stock, bond, and cash markets. LG9-3 Measure and evaluate the total risk of an investment using several methods. LG9-4 Recognize the risk-return relationship and its implications. LG9-5 Plan investments that take advantage of diversification and its impact on total risk. LG9-6 Find efficient and optimal portfolios. LG9-7 Compute a portfolioÕs return.Learning Goalsthis chapter, youÕll see how the risk-return relationship fundamentally affects finance theory. We focus on using historical information to char-acterize past returns and risks. We show how you can diversify to elimi-nate some risk and expect the highest return possible for your desired risk level. In Chapter 10, weÕll turn to estimating the risks and returns you should expect in the future.Final PDF to printer

298 part five Risk and Returncor91411_ch09_296-329.indd 298 01/20/17 04:22 PM 9.1 ∙ Historical ReturnsLetÕs begin our discussion of risk and return by characterizing the concept of return. First, we need a method for calculating returns. After computing a return, investors need to assess whether it was a good, average, or bad investment return. Examining returns from the past gives us a general idea of what we might expect to see in the future. We should think in terms of return for the long run because a return for any one year can be quite different from the average returns from the past couple of decades.Computing ReturnsHow much have you earned on each of your investments? Two ways to determine this are to compute the actual dollar return or compute the dollar return as a percentage of the money invested.DOLLAR RETURN The dollar return earned includes any capital gain (or loss) that occurred as well as any income that you received over the period. Equation 9-1 illustrates the dollar return calculation: Dollar return = Capital gain or loss + Income= (Ending value Ð Beginning value) + Income (9-1)For example, say you held 50 shares of Alphabet (GOOG), the parent company of Google. The stock price had a market price of $526.40 per share at the end of 2014. Alphabet paid no dividends during 2015. At the end of 2015, AlphabetÕs stock price was $758.88. For the whole of 2015, you earned a capital gain of ($758.88 Ð $526.40) × 50 shares, or $11,624.In AlphabetÕs case, the stock price increased, so you experienced a capital gain. On the other hand, the toy and game producer Mattel, Inc. (MAT) started the year at $30.95 per share, paid $1.52 in dividends, and ended 2015 at $27.17. If you owned 200 shares of Mattel, you would have experienced a capital loss of Ð$756 (= [$27.17 Ð $30.95] × 200 shares). This loss would have been partially offset by the $304 of dividends received. However, the total dollar return would still have been Ð$452 (= Ð$756 + $304). Stock prices can fluctuate substantially and cause large positive or negative dollar returns.Does your dollar return depend on whether you continue to hold the Alphabet and Mattel stock or sell it? No. In general, finance deals with market values. Alphabet stock was worth $758.88 at the end of 2015 regardless of whether you held the stock or sold it. If you sell it, then we refer to your gains as ÒrealizedÓ gains. If you continue to hold the stock, the gains are ÒunrealizedÓ gains.PERCENTAGE RETURN We usually find it more useful to characterize investment earnings as percentage returns so that we can easily compare one investmentÕs return to other alternativesÕ returns. We calculate percentage return by dividing the dollar return by the investmentÕs value at the beginning of the time period. Percentage return = Ending value Ð Beginning value + Income ___________________________________ Beginning value × 100% (9-2)Because itÕs standardized, we can use percentage returns for almost any type of invest-ment. We can use beginning and ending values for stock positions, bond prices, real estate values, and so on. Investment income may be stock dividends, bond interest pay-ments, or other receipts. The percentage return for holding the Mattel stock during calen-dar year 2015 was Ð7.3 percent, computed as Mattel percentage return = ($27.17 × 200) − ($30.95 × 200) + ($1.52 × 200) _________________________________________ $30.95 × 200 = −0.073, or −7.3% LG9-1dollar returnThe amount of profit or loss from an investment denoted in dollars.percentage returnThe dollar return character-ized as a percentage of money invested.Final PDF to printer

chapter 9 Characterizing Risk and Return 299cor91411_ch09_296-329.indd 299 01/20/17 04:22 PMThe return for the Alphabet position during the same period was a whopping 44.16 percent: Alphabet percentage return = ( $758.88 × 50 ) − ( $526.40 × 50 ) _______________________________ $526.40 × 50 = 0.4416, or 44.16% Both firms belong to the S&P 500 Index, which earned 1.38 percent in 2015.EXAMPLE 9-1Computing ReturnsYou are evaluating a stockÕs short-term performance. On August 16, 2010, technology firm 3PAR saw its stock price surge on news of a takeover battle between Dell and Hewlett-Packard. 3PAR stock had closed the previous trading day at $9.65 and was up to $18.00 by the end of the day. 3PAR had ended 2009 at $11.85 and does not pay a dividend. What is the dollar return and percentage return of 300 shares of 3PAR for the day and year to date?SOLUTION: For the day, realize that no income is paid. Therefore, the dollar return is $2,505 = 300 × ($18.00 Ð $9.65) + 0 and the percent return is 86.53% = $2,505 Ö (300 × $9.65). The year to date (YTD) return also does not include dividend income. So the dollar YTD return is $1,845 = 300 × ($18.00 Ð $11.85). The 3PAR YTD percentage return is 3PAR YTD return = ( $18.00 × 300 ) − ( $11.85 × 300 ) + ( $0 ) ________________________________ $11.85 × 300 = 0.5190, or 51.90% Hewlett-Packard eventually won the bidding war and purchased 3PAR for $33 per share!Similar to Problems 9-1, 9-2, 9-3, 9-4, Self-Test Problem 1LG9-1 Are one-year returns typical for expectations in the long run? We look to average returns to examine performance over time. The arithmetic average return provides an estimate for how the investment has performed over longer periods of time. The formula for the average return is Average return = Sum of all returns Ö Number of returns = Σ t=1 N Return t __________ N (9-3)where the return for each subperiod is summed up and divided by the number of subperi-ods. You can state the returns in either percentage or decimal format. Alphabet has only been a public company for a relatively brief period, so it will not have a long history of returns. Thus, Table 9.1 shows the annual returns for Mattel and office supply store Staples, Inc., from 1991 to 2015. First, notice that over time, the returns are quite varied for both firms. The stock return for Mattel has ranged from a low of Ð52.4 percent in 1999 to a high of 82.6 percent in 1991. StaplesÕ stock return varied between Ð45.7 percent (2015) to 171.6 percent (1991). Also note that the returns appear unpredictable or random. Sometimes a large negative return is followed by another bad year, like MattelÕs returns in 2007 and 2008. Other times, a poor year is fol-lowed by a very good year, like 2008 and 2009 for Staples. The table also reports aver-age annual returns for Mattel and Staples of 14.8 percent and 19.4 percent, respectively. Over the years, the annual returns for these stocks have been quite different from their average returns.average returnsA measure summarizing the past performance of an investment.For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer

300 part five Risk and Returncor91411_ch09_296-329.indd 300 01/20/17 04:22 PMABCDEF1MattelStaplesMattelStaples2199182.6%171.6%20045.4%24.0%3199233.0%14.9%2005−12.6%9.5%419936.9%13.5%200652.1%9.4%5199415.5%30.0%2007−10.5%−5.9%6199559.8%46.3%2008−28.5%−32.5%7199610.5%24.9%200944.3%49.5%8199746.6%32.9%201024.0%−3.3%91998−43.0%136.4%201135.6%−32.7%101999−52.4%−16.8%201225.9%−4.6%11200047.4%−30.5%201334.3%0.8%12200128.8%10.0%2014−32.1%34.5%1320025.5%−5.8%2015−5.2%−45.7%142003−3.5%55.0%15Average =14.8%19.4% Note the range of returns. Few annual returns are close to the average return.Data Source: Yahoo! FinanceTABLE 9.1 Annual and Average Returns for Mattel and Staples, 1991 to 2015The average returns shown in this chapter are more precisely called arithmetic aver-age returns. These average returns are appropriate for statistical analysis. However, they do not accurately illustrate the historical performance of a stock or portfolio. To see this, consider the $100 stock that earned a 50 percent return one year (to $150) and then earned a Ð50 percent return the next year (to $75). The arithmetic average return is therefore (50% + Ð50%) Ö 2 = 0%. Do you believe the average return was zero percent per year? If you started with a $100 stock and ended with a $75 stock, did you earn zero per-cent? No, you lost money. A measure of that performance should illustrate a negative return. The accurate measure to be used in performance analysis is called the geometric mean return, or the mean return computed by finding the equivalent return that is com-pounded for N periods. In this example, the mean return is [(1 + 0.50) × (1 + Ð0.50)]1/2 Ð 1 = Ð0.134, or Ð13.4 percent. Given the loss of $25 over two years, this Ð13.4 percent per year mean return seems more reasonable than the zero percent average return.The general formula for the geometric mean return is Geometric mean return = [ Π t=1 N (1 + Return t _______ 100 ) ] 1 __ N −1 (9-4)Performance of Asset ClassesDuring any given year, the stock market may perform better than the bond market, or it may perform worse. Over longer time periods, how do stocks, bonds, or cash securities perform? Historically, stocks have performed better than either bonds or cash. Table 9.2 shows the average returns for these three asset classes over the period 1950 to 2015, as well as over various subperiods. Over the entire period, stocks (as measured by the S&P 500 Index) earned an average 12.6 percent return per year. This is nearly double the 6.6 percent return earned by long-term Treasury bonds. Cash securities, measured by U.S. Treasury bills, earned an average 4.4 percent return.The table also shows each asset classÕs average return for each decade since 1950. The best decade for the stock market was the 1950s, when stocks earned an aver-age 20.9 percent per year. The 1990s ran a close second with a 19 percent per year geometric mean returnThe mean return computed by finding the equivalent return that is compounded for N periods.LG9-2Final PDF to printer

chapter 9 Characterizing Risk and Return 301cor91411_ch09_296-329.indd 301 01/20/17 04:22 PMABCDE1StocksLong-Term Treasury BondsT-Bills21950 to 2015Average12.6%6.6%4.4%31950 to 1959Average20.9%0.0%2.0%41960 to 1969Average8.7%1.6%4.0%51970 to 1979Average7.5%5.7%6.3%61980 to 1989Average18.2%13.5%8.9%71990 to 1999Average19.0%9.5%4.9%82000 to 2009Average0.9%8.0%2.7%92010Annual Return15.1%9.4%0.01%102011Annual Return2.1%29.9%0.02%112012Annual Return16.0%3.6%0.02%122013Annual Return32.4%−12.7%0.07%132014Annual Return13.7%25.1%0.05%142015Annual Return1.4%−1.2%0.21%152010 to 2015Average13.4%9.0%0.06%Returns have been very different among decades.TABLE 9.2 Annual and Average Returns for Stocks, Bonds, and T-Bills, 1950 to 2015TIME OUT 9-1 How important were dividend payments to the total returns that Mattel and Staples offered investors?   9-2 Using the average returns shown in Table 9.2, compute how much a $10,000 invest-ment made in each asset class at the beginning of each decade would become at the end of each decade.  return. The best decade for the bond market was the 1980s, when it earned an average 13.5  percent per year return due to capital gains as interest rates fell. Stocks have out-performed bonds in every decade since 1950 except the recent 2000s. Notice that the average return in the stock and bond markets has not been negative during any decade since 1950. But average stock returns do not really paint a very accurate picture of annual returns. Individual annual returns can vary strongly and be quite negative in any particular year. Indeed, this annual variability defines risk. The stock market return in 2008 was particularly poor because of the financial crisis. However, not all stocks fell the same amount. Notice that Mattel and Staples declined by only 28.5 and 32.5 percent while the stock market in general declined 35.5 percent. Financial company stocks fell the most during the crisis.9.2 ∙ Historical RisksWhen you purchase a U.S. Treasury bill, you know exactly what your dollar and per-centage return are going to be. Many people find comfort in the certainty from this safe investment. On the other hand, when you purchase a stock, you do not know what your return is going to beÑeither in the short term or in the long run. This uncertainty is pre-cisely what makes stock investing risky. ItÕs useful to evaluate this uncertainty quantita-tively so that we can compare risk among different stocks and asset classes.LG9-3Final PDF to printer

302 part five Risk and Returncor91411_ch09_296-329.indd 302 01/20/17 04:22 PMComputing VolatilityFinancial theory suggests that investors should look at an investmentÕs historical returns to assess how much uncertainty to expect in the future. If you see high vari-ability in historical returns, you should expect a high degree of future uncertainty. Table 9.2 shows that between 2010 and 2015, the stock market experienced a range of 1.4 percent return in 2015 to a 32.4 percent return in 2013. Bonds also experienced variability: Ð12.7 percent return in 2013 to 29.9 percent return in 2011. Examining the range of historical returns provides just one way to express the return volatility that we can expect. In practical terms, the finance industry uses a statistical return volatility measure known as the standard deviation of percentage returns. We cal-culate standard deviation as the square root of the variance, and this figure represents the securityÕs or portfolioÕs total risk. WeÕll discuss other risk measurements in the next chapter.Our process of computing standard deviation starts with the average return over the period. The average annual return for the stock market since 1950 is 12.6 percent. How much can the return in any given year deviate from this average? We compute the actual annual deviation by subtracting the return each year from this average return: Return(1950) Ð Average return; Return(1951) Ð Average return; Return(1952) Ð Average return, and so on. Note that many of these deviations will be negative (from a lower-than-average return that year) and others will be positive (from a higher-than-average return). If we computed the average of these return deviations, our result would be zero. Large positive deviations cancel out large negative deviations and hide the variability. To really see the size of the variations without the distractions that come with including a positive or negative sign, we square each deviation before adding them up. Dividing by the number of returns in the sample minus one provides the return variance.1 The square root of the return vari-ance is the standard deviation: Standard deviation = Square root of the average squared deviation of returns = √ _________________________ Σ t=1 N ( Return t − Average return ) 2 _________________________ N − 1 (9-5)Note that this equation provides an estimate of the true population standard devia-tion using a specific historical sample. A large standard deviation indicates greater return volatilityÑor high risk. Table 9.3 shows the standard deviations of Mattel stock returns over 25 years. The Deviation column shows the annual return minus MattelÕs average return of 14.8 percent. The last column squares each deviation. Then we sum up these squared deviations and divide the result by the number of observations less one (24) to compute the return variance. If we want to use a measure that makes sense in the real world (how would you interpret a squared percentage, anyway?), we take the square root of the variance to get the standard deviation. MattelÕs standard devia-tion of returns during this sample period comes to 33.4 percent. In comparison, the standard deviation of Staples stock returns for this same period is 48.7 percent. Since StaplesÕ standard deviation is higher, its stock features more total risk than MattelÕs stock does.Although analysts and investors use a stock returnÕs standard deviation as an impor-tant and common measure of risk, itÕs laborious to compute by hand. Most people use a spreadsheet or statistical software to calculate stock return standard deviations.standard deviationA measure of past return volatility, or risk, of an investment.total riskThe volatility of an invest-ment, which includes cur-rent portions of firm-specific risk and market risk.1We use the denominator of N − 1 to compute a sampleÕs standard deviation, which is the most common for finance applications. We would divide the standard deviation of a population simply by N. Final PDF to printer

chapter 9 Characterizing Risk and Return 303cor91411_ch09_296-329.indd 303 01/20/17 04:22 PMTABLE 9.3 Computation of Mattel Stock Return Standard DeviationABCD1Mattel ReturnDeviationSquared Deviation2199182.6%67.8%46.0%3199233.0%18.1%3.3%419936.9%−7.9%0.6%5199415.5%0.6%0.0%6199559.8%45.0%20.3%7199610.5%−4.3%0.2%8199746.6%31.7%10.1%91998−43.0%−57.8%33.4%101999−52.4%−67.2%45.1%11200047.4%32.6%10.6%12200128.8%14.0%2.0%1320025.5%−9.3%0.9%142003−3.5%−18.3%3.3%1520045.4%−9.5%0.9%162005−12.6%−27.4%7.5%17200652.1%37.2%13.9%182007−10.5%−25.4%6.4%192008−28.5%−43.3%18.8%20200944.3%29.5%8.7%21201024.0%9.2%0.8%22201135.6%20.8%4.3%23201225.9%11.1%1.2%24201334.3%19.5%3.8%252014−32.1%−46.9%22.0%262015−5.2%−20.1%4.0%27Average =   14.8%Sum =268.2% 28Variance =  11.2% 29Std Dev = 33.4%30=AVERAGE(B2:B26)31=D27/(COUNT(D2:D26)-1)=D28^0.5Investors use standard deviation as a measure of risk; the higher the standard deviation, the riskier the asset.Data Source: Yahoo! FinanceRisk and ReturnFind the average return and risk (as measured by standard deviation) for Mattel since 2006. Table 9.3 shows the annual returns for years 2006 to 2015.SOLUTION: First, compute the average annual return for the period. Using equation 9-3: 52.1% − 10.5% − 28.5% + 44.3% + 24.0% + 35.6% + 25.9% + 34.3% − 32.1% − 5.2% _______________________________________________________________________________ 10 = 140.0% ________ 10 = 14.0% EXAMPLE 9-2LG9-1, LG9-3For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer

304 part five Risk and Returncor91411_ch09_296-329.indd 304 01/20/17 04:22 PMStocksLong-Term Treasury BondsT-Bills1950 to 201517.3%11.1%3.0%1950 to 195919.8%4.9%0.8%1960 to 196914.4%6.2%1.3%1970 to 197919.2%6.8%1.8%1980 to 198912.7%15.1%2.6%1990 to 199914.2%12.8%1.2%2000 to 200920.4%10.3%1.9%2010 to 201511.3%16.1%0.1%Some decades experience higher risk than others in each asset class.TABLE 9.4 Annual Standard Deviation of Returns for Stocks, Bonds, and T-Bills, 1950 to 2015Mattel has averaged a 14.0 percent return per year since 2006. To compute the risk, use the standard deviation equation 9-5. First, find the deviations of return for each year:Year 200620072008200920102011201220132014201552.1%Ð14.0%Ð10.5%Ð14.0%Ð28.5%Ð14.0%44.3%Ð14.0%24.0%Ð14.0%35.6%Ð14.0%25.9%Ð14.0%34.3%Ð14.0%Ð32.1%Ð14.0%Ð5.2%Ð14.0%Square those deviations:Year 2006200720082009201020112012201320142015(52.1%Ð14.0%)2(Ð10.5%Ð14.0%)2(Ð28.5%Ð14.0%)2(44.3%Ð14.0%)2(24.0%Ð14.0%)2(35.6%Ð14.0%)2(25.9%Ð14.0%)2(34.3%Ð14.0%)2(Ð32.1%Ð14.0%)2(Ð5.2%Ð14.0%)2Then add them up, divide by n − 1, and take the square root: = √ ___________________________________________________________________________ 1449.3 + 602.2 + 1805.4 + 920.5 + 100.4 + 467.4 + 142.3 + 412.5 + 2122.4 + 370.2 ___________________________________________________________________________ 9 = √ ______ 932.5 = 30.5% Mattel stock has averaged a 14.0 percent return with a standard deviation of 30.5  percent since 2006.Similar to Problems 9-15, 9-16, 9-17, 9-18, 9-33, 9-34, Self-Test Problem 2Risk of Asset ClassesWe report the standard deviations of return for stocks, bonds, and T-bills in Table 9.4 for 1950 to 2015 and for each decade since 1950. Over the entire sample, the stock market returnsÕ standard deviation is 17.3 percent. As we would expect, stock market volatility is higher than bond market volatility (11.1 percent) or for T-bills (3.0 percent). These vola-tility estimates are consistent with our previously stated position that the stock market carries more risk than the bond or cash markets do. Every decade since 1950 has seen a lot of stock market volatility. The bond market has experienced the most volatility since the 1980s as interest rates varied dramatically.You will recall from Chapter 7 that since any bondÕs par value and coupon rate are fixed, bond prices must fluctuate to adjust for changes in interest rates. Bond prices respond inversely to interest rate changes: As interest rates rise, bond prices fall, and if interest rates fall, bond prices rise. T-bill returns have experienced very low volatility over each decade. Indeed, T-bills are commonly considered to be one of the only risk-free assets. Higher-risk investments offer higher returns over time. But short-term fluc-tuations in the value of higher risk investments can be substantial. The stock market is LG9-2Final PDF to printer

chapter 9 Characterizing Risk and Return 305cor91411_ch09_296-329.indd 305 01/20/17 04:22 PMriskyÑwhile it has offered a good annual return of 12.6 percent, that return comes with volatility of 17.3 percent standard deviation. Many investors may intellectually under-stand that this high risk means that they may receive very poor returns in the short term. Investors really felt the full force of this risk when the stock market declined three years in a row (2000 to 2002). Some investors even decided that this was too much risk for them and they sold out of the stock market before the 2003 rally. Other investors got out of the stock market after it plunged to lows in March 2009. Market volatility can cause investors to make emotionally based decisionsÑselling at low prices.The stock market returnsÕ standard deviations that appear in Table 9.4 are all consider-ably lower than the standard deviations of Mattel and of Staples stocks (33.4 percent and 48.7 percent, respectively). In this case, we measure stock market return and standard deviation using the S&P 500 Index. Mattel and Staples are both included in the S&P 500 Index. Why do these two large firms have measures of total riskÑstandard deviationsÑthat are at least twice as large as the standard deviations on the stock market returns? Are Mattel and Staples just two of the most risky firms in the Index? Actually, no. The differ-ences in standard deviations between these individual companies and the entire market have much more to do with diversification. Owning 500 companies, such as all of those included in the S&P 500 Index, generates much less risk than owning just one company. This phenomenon appears in the standard deviation measure. WeÕll discuss the effects of diversification in detail later in this chapter.Risk versus ReturnInvestors can buy very safe T-bills. Or they can take some risk to seek higher returns. How much extra return can you expect for taking more risk? This is known as the trade-off between risk and return. The coefficient of variation (CoV) is a common relative measure of this risk-vs-reward relationship. The equation for the coefficient of variation is simply the standard deviation divided by average return. It is interpreted as the amount of risk (measured by volatility) per unit of return: Coefficient of variation = Amount of risk Ö Return = Standard deviation ________________ Average return (9-6)As an investor, you would want to receive a very high return (the denominator in the equation) with a very low risk (the numerator). So, a smaller CoV indicates a better risk-reward relationship. Since the average return and standard deviation for Mattel stock are 14.8 percent and 33.4 percent, its CoV is 2.26 (= 33.4 Ö 14.8). This is better than StaplesÕ CoV of 2.51 (= 48.7 Ö 19.4). For all asset classes for the period 1950 to 2015, the stock market earned a higher return than bonds and was also riskier. But which one had a better risk-return relationship? The CoV for common stock is 1.37 (= 17.3 Ö 12.6). For Treasury bonds, the coefficient of variation is 1.68 (= 11.1 Ö 6.6). Even though stocks are riskier than bonds, they involve a somewhat better risk-reward trade-off.LG9-4coefficient of variationA measure of risk to reward (standard deviation divided by average return) earned by an investment over a specific period of time.EXAMPLE 9-3Risk versus ReturnYou are interested in the risk-return relationship of stocks in each decade since 1950. Obtain the average returns and risks in Table 9.2 and Table 9.4.LG9-4 For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer

306 part five Risk and Returncor91411_ch09_296-329.indd 306 01/20/17 04:22 PM9.3 ∙ Forming PortfoliosAs we noted previously, Mattel and Staples stocksÕ risk as measured by their standard deviations appear quite high compared to the standard deviation of the S&P 500 Index. This is by no means a coincidence. Combining stocks into portfolios can reduce many sources of stock risk. Diversification reduces risk. The S&P 500 Index, for example, tracks 500 companies, which allows for a great deal of diversification.Diversifying to Reduce RiskThink about a stockÕs total risk as having two components. The first component includes risks that are both specific to that company and common to other companies in the same industry. We call this risk firm-specific risk. The stockÕs other risk component is gen-eral risk that all firmsÑand all individuals, for that matterÑface based upon economic strength both domestically and globally. We call this type of risk market risk. These risks appear in the equation Total risk = Firm-specific risk + Market risk (9-7)Standard deviations measure total risk. Individual stocks are subject to many firm-specific risks. We can reduce firm-specific risk by combining stocks into a portfolio. Since we can reduce firm-specific risk by diversifying, this risk is sometimes referred to as diversifiable risk. If Staples announces lower-than-expected profits, its stock price will decline. However, since this news is specific to Staples, the news should not affect Mattel stockÕs price. On the other hand, if the government announces a change in unem-ployment, both stocksÕ prices will change to some degree. Macroeconomic events rep-resent market risks because such eventsÑunemployment claims, interest rate changes, national budget deficits or surplusesÑaffect all companies.LG9-5portfolioA combination of invest-ment assets held by an investor.diversificationThe process of putting money in different types of investments for the pur-pose of reducing the over-all risk of the portfolio.firm-specific riskThe portion of total risk that is attributable to firm or industry factors. Firm- specific risk can be reduced through diversification.market riskThe portion of total risk that is attributable to over-all economic factors.diversifiable riskAnother term for firm- specific risk.SOLUTION:Using the coefficient of variation, the average returns, and standard deviation of return, com-pute the following risk-return relationships: Co V 1950s = 19.8% _______ 20.9% = 0.95 Co V 1960s = 14.4% _______ 8.7% = 1.66 Co V 1970s = 19.2% _______ 7.5% = 2.56 Co V 1980s = 12.7% _______ 18.2% = 0.70 Co V 1990s = 14.2% _______ 19.0% = 0.75 Co V 2000s = 20.4% _______ 0.9% = 22.67 Note that over short time periods, the stock risk-return relationship varies significantly.Similar to Problems 9-7, 9-8, 9-19, 9-20, 9-33, and 9-34, Self-Test Problem 3TIME OUT 9-3 What volatility measure can we use to evaluate and compare risk among different investment alternatives? 9-4 Explain why the coefficients of variation for Mattel and Staples are so much higher than the CoV for the stock market as a whole.Final PDF to printer

chapter 9 Characterizing Risk and Return 307cor91411_ch09_296-329.indd 307 01/20/17 04:22 PMSuppose that you own only Mattel stock and have earned the annual returns shown in Table 9.5. Then someone suggests that you add Staples to your Mattel stock to form a two-stock portfolio. Both Mattel and Staples stocks carry a lot of total risk. But look at the risk and return characteristics of a portfolio consisting of 50 percent Staples stock and 50 percent Mattel stock. You start with Mattel stock, which provided an average return of 14.8 percent with a risk of 33.4 percent. The Staples stock you are adding has more risk than Mattel. The two-stock portfolio earns an average 17.1 percent return with a standard deviation of only 32.1 percent. You added a high-risk stock to a high-risk stock and you ended up with a portfolio with lower risk and a higher return! This is a hallmark of most portfolios, which pool market risk but often provide offsetting, reduced firm-specific risks overall.Next, add IBM stock to your Mattel and Staples stock portfolio. Figure 9.1 shows that the total risk of this three-stock portfolio declines to 25.7 percent. Note that adding Newmont Mining, Disney, and General Electric also reduces the total risk of the stock ABCD1Mattel ReturnStaples ReturnPortfolio of Mattel and Staples2199182.6%−171.6%127.1%3199233.0%14.9%23.9%419936.9%13.5%10.2%5199415.5%30.0%22.8%6199559.8%46.3%53.1%7199610.5%24.9%17.7%8199746.6%32.9%39.7%91998−43.0%136.4%46.7%101999−52.4%−16.8%−34.6%11200047.4%−30.5%8.5%12200128.8%10.0%19.4%1320025.5%−5.8%−0.1%142003−3.5%55.0%25.8%1520045.4%24.0%14.7%162005−12.6%9.5%−1.5%17200652.1%9.4%30.8%182007−10.5%−5.9%−8.2%192008−28.5%−32.5%−30.5%20200944.3%49.5%46.9%21201024.0%−3.3%10.4%22201135.6%−32.7%1.5%23201225.9%−4.6%10.7%24201334.3%0.8%17.5%252014−32.1%34.5%1.2%262015−5.2%−45.7%−25.5%2728Average =14.8%19.4%17.1%29Std Dev =33.4%48.7%32.1%3031=AVERAGE(B2:B26)=STDEV(C2:C26)=0.5*B26+0.5*C26The risk-reducing power of diversification! Note that the risk of the portfolio is lower than the risk of the two stocks individually.Data Source: Yahoo! FinanceTABLE 9.5 Combining Stocks Can Greatly Reduce RiskFinal PDF to printer

!Want to Know More?Key Words to Search for Updates: diversification, pension plan choices, asset allocationExperts have examined investor behavior using detailed data-sets of stock brokerage accounts, employee pension plans, and the Survey of Consumer Finances. Studies have identi-fied many investor behaviors that are inconsistent with the principle of full diversification: ¥ Many households own relatively few individual stocksÑthey held a median number of two stocks until 2001, when it rose to three. Of course, many households own equity indirectly, through mutual funds or retirement accounts, and these indirect holdings tend to be much better diversified. ¥ Ten to 15 percent of households with between $100,000 and $1 million in financial asset wealth own no stocks ( neither directly nor indirectly through funds). ¥ Investors seem to prefer securities of local firms. Many geographic regions feature companies that are heavily INVESTOR DIVERSIFICATION PROBLEMSfinance at work personalconcentrated in few industries. Thus, a local preference could reduce diversification opportunities. ¥ Many employees hold mostly their employersÕ stocks (more than 50 percent of employee holdings), particularly within their 401(k) retirement savings accounts. Holding a lot of a single stock creates a ÒportfolioÓ with high total risk.Finance professionals and the investment industry have established diversification concepts for many decades and can help investors maximize their returns with appropriate risk levels. But many investors do not consult professionals; they fail to diversify and thus take unnecessary diversifiable risk.Sources: Stephen G. Dimmock, Roy Kouwenberg, Olivia S. Mitchell, and Kim Peijnenburg, ÒAmbiguity Aversion and Household Portfolio Choice Puzzles: Empirical Evidence,Ó Journal of Financial Economics in press (2016); and Hans-Martin Von Gaudecker, ÒHow Does Household Portfolio Diversification Vary with Financial Literacy and Financial Advice?,Ó Journal of Finance 70 (2015): 489Ð507.308 part five Risk and Returncor91411_ch09_296-329.indd 308 01/27/17 06:26 PM0%Staples onlyAdd MattelAdd IBMAdd Newmont MiningAdd DisneyAdd General ElectricAll S&P 500 Index10%20%30%40%50%60%Standard Deviation of PortfolioMarket riskFirm-speciÞc riskFIGURE 9.1 Adding Stocks to a Portfolio Reduces RiskThe total portfolio risk is greatly reduced by adding the first few stocks to a portfolio.portfolio. As you add more stocks, the firm-specific risk portion of the total portfolio risk declines. The total risk falls rapidly as we add the first few stocks. DiversificationÕs power to reduce firm-specific risk weakens for the later stocks added to the portfolio, because we have already eliminated much of the firm-specific risk. We could continue to add stocks until the portfolio comprises all S&P 500 Index firms, in which case the standard deviation of the portfolio would be 17.3 percent. At this point, virtually all of Final PDF to printer

chapter 9 Characterizing Risk and Return 309cor91411_ch09_296-329.indd 309 01/20/17 04:22 PMefficient portfoliosThe set of portfolios that have the maximum expected return for each level of risk.the firm-specific risk has been purged and the portfolio carries only market risk, which is sometimes called nondiversifiable risk.Modern Portfolio TheoryThe concept that diversification reduces risk was formalized in the early 1950s by Harry Markowitz, who eventually won the Nobel Prize in Economics for his work. MarkowitzÕs modern portfolio theory shows how risk reduction occurs when securities are com-bined. The theory also describes how to combine stocks to achieve the lowest total risk possible for a given expected return. Or, said differently, it describes how to achieve the highest expected return for the desired risk level. The combination of securities that achieves the highest expected return for a personÕs desired level of risk is called the investorÕs optimal portfolio.In our Mattel and Staples portfolio example, we allocated 50 percent of the portfolio to Mattel and 50 percent to Staples. Is this the best allocation for the portfolio? Consider the different allocations shown in Figure 9.2 for the two stocks. The graph shows the expected return (computed as average return) and risk (computed as standard deviation) of various portfolios. It would be terrific if you could find a portfolio located in the upper left-hand corner. That is, investors would like a high expected return with low risk. One large dot shows the risk-return point for owning only Mattel. The other large dot shows owning only Staples. The smaller diamonds show 10/90, 25/75, 40/60, 50/50, 60/40, 75/25, and 90/10 allocations of Mattel/Staples stocks.While all these portfolios are possible, not all are desirable. For example, the portfo-lio of 75 percent Mattel and 25 percent Staples is not desirable. Other portfolios provide both higher return and lower risk. We say that one portfolio dominates the other if it has higher expected return for the same (or less) risk, or the same (or higher) expected return with lower risk. The dominating portfolios appear higher and to the left in the figure. One such portfolio consists of 25 percent Mattel stock and 75 percent Staples stock. The 50/50 portfolio (circled in the figure) is also better than the 75/25 portfolio. Portfolios with the highest return possible for each risk level are called efficient portfolios. Notice that if you drew a line connecting the dots, the figure would appear like the end of a bullet. The portfolios on the top of the bullet dominate the portfolios on the bottom; the top portfolio dots show the efficient portfolios for these two stocks.LG9-6modern portfolio theoryA concept and procedure for combining securities into a portfolio to minimize risk.optimal portfolioThe best portfolio of securi-ties for the investorÕs level of risk aversion.12%13%14%15%16%17%19%20%18%15%20%25%30%35%40%45%50%55%Risk (Standard Deviation)Expected ReturnMattelPortfolio of 50% Matteland 50% Staples60% Mattel & 40% StaplesStaples25% Mattel & 75% Staples75% Mattel & 25% StaplesFIGURE 9.2Risk and Return Ramifications of Portfolio Allocations to Mattel and StaplesInvestors only value the port-folios at the top of the graph because they offer the same risk as the lower portfolios but with higher expected return!nondiversifiable riskAnother term for market risk.Final PDF to printer

310 part five Risk and Returncor91411_ch09_296-329.indd 310 01/20/17 04:22 PMFigure 9.3 shows efficient portfolios for combining the four stocks: Staples, Mattel, IBM, and Newmont Mining. We used this portfolio to demonstrate how diversification reduces risk in Figure 9.1. These portfolios appear as diamonds in the figure with each diamond representing a different allocation of the four stocks. The single square repre-sents the portfolio that consists of 25 percent in each of the four stocks. Notice that other, efficient portfolios dominate this portfolio.If we showed all efficient portfolios, they would appear as a line that connects the upper side of the bullet shape. If we added all available securities to the graph, then all of the efficient portfolios of those securities form the efficient frontier. Efficient fron-tier portfolios dominate all other possible stock portfolios. The shape of the efficient frontier implies that diminishing returns apply to risk-taking in the investment world. To gain ever-higher expected rates of return, investors must be willing to take on ever-increasing amounts of risk. The optimal portfolio for you is one on the efficient frontier that reflects the amount of risk that youÕre willing to take. Clearly, optimal portfolio choice depends on individual risk preferences. Highly risk-averse investors will select low-risk portfolios on the efficient frontier, while more adventuresome investors will select higher-risk portfolios. Any choice may be appropriate, given differences in indi-vidual risk preferences.Investors can further diversify by adding foreign stocks and commodities to their port-folio. For example, a U.S. investor can lower total risk by adding stocks from emerging market countries and gold.HOW DOES DIVERSIFICATION WORK? Will combining any two stocks greatly reduce total risk as much as combining Staples and Mattel did? The answer is no. If two stocks are subject to exactly the same kinds of events such that their returns always behave the same way over time, then we have no need to own both stocksÑsimply pick the one that performs better. Diversification comes when two stocks are subject to differ-ent kinds of events such that their returns differ over time.Consider the illustration in Figure 9.4. You own Stock A in Panel A of the figure. The stock features risk, as demonstrated by its price volatility over time. You would like to reduce the risk by combining your position in Stock A with an equal position in Stock B. In this case, the alternative stock, Stock B, moves the same way over time as Stock A efficient frontierThe combination of all efficient portfolios.LG9-50%3%6%9%12%18%21%15%10%15%20%25%30%35%40%45%50%55%Risk (Standard Deviation)Expected ReturnNewmont MiningEfficient portfoliosMattelIBMStaplesEqually weightedportfolioFIGURE 9.3Efficient Portfolios from Four StocksThe efficient portfolios dominate all of the individual stocks.Final PDF to printer

312 part five Risk and Returncor91411_ch09_296-329.indd 312 01/20/17 04:22 PM!Want to Know More?Key Words to Search for Updates: international diversification, global asset allocationThe U.S. stock market represents nearly 47 percent of all stock value worldwide. Japanese and U.K. stock markets rep-resent 11 percent and 8 percent of the worldwide stock mar-ket value, respectively. Many investment and diversification opportunities present themselves internationally! However, most people allocate very little or none of their portfolios to international securities. If worldwide opportunities can create greater diversification, then those who donÕt invest in interna-tional stocks miss out on an important opportunity to reduce risk in their portfolios.MSCI Barra is the leading provider of global stock market indexes. Some MSCI Barra indexes follow individual countries. In addition, MSCI Barra compiles composite indexes for groups of companies in developed markets, emerging markets, frontier markets, and by geographic regions. Investment managers use the MSCI World Index, the MSCI EAFE (Europe, Australasia, Far East) Index, and the MSCI Emerging Markets Index as premier benchmarks to measure global stock market performance.The following table shows the average annual returns and standard deviations for the U.S. stock market, Treasury bonds, and the MSCI EAFE and MSCI Emerging Markets indexes for the period 1988 to 2015. Note that both the EAFE and the Emerging Markets indexes feature higher risk than the S&P 500 Index. The Emerging Markets return has been high, but the EAFE return has been low compared to the U.S. stock and bond markets.INTERNATIONAL OPPORTUNITIES FOR DIVERSIFICATIONfinance at work marketsThe correlations among these markets appear as follows:S&P 500BondsEAFEEmerging MarketsS&P 5001Bonds−0.151EAFE0.74−0.411Emerging Markets0.48−0.310.731S&P 500BondsEAFEEmerging MarketsAverage11.7%9.2%5.6%13.3%Std. Deviation17.611.919.433.7The correlation between the S&P 500 Index and the MSCI EAFE is 0.74 and between the Emerging Markets is 0.48. These correlations indicate that diversification might work. Even better diversification appears to be possible between the U.S. Treasury Bond Market and the EAFE and Emerging Markets indexesÐlook at the negative correlations!Source: www.msci.comexactly opposite. A value of 0 means that the movements of the two returns over time are unrelated to one another. Investors seeking diversification look for stocks where the returns have low or negative correlations with each other.What return correlations are common between stocks? Panel A of Table 9.6 shows the correlations between many companies. One high correlation shown is the 0.690 correlation between Citigroup and the Bank of New York. This shouldnÕt be surpris-ing, because these are two similar firms in the same industry. Combining these two stocks wouldnÕt reduce risk very much in a portfolio. The largest negative correlation is the correlation of Ð0.212 between Newmont Mining and the Bank of New York. These firms practice in very different industries and provide large risk reduction pos-sibilities. Note that the correlation between Staples and Mattel is 0.198. This low cor-relation gives us an answer to the question of why total risk (in the form of standard deviations) fell so much when we combined the two stocks relative to their individual standard deviations as shown in Figure 9.2. Most of the correlations in Table 9.6 are positive. Because most stocks are positively correlated, we typically add many stocks together to fully eliminate all the firm-specific risk in the portfolio, as we showed in Figure 9.1.Panel B of Table 9.6 shows correlations between stocks, bonds, and T-bills. At Ð0.035, the correlation between stocks and bonds is small. The small correlation allows for the LG9-2 Final PDF to printer

chapter 9 Characterizing Risk and Return 313cor91411_ch09_296-329.indd 313 01/20/17 04:22 PMPANEL A: COMPANY ANNUAL RETURNS, 1991 TO 2015StaplesMattelIBMNewmont MiningDisneyGeneral ElectricCitigroupStaples1Mattel0.1981IBM0.314−0.0291Newmont Mining−0.036−0.117−0.0871Disney0.1630.4400.076−0.1711General Electric0.3800.1340.396−0.0380.5171Citigroup0.2970.3280.0560.1390.4140.7731Bank of New York0.5840.4590.045−0.2120.6060.6710.690PANEL B: ASSET CLASS ANNUAL RETURNS, 1950 TO 2015StocksLong-Term Treasury BondsT-BillsStocks1Long-term Treasury bonds−0.0351T-bills−0.0630.1371TABLE 9.6 Correlation between Various Stocks and Asset ClassesMATH COACH When computing portfolio returns, use the decimal format for the portfolio weights and the percentage format for the security returns. The result of equation 9-8 will then be in percentage format.possibility of good risk reduction by adding bonds to a stock portfolio. Therefore, a well-diversified portfolio will contain both stocks and bonds.PORTFOLIO RETURN A portfolioÕs return calculation is straightforward. A portfo-lioÕs return comes directly from the returns of the portfolio securities and the proportion of the portfolio invested in each security. For example, General Electric stock earned Ð1.9 percent. The Newmont Mining earned 17.3 percent over the same period. If you had invested a quarter of your money in General Electric stock and three quarters of it in Newmont Mining stock, then your portfolio return would be Return contribution from GE + Contribution from NEM = (0.25 × −1.9%) + (0.75 × 17.3%) = 12.50% To calculate the return on a three-stock portfolio, you will need the proportion of each stock in the portfolio and each stockÕs return. We typically call these proportions weights, signified by w. So, a portfolio with n securities will have a return of R p = (Proportion of portfolio in first stock × That stockʼs return) + (Second stock portion × Second stock return) + . . . = ( w 1 × R 1 ) + ( w 2 × R 2 ) + ( w 3 × R 3 ) + . . . + ( w n × R n ) = Σ i=1 n w i R i (9-8)where the sum of the weights, w, must equal one. The portfolioÕs rate of return is a simple weighted sum of the returns of each stock in the portfolio. Investors choose portfolio weights by determining how much of each stock they want in their portfolios. Ideally, investors will choose weights for their portfolios located on the efficient frontier (shown in Figure 9.3).LG9-7 Final PDF to printer

314 part five Risk and Returncor91411_ch09_296-329.indd 314 01/20/17 04:22 PMviewpoints REVISITEDBusiness Application SolutionWe can apply diversification concepts and modern portfolio theory to many more applications than just investment portfolios. For example, a manufacturing facility can be more efficient by producing different products during the year as demand dictates the need for one product over another. Salespeople can reduce the volatility of their commission incomes by having many different products to sell.Although new project ideas have more risk, they could actually reduce the firmÕs overall risk if the projects diversify the firmÕs current business operations. You could evaluate this possibility by determining the correlation between the expected cash flows from each project idea with the expected cash flows of the firmÕs current business operations. A low or negative correlation would mean that the new projects could actually reduce risk for the firm. Note that some firms may find that their position is too conservative and that they wish to increase their risk to increase the possibility of earning a higher return.Personal Application SolutionTables 9.2 and 9.4 show that since 1950 the bond market experienced an average return and standard deviation of 6.6 percent and 11.1 percent, respectively. Stocks earned a 12.6 percent return with a 17.3 percent standard deviation. The investor is correct in the belief that the stock market is riskier than the bond market.Computing Portfolio ReturnsAt the beginning of the year, you owned $5,000 of Disney stock, $10,000 of Bank of New York stock, and $15,000 of IBM stock. During the year, Disney, Bank of New York, and IBM returned − 4.8 percent, 19.4 percent, and 12.8 percent, respectively. What is your portfolioÕs return?SOLUTION:First determine your portfolio weights. The three stocks make up a $30,000 portfolio. Disney makes up a 16.67 percent (= $5,000 Ö $30,000) portion of the portfolio. Bank of New York stock makes up a 33.33 percent (= $10,000 Ö $30,000) portion, and IBM a 50.0 percent (= $15,000 Ö $30,000) portion.The portfolio return can now be computed as R p = (0.1667 × −4.8%) + (0.3333 × 19.4%) + (0.50 × 12.8%) = −0.80% + 6.47% + 6.40% = 12.07% Similar to Problems 9-11, 9-12, 9-13, 9-14, 9-23, 9-24, 9-25, 9-26, 9-29, 9-30, 9-31, 9-32, Self-Test Problem 1EXAMPLE 9-4LG9-7 TIME OUT 9-5 Describe characteristics of companies that would be good to combine into a portfolio.   9-6 Explain why one portfolio made up of the same companies (but not in the same propor-tions) as another portfolio can be undesirable in comparison.   9-7 Combining which two companies in Table 9.6 would reduce risk the most? Combining which two would create the least diversification?  For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer

chapter 9 Characterizing Risk and Return 315cor91411_ch09_296-329.indd 315 01/20/17 04:22 PMsummary of learning goalsIn this chapter, we described how to measure investment risk and return. In the long run, higher risk should be associated with higher returns. In the short term, though, high-risk investments experience a great deal of volatility and produce extreme returns. Recall that the market does not reward all risks. We can, for example, reduce firm-specific risk by diversifying our holdings. We get the best diversification opportunities when we combine securities that have very different return characteristics.However, Table 9.6 shows that the correlation between the stock and bond market is very low, at −0.035. This result allows some diversification opportunity. Indeed, a portfolio of 10 percent stocks and 90 percent bonds would have experienced an average annual return of 7.2 percent with a standard deviation of 10.1 percent since 1950. The broker is correct; adding a small portion of stocks to a bond portfolio actually reduces total risk!Compute an investmentÕs dollar and percentage return. Dollar returns on an investment include both the capital gain (or loss) from any price change in the investment and any income received. Stocks pay dividend income and fixed income securities, such as bonds, pay regularly scheduled interest payments as income. We can find the percentage return by dividing the dollar return by the investmentÕs value at the beginning of the period. Percentage return is a more useful measure to compare performance among different securities. To make meaningful comparisons, we typically average annual percentage returns to assess the investmentÕs historical performance.Find information about the historical returns and volatility for the stock, bond, and cash markets. Stocks have earned an average 12.6 percent return per year since 1950. However, stock market performance can be very volatile. Investors have frequently seen double-digit percentage stock price declines as well as spectacular increases. This high volatility is illustrated by the stock marketÕs standard deviation of 17.3 percent on average returns of 12.6 percent.Bonds have earned lower average returns of 6.6 percent annually, but have also experienced less risk (standard deviation of 11.1 percent). The cash market, as measured by T-bill performance, shows an average return and standard deviation of 4.4 percent and 3.0 percent, respectively.Measure and evaluate the total risk of an investment using several methods. An investmentÕs total risk encompasses the total range of expected LG9-1LG9-2LG9-3outcomes. We measure the likelihood of any particular expected outcome by the past return volatility of the security. We calculate volatility using the statistical concept of the standard deviation of returns. A larger standard deviation indicates higher total risk.Recognize the risk-return relationship and its implications. When low-return, safe investments are available, why would an investor take risk? The motivation for taking on riskier investments is that they offer a higher return. The performance and risk of the stock and bond markets over a long period of time illustrate the direct risk-return relationship that lies at the heart of investment philosophy. Recognize that this relationship can be interpreted in the reverse. When an investment achieves a high return, know that it must be risky.We commonly measure the risk-return relationship using the coefficient of variation (CoV). The CoV is the standard deviation of an investmentÕs returns divided by its average return. The CoV reports the amount of risk taken for every 1 percent of return earned. So lower CoV values indicate more favorable risk-return relationships.Plan investments that take advantage of diversification and its impact on total risk. Recall that an investmentÕs total risk comprises firm-specific risk and market risk. Combining stocks can potentially reduce firm-specific risk in the portfolio. Firms whose returns differ from each other offer the best diversification possibilities. A correlation measures how two different stocks have performed over time relative to one another. Correlations range between −1 and +1. Combining stocks with low or negative correlations can LG9-4LG9-5Final PDF to printer

316cor91411_ch09_296-329.indd 316 01/20/17 04:22 PMaverage returns A measure summarizing the past performance of an investment. p. 299coefficient of variation A measure of risk to reward (standard deviation divided by average return) earned by an investment over a specific period of time. p. 305correlation A measurement of the co-movement between two variables that ranges between −1 and +1. p. 311diversifiable risk Another term for firm- specific risk. p. 306diversification The process of putting money in differ-ent types of investments for the purpose of reducing the overall risk of the portfolio. p. 306dollar return The amount of profit or loss from an investment denoted in dollars. p. 298 efficient frontier The combination of all efficient portfolios. p. 310efficient portfolios The set of portfolios that have the maximum expected return for each level of risk. p. 309firm-specific risk The portion of total risk that is attrib-utable to firm or industry factors. Firm-specific risk can be reduced through diversification. p. 306significantly reduce firm-specific risk and thus reduce total risk in an investorÕs portfolio.Find efficient and optimal portfolios. Investors want the highest return possible for their preferred risk level. If two portfolios have the same risk level, the one that gives the higher expected return dominates the other. A portfolio that has the highest expected return for its risk level dominates all other portfolios with the same risk level; we call this dominating mix an efficient portfolio. The set of all efficient portfolios forms the efficient frontier. Investors pick the efficient portfolio with their own desired risk level to find their optimal portfolios.Compute a portfolioÕs return. A portfolioÕs return comes directly from the returns of the securities in the portfolio and the proportions, or weights, of each investment in the portfolio. In other words, the portfolio return is the weighted average of the portfolioÕs securitiesÕ returns.LG9-6LG9-7chapter equations9-1 Dollar return = Capital gain or loss) + Income = ( Ending value − Beginning value) + Income 9-2 Percentage return = Ending value − Beginning value + Income ___________________________________ Beginning value × 100% 9-3 Average return = ∑ t=1 N Return t ___________ N 9-4 Geometric mean return = [ Π t=1 N (1 + Return t _______ 100 ) ] 1 __ N − 1 9-5 Standard deviation = √ ___________________________ ∑ t=1 N ( Return t − Average return) 2 ___________________________ N − 1 9-6 Coefficient of variation = Standard deviation ________________ Average return 9-7 Total risk = Firm − specific risk + Market risk 9-8 R p = ( w 1 × R 1 ) + ( w 2 × R 2 ) + ( w 3 × R 3 ) + . . . + ( w n × R n ) = Σ i=1 n w i R i key termsFinal PDF to printer

317cor91411_ch09_296-329.indd 317 01/20/17 04:22 PMgeometric mean return The mean return computed by finding the equivalent return that is compounded for N periods. p. 300market risk The portion of total risk that is attributable to over-all economic factors. p. 306modern portfolio theory A concept and procedure for combining securities into a portfolio to minimize risk. p. 309nondiversifiable risk Another term for market risk.  p. 309optimal portfolio The best portfolio of securities for the investorÕs level of risk aversion. p. 309percentage return The dollar return characterized as a percentage of money invested. p. 298portfolio A combination of investment assets held by an investor. p. 306standard deviation A measure of past return volatility, or risk, of an investment. p. 302total risk The volatility of an investment, which includes current portions of firm-specific risk and market risk. p. 302self-test problems with solutions1 Computing Returns Consider that you own the following position at the beginning of the year: 200 shares of US Bancorp at $29.89 per share, 300 shares of Micron Technology at $13.31 per share, and 250 shares of Hilton Hotels at $24.11 per share. During the year, US Bancorp and Hilton Hotels both paid a dividend of $1.39 and $0.16, respectively. At the end of the year, the stock prices of US Bancorp, Micron, and Hilton Hotels were $36.19, $13.12, and $34.90, respectively. What are the dollar and percentage return of the stocks and the return of the portfolio?Solution:You can compute the dollar and percentage returns as US Bancorp dollar return = 200 × ($36.19 − $29.89 + $1.39) = $1,538.00 Percent return = $1,538.00 Ö (200 × $29.89) = 25.73% Micron dollar return = 300 × ($13.12 − $13.31) = $ −57.00 Percent return = $ −57.00 Ö (300 × $13.31) = −1.43% Hilton Hotels dollar return = 250 × ($34.90 − $24.11 + $0.16) = $2,737.50 Percent return = $2,737.50 Ö (250 × $24.11) = 45.42% Now you need the portfolio weights of each stock. The total value of the portfolio at the beginning of the year was Beginning of year value = 200 × $29.89 + 300 × $13.31 + 250 × $24.11 = $15,998.50 So the stock weights are US Bancorp weight = 200 × $29.89 Ö $15,998.50 = 0.3737 Micron weight = 300 × $13.31 Ö $15,998.50 = 0.2496 Hilton Hotels weight = 250 × $24.11 Ö $15,998.50 = 0.3768 Now compute the portfolio return as Portfolio return = 0.3737 × 25.73% + 0.2496 × −1.43% + 0.3768 × 45.42% = 26.37% LG9-1, 9-7Final PDF to printer

318cor91411_ch09_296-329.indd 318 01/20/17 04:22 PM2 Risk and Returns The annual returns for GlaxoSmithKline and for Aetna are shown in the table:LG9-3, 9-5GlaxoSmithKlineAetnaYear 17.94%−8.34%Year 29.8751.28Year 35.6384.70Year 428.7364.49Year 5−21.5924.70GlaxoSmithKlineAetna75/25 PortfolioYear 17.94%−8.34%3.87%Year 29.8751.2820.22Year 35.6384.7025.40Year 428.7364.4937.67Year 5−21.5924.70−10.02Average6.1243.3715.43Std. deviation18.0036.1918.70This combination of the two stocks forms a portfolio that is only slightly riskier than GlaxoSmithKline alone, but earns more than twice the return of GlaxoSmithKline.What is the average return and standard deviation of returns for these two firms? What is the average return and risk of a portfolio consisting of 75 percent of GlaxoSmithKline and 25 percent Aetna?Solution:Using the average and standard deviation equations for the GlaxoSmithKline returns results in Average = 7.94% + 9.87% + 5.63% + 28.73% − 21.59% ____________________________________ 5 = 30.58% _______ 5 = 6.12% Standard deviation = √ ____________________________________________________________________________________ (7.94% − 6.12%) 2 + (9.87% − 6.12%) 2 + (5.63% − 6.12%) 2 + (28.73% − 6.12%) 2 + (−21.59% − 6.12%) 2 ____________________________________________________________________________________ 5 − 1 = √ ______ 324.00 = 18.00% For the portfolio, to compute the return for the portfolio each year, use the 75 percent and 25 percent weights:0.75 × 7.94% + 0.25 × Ð8.34% = 3.87%.The risk and return of these two stocks and the portfolio areFinal PDF to printer

319cor91411_ch09_296-329.indd 319 01/20/17 04:22 PM3 Risk versus Return You have gathered average return and standard deviation data for five stocks (A-E). How have these stocks performed on a risk-versus-return basis? Compute the coefficient of variation for each one.  Solution:Compute the CoVs as CoV A = 35% _____ 13% = 2.69 CoV B = 44% _____ 14% = 3.14 CoV C = 18% _____ 9% = 2.00 CoV D = 25% _____ 11% = 2.27 CoV E = 30% _____ 9% = 3.33 Since lower values represent a better risk-reward trade-off, the stocks can be ordered from best to worst as C, D, A, B, and E.4 Diversification Opportunities You have also computed the correlation between each of the five stocks in ST-3. These correlations are reported in the following table. Assess which stocks should be combined into a portfolio.  Solution:First, note that stocks D and E do not seem to provide much diversification potential with each other because they have a correlation of nearly 1, at 0.95. They also have similar correlations with the other stocks. For example, stock D has a correlation with stock C of 0.33 while stock E has a correlation with stock C of 0.35. Realize that you gain very little in owning both stock D and stock E. Therefore, select stock D for the portfolio because it has exhibited a better risk-reward relationship (see ST-3). Also note that all of the other stocks appear to have reasonably low correlations with one another and therefore would benefit a portfolio. You should look into forming a portfolio of stocks A, B, C, and D.LG9-4LG9-5Annual ReturnCompany ABCDEAverage13%14%9%11%9%Standard deviation3544182530CorrelationsABCDB0.45C0.320.25D0.11−0.18 0.33E0.20−0.07 0.350.95Final PDF to printer

320cor91411_ch09_296-329.indd 320 01/20/17 04:22 PM 1. Why is the percentage return a more useful measure than the dollar return? (LG9-1) 2. Characterize the historical return, risk, and risk-return relationship of the stock, bond, and cash mar-kets. (LG9-2) 3. How do we define risk in this chapter and how do we measure it? (LG9-3) 4. What are the two components of total risk? Which component is part of the risk-return relationship? Why? (LG9-3) 5. WhatÕs the source of firm-specific risk? WhatÕs the source of market risk? (LG9-3) 6. Which company is likely to have lower total risk, General Electric or Coca-Cola? Why? (LG9-3) 7. Can a company change its total risk level over time? How? (LG9-3) 8. What does the coefficient of variation measure? Why is a lower value better for the investor? (LG9-4) 9. You receive an investment newsletter advertisement in the mail. The letter claims that you should invest in a stock that has doubled the return of the S&P 500 Index over the last three months. It also claims that this stock is a surefire safe bet for the future. Explain how these two claims are inconsistent with finance theory. (LG9-4) 10. What does diversification do to the risk and return characteristics of a portfolio? (LG9-5) 11. Describe the diversification potential of two assets with a Ð0.8 correlation. WhatÕs the potential if the correlation is +0.8? (LG9-5) 12. You are a risk-averse investor with a low-risk port-folio of bonds. How is it possible that adding some stocks (which are riskier than bonds) to the portfolio can lower the total risk of the portfolio? (LG9-5) 13. You own only two stocks in your portfolio but want to add more. When you add a third stock, the total risk of your portfolio declines. When you add a tenth stock to the portfolio, the total risk declines. Adding which stock, the third or the tenth, likely reduced the total risk more? Why? (LG9-5) 14. Many employees believe that their employerÕs stock is less likely to lose half of its value than a well-diversified portfolio of stocks. Explain why this belief is erroneous. (LG9-5) 15. Explain what we mean when we say that one portfo-lio dominates another portfolio. (LG9-6) 16. Explain what the efficient frontier is and why it is important to investors. (LG9-6) 17. If an investorÕs desired risk level changes over time, should the investor change the composition of his or her portfolio? How? (LG9-6) 18. Say you own 200 shares of Mattel and 100 shares of Staples. Would your portfolio return be differ-ent if you instead owned 100 shares of Mattel and 200 shares of Staples? Why? (LG9-7)questionsproblems 9-1 Investment Return FedEx Corp. stock ended the previous year at $103.39 per share. It paid a $0.35 per share dividend last year. It ended last year at $106.69. If you owned 200 shares of FedEx, what was your dollar return and percent return? (LG9-1) 9-2 Investment Return Sprint Nextel Corp. stock ended the previous year at $23.36 per share. It paid a $2.37 per share dividend last year. It ended last year at $18.89. If you owned 500 shares of Sprint, what was your dollar return and percent return? (LG9-1) 9-3 Investment Return A corporate bond that you own at the beginning of the year is worth $975. During the year, it pays $35 in interest payments and ends the year valued at $965. What was your dollar return and percent return? (LG9-1) 9-4 Investment Return A Treasury bond that you own at the beginning of the year is worth $1,055. During the year, it pays $35 in interest payments and ends the year valued at $1,065. What was your dollar return and percent return? (LG9-1)basic problemsFinal PDF to printer

321cor91411_ch09_296-329.indd 321 01/20/17 04:22 PM 9-5 Total Risk Rank the following three stocks by their level of total risk, highest to lowest. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15  percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent. (LG9-3) 9-6 Total Risk Rank the following three stocks by their total risk level, highest to lowest. Night Ryder has an average return of 12 percent and standard devia-tion of 32 percent. The average return and standard deviation of WholeMart are 11  percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. (LG9-3) 9-7 Risk versus Return Rank the following three stocks by their risk-return rela-tionship, best to worst. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20  percent. (LG9-4) 9-8 Risk versus Return Rank the following three stocks by their risk-return rela-tionship, best to worst. Night Ryder has an average return of 13 percent and standard deviation of 29 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. (LG9-4) 9-9 Dominant Portfolios Determine which one of these three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Blue has an expected return of 12 percent and risk of 18 percent. The expected return and risk of portfolio Yellow are 15 percent and 17 percent, and for the Purple portfolio are 14 percent and 21 percent. (LG9-6) 9-10 Dominant Portfolios Determine which one of the three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Port-folio Green has an expected return of 15 percent and risk of 21 percent. The expected return and risk of portfolio Red are 13 percent and 17 percent, and for the Orange portfolio are 13 percent and 16 percent. (LG9-6) 9-11 Portfolio Weights An investor owns $6,000 of Adobe Systems stock, $5,000 of Dow Chemical, and $5,000 of Office Depot. What are the portfolio weights of each stock? (LG9-7) 9-12 Portfolio Weights An investor owns $3,000 of Adobe Systems stock, $6,000 of Dow Chemical, and $7,000 of Office Depot. What are the portfolio weights of each stock? (LG9-7) 9-13 Portfolio Return Year-to-date, Oracle had earned a −1.34 percent return. Dur-ing the same time period, Valero Energy earned 7.96 percent and McDonaldÕs earned 0.88 percent. If you have a portfolio made up of 30 percent Oracle, 25 percent Valero Energy, and 45 percent McDonaldÕs, what is your portfolio return? (LG9-7) 9-14 Portfolio Return Year-to-date, Yum Brands had earned a 3.80 percent return. During the same time period, Raytheon earned 4.26 percent and Coca-Cola earned −0.46 percent. If you have a portfolio made up of 30 percent Yum Brands, 30 percent Raytheon, and 40 percent Coca-Cola, what is your portfolio return? (LG9-7)?intermediate problems 9-15 Average Return The past five monthly returns for Kohls are 4.11 percent, 3.62 percent, −1.68 percent, 9.25 percent, and −2.56 percent. What is the aver-age monthly return? (LG9-1) 9-16 Average Return The past five monthly returns for PG&E are −3.17 percent, 3.88 percent, 3.77 percent, 6.47 percent, and 3.58 percent. What is the average monthly return? (LG9-1)Final PDF to printer

322cor91411_ch09_296-329.indd 322 01/20/17 04:22 PMadvanced problems 9-17 Standard Deviation Compute the standard deviation of KohlsÕ monthly returns shown in problem 9-15. (LG9-3) 9-18 Standard Deviation Compute the standard deviation of PG&EÕs monthly returns shown in problem 9-16. (LG9-3) 9-19 Risk versus Return in Bonds Assess the risk-return relationship of the bond market (see Tables 9.2 and 9.4) during each decade since 1950. (LG9-2, LG9-4) 9-20 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see Tables 9.2 and 9.4) during each decade since 1950. (LG9-2, LG9-4) 9-21 Diversifying Consider the characteristics of the following three stocks:Expected ReturnStandard DeviationThumb Devices13%23%Air Comfort10 19Sport Garb10 17Expected ReturnStandard DeviationPic Image11%19%Tax Help919Warm Wear1425 The correlation between Thumb Devices and Air Comfort is Ð0.12. The correlation between Thumb Devices and Sport Garb is Ð0.21. The correlation between Air Comfort and Sport Garb is 0.77. If you can pick only two stocks for your portfolio, which would you pick? Why? (LG9-4, LG9-5) 9-22 Diversifying Consider the characteristics of the following three stocks: The correlation between Pic Image and Tax Help is 0.88. The correlation between Pic Image and Warm Wear is Ð0.21. The correlation between Tax Help and Warm Wear is Ð0.19. If you can pick only two stocks for your portfolio, which would you pick? Why? (LG9-4, LG9-5) 9-23 Portfolio Weights If you own 200 shares of Alaska Air at $42.88, 350 shares of Best Buy at $51.32, and 250 shares of Ford Motor at $8.51, what are the portfo-lio weights of each stock? (LG9-7) 9-24 Portfolio Weights If you own 400 shares of Xerox at $17.34,500 shares of Qwest at $8.15, and 350 shares of Liz Claiborne at $44.73, what are the portfolio weights of each stock? (LG9-7) 9-25 Portfolio Return At the beginning of the month, you owned $5,500 of General Dynamics, $7,500 of Starbucks, and $8,000 of Nike. The monthly returns for General Dynamics, Starbucks, and Nike were 7.44 percent, Ð1.36 percent, and Ð0.54 percent. What is your portfolio return? (LG9-7) 9-26 Portfolio Return At the beginning of the month, you owned $6,000 of News Corp, $5,000 of First Data, and $8,500 of Whirlpool. The monthly returns for News Corp, First Data, and Whirlpool were 8.24 percent, Ð2.59 percent, and 10.13 percent. WhatÕs your portfolio return? (LG9-7) 9-27 Asset Allocation You have a portfolio with an asset allocation of 50 percent stocks, 40 percent long-term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and stan-dard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. (LG9-2, LG9-5)Final PDF to printer

323cor91411_ch09_296-329.indd 323 01/20/17 04:22 PMCompanySharesBeginning of Year PriceDividend Per ShareEnd of Year PriceUS Bank300$43.50$2.06 $43.43PepsiCo20059.081.1662.55JDS Uniphase50018.8816.66Duke Energy25027.451.2633.21 9-28 Asset Allocation You have a portfolio with an asset allocation of 35 percent stocks, 55 percent long-term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and stan-dard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. (LG9-2, LG9-5) 9-29 Portfolio Weights You have $15,000 to invest. You want to purchase shares of Alaska Air at $42.88, Best Buy at $51.32, and Ford Motor at $8.51. How many shares of each company should you purchase so that your portfolio consists of 30 percent Alaska Air, 40 percent Best Buy, and 30 percent Ford Motor? Report only whole stock shares. (LG9-7) 9-30 Portfolio Weights You have $20,000 to invest. You want to purchase shares of Xerox at $17.34, Qwest at $8.15, and Liz Claiborne at $44.73. How many shares of each company should you purchase so that your portfolio consists of 25  percent Xerox, 40 percent Qwest, and 35 percent Liz Claiborne? Report only whole stock shares. (LG9-7) 9-31 Portfolio Return The following table shows your stock positions at the begin-ning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio dollar return and percentage return? (LG9-7) 9-32 Portfolio Return The following table shows your stock positions at the begin-ning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio dollar return and percentage return? (LG9-7)CompanySharesBeginning of Year PriceDividend Per ShareEnd of Year PriceJohnson Controls350$72.91$1.17$85.92Medtronic20057.570.4153.51Direct TV50024.9424.39Qualcomm25043.080.4538.92 9-33 Risk, Return, and Their Relationship Consider the following annual returns of Estee Lauder and LoweÕs Companies:Estee LauderLoweÕs CompaniesYear 123.4%−6.0%Year 2−26.016.1Year 317.64.2Year 449.948.0Year 5−16.8−19.0 Compute each stockÕs average return, standard deviation, and coefficient of variation. Which stock appears better? Why? (LG9-3, LG9-4)Final PDF to printer

324cor91411_ch09_296-329.indd 324 01/20/17 04:22 PMMolson CoorsInternational PaperYear 116.3%4.5%Year 2−9.7−17.5Year 336.5−0.2Year 4−6.926.6Year 516.2−11.1DateAll OrdinariesNIKKEI 225FTSEFeb-16−0.35%−8.37%−2.00%Jan-16−5.39%−7.96%−2.54%Dec-15 2.42%−3.61%−1.79%Nov-15−1.33% 3.48%−0.08%Oct-15 4.55% 9.75% 4.94%Sep-15−3.13%−7.95%−2.98%Aug-15−8.09%−8.23%−6.70%Jul-15 4.23% 1.73% 2.69%Jun-15−5.61%−1.59%−6.63%May-15 0.02% 5.34% 0.34%Apr-15−1.50% 1.63% 2.77%Mar-15−0.62% 2.18%−2.50%Feb-15 6.25% 6.36% 2.92%Jan-15 3.02% 1.28% 2.79%Dec-14 1.71%−0.05%−2.33%Nov-14−3.76% 6.37% 2.69%Oct-14 3.93% 1.49%−1.15%Sep-14−5.83% 4.86%−2.89%Aug-14 0.03%−1.26% 1.33%Jul-14 4.48% 3.03%−0.20%Jun-14−1.68% 3.62%−1.47%May-14 0.05% 2.29% 0.95%Apr-14 1.25%−3.53% 2.75%Mar-14−0.23%−0.09%−3.10%Feb-14 4.04%−0.49% 4.60%Jan-14−2.76%−8.45%−3.54%Dec-13 0.73% 4.02% 1.48%Nov-13−1.96% 9.31%−1.20%Oct-13 3.88%−0.88% 4.17%Sep-13 1.80% 7.97% 0.77%Aug-13 1.78%−2.04%−3.14%Jul-13 5.45%−0.07% 6.53%Jun-13−2.82%−0.71%−5.58%May-13−4.93%−0.62% 2.38%Apr-13 3.79%11.80% 0.29%Mar-13−2.74% 7.25% 0.80%Feb-13 4.48% 3.78% 1.34%Jan-13 5.07% 7.15% 6.43% 9-34 Risk, Return, and Their Relationship Consider the following annual returns of Molson Coors and International Paper: Compute each stockÕs average return, standard deviation, and coefficient of variation. Which stock appears better? Why? (LG9-3, LG9-4) 9-35 Spreadsheet Problem Following are the monthly returns for March 2011 to February 2016 of three international stock indices: All Ordinaries of Australia, Nikkei 225 of Japan, and FTSE 100 of England.DateAll OrdinariesNIKKEI 225FTSEDec-12 3.24%10.05% 0.53%Nov-12−0.38% 5.80% 1.45%Oct-12 2.93% 0.66% 0.71%Sep-12 1.55% 0.34% 0.54%Aug-12 1.16% 1.67% 1.35%Jul-12 3.72%−3.46% 1.15%Jun-12 0.04% 5.43% 4.70%May-12−7.47%−10.27% −7.27%Apr-12 1.07%−5.58%−0.53%Mar-12 0.73% 3.71%−1.75%Feb-12 1.44%10.46% 3.34%Jan-12 5.22% 4.11% 1.96%Dec-11−1.76% 0.25% 1.22%Nov-11−4.03%−6.16%−0.70%Oct-11 7.13% 3.31% 8.11%Sep-11−6.86%−2.85%−4.93%Aug-11−2.90%−8.93%−7.23%Jul-11−3.42% 0.17%−2.19%Jun-11−2.70% 1.26%−0.74%May-11−2.25%−1.58%−1.32%Apr-11−0.60% 0.97% 2.73%Mar-11 0.10%−8.18%−1.42%Feb-11 1.52% 3.77% 2.24%Jan-11 0.06% 0.09%−0.63%Dec-10 3.65% 2.94% 6.72%Nov-10−1.20% 7.98%−2.59%Oct-10 2.08%−1.78% 2.28%Sep-10 4.46% 6.18% 6.19%Aug-10−1.52%−7.48%−0.62%Jul-10 4.22% 1.65% 6.94%Jun-10−2.89%−3.95%−5.23%May-10−7.87%−11.65%−6.57%Apr-10−1.21%−0.29%−2.22%Mar-10 5.20% 9.52% 6.07%Feb-10 1.18%−0.71% 3.20%Jan-10−5.85%−3.30%−4.15%Dec-09 3.55%12.85% 4.28%Nov-09 1.48%−6.87% 2.90%Final PDF to printer

325cor91411_ch09_296-329.indd 325 01/20/17 04:22 PMDateAll OrdinariesNIKKEI 225FTSEOct-09−1.95%−0.97%−1.74%Sep-09 5.69%−3.42% 4.58%Aug-09 5.52% 1.31% 6.52%Jul-09 7.64% 4.00% 8.45%Jun-09 3.53% 4.58%−3.82%May-09 1.83% 7.86% 4.10%Apr-09 6.01% 8.86% 8.09%Mar-09 7.14% 7.15% 2.51%Feb-09−5.21%−5.32%−7.70%Jan-09−4.95%−9.77%−6.42%Dec-08−0.36% 4.08% 3.41%Nov-08−7.78%−0.75%−2.04%Oct-08−14.00% −23.83% −10.71% DateAll OrdinariesNIKKEI 225FTSESep-08−11.20% −13.87% −13.02% Aug-08 3.22%−2.27%  4.15% Jul-08−5.26%−0.78%−3.80%Jun-08−7.64%−5.98%−7.06%May-08 2.07% 3.53%−0.56%Apr-08 4.57%10.57% 6.76%Mar-08−4.67%−7.92%−3.10%Feb-08−0.39% 0.08% 0.08%Jan-08−11.28% −11.21% −8.94%Dec-07−2.62%−2.38% 0.38%Nov-07−2.74%−6.31%−4.30%Oct-07 3.01%−0.29% 3.94% a. Compute and compare each indexÕs monthly average return and standard deviation. b. Compute the correlation between (1) All Ordinaries and Nikkei 225,(2) All Ordi-naries and FTSE 100, and (3) Nikkei 225 and FTSE 100, and compare them. c. Form a portfolio consisting of one-third of each of the indexes and show the portfolio return each year, and the portfolioÕs return and standard deviation. 9-36 Spreadsheet Problem a. Create a spreadsheet like the one shown below. The spreadsheet should use the returns for assets A and B to form a portfolio return using the weights for each asset shown in cells E1 and E2. The average portfolio return and standard deviation should compute at the bottom of the column of portfolio returns. When you change the weights, the portfolio returns, average, and standard deviation should recalculate.ABCDEF1ABWeight A =0.50Portfolio2−9.1%20.11%Weight B =0.505.51%311.9%4.56%Sum =1 8.23%4−22.1%7.17%−7.47% 528.7%2.06%15.38% 610.9%7.70%9.30%74.9%−6.50%−0.80% 815.8%1.85%8.82%93.5%9.81%6.66%10−5.5%22.7% 8.60%1123.45%−12.19% 5.63%1215.06%9.38%12.22% 132.11%29.93%16.02% 1416.00%3.56%9.78%1532.39%−12.66% 9.87%1613.69%15.07%14.38% 17189.4%6.8%= AverageAverage =8.1%1914.41%12.04%= StDevStDev =6.07%Final PDF to printer

326cor91411_ch09_296-329.indd 326 01/20/17 04:22 PM b. Use the Solver function to find the weights that provide the highest return for a standard deviation of 6 percent, 7.5 percent, 9 percent, 10.5 percent, 12 percent, and 13.5 percent. Report the weights and the return for each of these portfolio standard deviations. The Solver function is found in the Data tab. (You may have to enable the function through the File tab, then Options, then Add-ins.) The solver image illustrates the maximizing of the average return for the specific constraints. The constraints are that the weights must be between 0 and 1, inclusive, and must sum to 1. Lastly, set the standard devia-tion constraint to the desired level.research it! Following a PortfolioFollowing stocks in a portfolio is easier than ever. Many financial websites have the capability to follow the stocks in your portfolio over time. Just enter your stocks, the number of shares, your purchase price, and your commission cost and you can see how your portfolio is doing. These portfolio managers will update your portfolio as stock prices change, minute to minute. Yahoo! Finance has a ÒMy PortfolioÓ portfolio management tool. Go to the site and start a portfolio to watch (which requires free registration). Try entering symbols EBAY, T, LMT, DUK, and GSK. As a start, assume you own 200 shares of each. You can watch the value of the portfolio change and see how each stock is doing every day. (http://finance.yahoo.com)Final PDF to printer

327cor91411_ch09_296-329.indd 327 01/20/17 04:22 PMintegrated mini-case: Diversifying with Other Asset ClassesMany more types of investments are available besides stocks, bonds, and cash securities. Many people invest in real estate and in precious metals, primarily gold. What are the risk and return characteristics of these investments and do they provide diversification opportunities to the typical stock investor?You can invest in real estate in many ways. You can build properties, own rental units, and trade raw land. These activities take enormous time and expertise. One of the easiest ways to invest in real estate is through real estate investment trusts (REITs) that trade like stocks on the stock exchanges. A REIT represents ownership in a portfolio consisting of a pool of real estate assets. An index of all REITs is a good measure of the performance of the real estate market. The following table shows the annual returns for the All REITs Index alongside the returns of the S&P 500 Index.S&P 500 IndexAll REITs IndexGold Price Changes197537.2%36.3% −19.9%197623.849.0−4.11977−7.219.122.619786.6−1.637.0197918.430.5126.5198032.428.015.21981−4.98.6−32.6198221.431.614.9198322.525.5−16.319846.314.8−19.2198532.25.95.7198618.519.221.319875.2−10.722.2198816.811.4−15.3198931.5−1.8−2.81990−3.2−17.3−1.5199130.635.7−10.119927.712.2−5.7199310.018.527.719941.30.8−2.2199537.418.31.0199623.135.8−4.6199733.418.9−21.4199828.6−18.8−0.8199921.0−6.50.92000−9.125.9−5.42001−11.9 15.50.72002−22.1 5.225.6200328.738.529.9200410.930.44.620054.98.327.8200615.834.424.020073.5−17.831.12008−35.5 −40.04.3200923.520.925.0201015.122.825.320112.13.68.9201216.015.58.3201332.42.9−27.3201413.728.00.120151.42.8−11.9Final PDF to printer

328cor91411_ch09_296-329.indd 328 01/20/17 04:22 PMGold has been a highly sought-after asset all over the world, and has retained at least some economic value over thousands of years. The United States has had a very chaotic history with gold. Americans have sought to Òstrike it richÓ through gold rushes in North Carolina (early 1800s), California and Nevada (mid-1800s), and Alaska (late 1800s). Struggling in the Great Depression, President Franklin D. Roosevelt ordered U.S. citizens to hand in all the gold they possessed. The ban on U.S. citizens owning gold was not lifted until the end of 1974. The table also shows the return from gold prices.The returns for stocks, real estate, and gold are all volatile. However, during many years, the return of one asset is up while the others are down. This looks promising for diversification opportunities. a. Using a spreadsheet, compute the average return and standard deviation of each of the three asset classes. b. Compute the annual returns of a portfolio consisting of 50 percent stocks/40 percent real estate/10 percent gold. What is the average return and standard deviation of this portfolio? Also compute the average return and standard deviation of the fol-lowing portfolios: 75 percent/20 percent/5 percent and 80  percent/5 percent/15 percent. How do these portfolios perform compared to owning just stocks? c. Plot the average return and standard deviation of the three assets and the three portfolios on a risk-return graph like Figure 9.3.ANSWERS TO TIME OUT 9-1 Dividends are a large portion of the return realized by stockholders in the long run. In any given year, the capital gain or loss may dominate the dividend. In many years, the capital gain is low and thus the dividend is a larger portion of the return. Since the capital gain is frequently negative and the dividend is always positive, the dividend plays an important role over time. 9-2  Use the future value equation. For example, for stocks FVend of 1950s = $10,000 × (1 + 0.209)10 = $66,721. Answers are:In StocksIn BondsIn Cash1950s$66,721$10,000$12,1901960s23,03011,72014,8021970s20,61017,40818,4221980s53,23235,47823,4571990s56,94724,78216,1342000s10,90521,64913,078 9-3  Standard deviation of returns measures the variability of returns over time. This vari-ability gives investors an idea of the likely range of potential returns. 9-4  The standard deviation (the numerator in the CoV equation) for individual companies is much higher than for the stock market as a whole. This is because it is a measure of total risk, which includes much firm-specific risk for firms. But firm-specific risk is diver-sified away in the overall market. 9-5  It is useful to find companies whose returns behave differently from each other over time. This comes about from companies that have different businesses. This is mea-sured by a statistical tool, correlation. It is also good if these companies have high expected returns.Final PDF to printer

329cor91411_ch09_296-329.indd 329 01/20/17 04:22 PM 9-6  The return on a portfolio depends on the proportions of each asset owned in the portfolio and the returns that each of those assets generates. If the first portfolio is weighted toward poor-performing stocks and the second owns more of the high- performing stocks, the first portfolio will be undesirable in comparison. 9-7  The lowest correlation in Table 9.6 is between the Bank of New York and Newmont Mining. So this combination has the best chance of reducing risk. The least opportu-nity for diversification is between General Electric and Citigroup because they have the highest correlation.Final PDF to printer

330cor91411_ch10_330-361.indd 330 01/13/17 11:59 AMviewpointsPART FIVEBusiness ApplicationConsider that you work in the finance department of a large corporation. Your team is analyzing several new projects the firm can pursue. To complete the analysis, the team needs to know what return stockholders require from the firm.You are to estimate this required return. ShareholdersÕ expected return will depend on your companyÕs risk level. What information do you need to gather and how might you compute this return? (See the solution at the end of the chapter.)Personal ApplicationYou have just started your first job in the corporate world and need to make some retirement plan decisions. The companyÕs 401(k) retirement plan offers three investment choices: a stock portfolio with a beta of 1, a bond portfolio with a beta of 0.18, and a money market account. For your allocation, you decide to contribute $200 per month to the stock portfolio, $100 to the bond portfolio, and $50 to the money market account.If the expected return to the market portfolio is 11 percent, what risk level are you taking in your retirement portfolio and what return should you expect over the long run? (See the solution at the end of the chapter.)Investing mainly in my own companyÕs stock is safer, right? Maybe not . . .Estimating Risk and Return10Final PDF to printer

331cor91411_ch10_330-361.indd 331 01/13/17 11:59 AM© Ingram Publishing/Getty Images RFIs it possible for investors to know the exact risk they have to take? In Chapters 9 and 10, we explore methods to find the return that indi-vidual or institutional investors require to make a particular investment attrac-tive. In the previous chapter, we estab-lished a positive relationship between risk and return using historical data. Risk and return play an undeniable role as investors seek the best return for the least risk. But until thereÕs some way to forecast the future, finan-cial managers and investors must make investment decisions armed only with their expectations about future risk and return. We need an exact specifi-cation that shows directly the amount of reward required for investors to take the level of risk in a given firmÕs stock or portfolio of securities. In this chapter we will also see how investors get the information they need to make risk-reward decisions.Investors need to know how much risk they have to take to confidently expect a 10 percent return. Managers also want to know what return share-holders require so that they can decide how to meet those expectations. In Chapter 11, weÕll explore how man-agers conduct financial analysis to find the shareholdersÕ required return. If we want to specify the exact riskÐreturn relationship, we need to develop a better measure of risk for individuals and institutional investors. As we saw in Chapter 9, any firmÕs total risk is specific to that particular firm. But the market doesnÕt reward firm-specific risk because investors can easily diversify away any single firmÕs specific risks by owning other offsetting firmsÕ stocks to create a portfolio subject only to market or undiversifiable risk. So, we need to find just the market risk portion of total risk for investors. The theory to find the market risk portion of stock ownership extends modern portfo-lio theory. Our search to find market risk will lead us to the capital asset pricing model (CAPM), which uti-lizes a measure of market risk called beta. CAPMÕs riskÐreturn specifica-tion provides us a powerful tool to make better investment decisions.Corporate finance managers and investment professionals commonly use the beta measure. But like any theory, CAPM has its limitations. WeÕll discuss the CAPMÕs limitations and concerns about beta and propose an alternate required return measure. Whether beta or any other riskÐreturn specification is useful relies in part on whether a stockÕs price represents a fair estimate of the true company value. Stock price validity and reliabilityÑtheir general correctnessÑare vitally important both to investors and corpo-rate managers.Learning Goals LG10-1 Compute forward-looking expected return and risk. LG10-2 Understand risk premiums. LG10-3 Know and apply the capital asset pricing model (CAPM). LG10-4 Calculate and apply beta, a measure of market risk. LG10-5 Differentiate the levels of market efficiency and their implications. LG10-6 Calculate and explain inves-torsÕ required return and risk. LG10-7 Use the constant-growth model to compute required return.Final PDF to printer

332 part five Risk and Returncor91411_ch10_330-361.indd 332 01/13/17 11:59 AM10.1 ∙ Expected ReturnsIn the previous chapter, we characterized risk and return in historical terms. We defined a stockÕs return as the actual profit realized while holding the stock or the average return over a longer period. We described risk simply as the standard deviation of those returnsÑa term already familiar to you from your statistics classes. So, we did a good job describing the risk and return that the stock experienced in the past. But do those risk and return figures hold into the future? Firms can quite possibly change their stocksÕ risk level by substantially changing their business. If a firm takes on riskier new projects over time, or changes the nature of its business, the firm itself will become riskier. Similarly, firms can reduce their risk levelÑand hence, their stockÕs riskinessÑby choosing low-risk new projects. Both investors and firms find expected return, a forward-looking return calculation that includes risk measures, very useful to estimate future stock performance.Expected Return and RiskWe can attribute a companyÕs business success over a year partly to its management tal-ent, strategies, and other firm-specific activities, but overall economic conditions will also affect a firmÕs level of success or failure. Consider a steel manufacturerÑNucor Corp. The steel business closely follows economic trends. In a good economy, demand for steel is strong as builders and manufacturers step up building and production. During economic recessions, demand for steel falls off quickly. So, if we want to assess NucorÕs probabilities for success next year, we know that we must look partly at NucorÕs manage-rial ability and partly at the economic outlook.Unfortunately, we cannot accurately predict what the economy will be like next year. Predicting economic activity is like predicting the weatherÑforecasts give the probability of rain or sunshine. Economists cannot say for sure whether the economy will be good or bad next year. Instead, they may forecast a 70 percent chance that the economy will be good and a 30 percent chance of a recession. Similarly, analysts might say that given NucorÕs managerial talent, if the economy is good, Nucor will perform well and the stock will increase 20 percent. If the economy goes into a recession, then NucorÕs stock will fall 10 percent. So what return do you expect from Nucor? The return still depends on the state of the economy.This leads us directly to a key concept: expected return. We compute expected return by multiplying each possible return by the probability, p, of that return occurring. We then sum them (recall that all probabilities must add to one). LetÕs place Nucor in an economy with only two states: good and recession. In this scenario, NucorÕs expected return would be 11 percent [= (0.7 × 20%) + (0.3 × Ð10%)]. Of course, nothing is quite that simple. Economists seldom predict simple two-state views of the economy as in the previous example. Rather, economists give much more detailed forecasts (such as three states: red-hot economy, average expansion, and recession). So our general equation for a stockÕs expected return with S different conditions of the economy is Expected return = Sum of (Each return × Probability of that return) = ( p 1  ×  Return 1 )  +  ( p 2  ×  Return 2 )  +  ( p 3  ×  Return 3 ) + á á á + ( p s  ×  Return s ) = ∑ j=1 s p j × Return j (10-1)The result of this expected return calculation has some interesting properties. First, the expected return figure expresses what the average return would be over time if the proba-bilistic states of the economy occur as predicted. For example, the 70/30 probability distribution for good/recession economic states suggests that the economy will be good in 7 of the next 10 years, earning Nucor shareholders a 20 percent return in each of those years. Shareholders would lose 10 percent in each of the three recession years. So the average return over those 10 years would be 11 percent, the same as the expected return. LG10-1 probabilityThe likelihood of occurrence.expected returnThe average of the possi-ble returns weighted by the likelihood of those returns occurring.probability distributionThe set of probabilities for all possible occurrences.Final PDF to printer

chapter 10 Estimating Risk and Return 333cor91411_ch10_330-361.indd 333 01/13/17 11:59 AMThe second interesting property: The expected return itself will not likely occur during any one year. Remember that Nucor will earn either a return of 20 percent or Ð10 percent. Yet its expected return is 11 percent, a value that it cannot earn because we have no eco-nomic condition for which the return is 11 percent. Again, this illustration seems extreme because we used only two economic states. Any real economic forecast would instead include a probability distribution of many potential economic conditions.We can also characterize risk via this expected return figure. The expected return procedure shows potential return possibilities, but we donÕt know which one will actu-ally occur, so we face uncertainty. In the last chapter, we measured risk using the stan-dard deviation of returns over time. We can use the same principle to measure risk for expected returns. What range of different expected returns will Nucor exhibit from the expected return of 11 percent? In our two-state description of the economy, the deviation could be either 9 percent (= 20% Ð 11%) or Ð21 percent (= Ð10% Ð 11%). We compute the standard deviation of expected returns the same way we did for historical returns. We square the deviations, then multiply by the probability of that deviation occurring, and then sum them all up. So NucorÕs return variance is 189.0 [= (0.7 × 92) + (0.3 × Ð212)]. As a final step, we take the square root of our result to put the figure back into sensible terms. The standard deviation for Nucor is 13.75 percent (= √ ____ 189 ). The general equation for the standard deviation of S different economic states is Standard deviation = Square root of the sum of (Probability of a return × Each returnÕs squared deviation from the average ) = √ ____________________________________________________________ p 1  × ( Return 1  − Expected return ) 2  +  p 2 × ( Return 2  − Expected return ) 2  + á á á = √ ______________________________ ∑ j=1 s p j  × ( Return j  − Expected return ) 2 (10-2)MATH COACH EXPECTED RETURN AND STANDARD DEVIATIONWhen you compute expected return and standard deviation, youÕll find it helpful to use the decimal format for the probability of the economic state and percentages to state the return in each state.EXAMPLE 10-1Expected Return and RiskBailey has a probability distribution for four possible states of the economy, as shown below. She has also calculated the return that Motor Music stock would earn in each state. Given this information, whatÕs Motor MusicÕs expected return and risk?Economic StateProbabilityReturnFast growth0.1525%Slow growth0.6015Recession0.20−5Depression0.05−20SOLUTION: Bailey can compute the expected return using equation 10-1: Expected return = (0.15 × 25%) + (0.60 × 15%) + (0.20 × −5%) + (0.05 × −20%) = 10.75%  Then Bailey can compute the expected return by computing the standard deviation using equation 10-2: LG 10-1For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.Final PDF to printer

334 part five Risk and Returncor91411_ch10_330-361.indd 334 01/13/17 11:59 AMRisk PremiumsThroughout the book, we have mentioned the positive relationship between expected return and risk. Consider this key question: You have a riskless investment available to you. The short-term government debt security, the T-bill, offers you a low return with no risk. Why would you invest in anything risky, when you could simply buy T-bills? The answer, of course, is that some investors want a higher return and are willing to take some risk to raise their returns. Investors who take on a little risk should expect a slightly higher return than the T-bill rate. People who take on higher risk levels should expect higher returns. Indeed, itÕs only logical that investors require this extra return to willingly take the added risk.The expected return of an investment is often expressed in two parts, a risk-free return and a risky contribution. The return investors require for the risk level they take is called the required return: Required return = Risk-free rate + Return premium (10-3)The risk-free rate is typically considered the return on U.S. government bonds and bills and equals the real interest rate and the expected inflation premium that we discussed in Chap-ter 6. The risk premium is the reward investors require for taking risk. How large are the rewards for taking risk? As we discussed in the previous chapter, the market doesnÕt reward all risks. The firm-specific portion of total risk for any stock can be diversified away, and since the investor takes on such risk out of ignorance or by mistake, an efficient market will not reward anyone for taking on this ÒsuperfluousÓ risk. So as we examine historical risk premiums, we do so with a diversified portfolio that contains no firm-specific risk.Table 10.1 shows the average annual return on the S&P 500 Index minus the T-bill rate for different time periods. The remainder after we subtract the T-bill rate is the risk premium; in this case, itÕs the market risk premiumÑthe reward for taking general (unsystematic) stock market risk. Since 1950, the average market risk premium has been 8.3 percent per year. Over the long run, this is the reward for taking stock market risk. The actual, realized risk premium during particular decades has varied. The average risk pre-mium has been as high as 18.8 percent for the 1950s and as low as Ð1.8 percent during the 2000s. The performance in the 2000s is unusual; the stock market return has been so poor that it has not beaten the risk-free rate. Investors require a risk premium for taking on mar-ket risk. But taking that risk also means that they will periodically experience poor returns.LG10-2required returnThe level of total return needed to be compen-sated for the risk taken. It is made up of a risk-free rate and a risk premium.risk premiumThe portion of the required return that represents the reward for taking risk.market risk premiumThe return on the market portfolio minus the risk-free rate. Risk premiums for spe-cific firms are based on the market risk premium. Standard deviation = √ ________________________________________________________ 0.15 × (25% − 10.75% ) 2  + 0.60 × (15% − 10.75% ) 2  + 0.20 × (− 5% − 10.75% ) 2  + 0.05 × (− 20% − 10.75% ) 2 = √ ____________________________ 30.46 + 10.84 + 49.61 + 47.28  = 11.76% The expected return and standard deviation are 10.75 percent and 11.76 percent, respec-tively. We could also show these equations in a table, such asEconomic StateProbabilityReturnp × ReturnDeviationSquared Dev.× pFast growth0.15 25% 3.75% 14.25%203.06 30.46Slow growth0.60 15 9.00 4.2518.06 10.84Recession0.20 −5−1.00 −15.7248.06 49.61Depression0.05−20−1.00 −30.75945.56 47.28Sum =1.0 10.75%138.19Square root = 11.76%Similar to Problems 10-1, 10-2, 10-17, 10-18, 10-23, 10-24, Self-Test Problem 1Final PDF to printer

chapter 10 Estimating Risk and Return 335cor91411_ch10_330-361.indd 335 01/13/17 11:59 AM10.2 ∙ Market RiskHow much risk should you take to achieve the return you want over time? In the previous chapter, we demonstrated that individual stocks and different portfolios exhibit different levels of total risk. Recall that the rewards for carrying risk apply only to the market risk (or undiversifiable) portion of total risk. But how do investors know how much of the 33.4 percent standard deviation of returns for Mattel Inc. is firm-specific risk and how much of that deviation is market risk? The answer to this important question will deter-mine how much of a risk premium investors should require for Mattel. The attempt to specify an equation that relates a stockÕs required return to an appropriate risk premium is known as asset pricing.The Market PortfolioThe best-known asset pricing equation is the capital asset pricing model, typically referred to as CAPM. Though many theorists formulated theories that, in the end, supported the CAPMÕs effectiveness, credit for the model goes to William Sharpe and John Lintner. Sharpe eventually won a Nobel Prize for his work in 1990. (Lintner died in 1983, and Nobel Prizes are not awarded posthumously.) Today, both investors and corporate finance professionals use CAPM widely. In developing the CAPM, Lintner and Sharpe sought to emphasize the individual investorÕs best strategy to maximize returns for a given amount of market risk.CAPM starts with modern portfolio theory. Remember from the previous chapter that when you combine securities into a portfolio, you can find a set of portfolios that dominate all others. The best combinations possible use all the risky securities available (but not the risk-free asset) to create efficient frontier portfolios, which would lie along a curved line in risk/return space, as shown in Figure 10.1, panel A. These portfolios represent combinations of various risky securities that give the highest expected return for each potential level of risk (i.e., they lie the furthest “up and to-the-left” that we can achieve when considering all possible combinations of the available risky securities).The idea of a risk premium in equation 10-3 implies a risk-free investment, like T-bills. Panel B shows where the risk-free asset would appear on the capital market line (CML). The risk-free asset must lie on the y-axis precisely because it carries no risk. Now we draw a line from the risk-free security to a point tangent to the efficient frontier. The CML relationship appears as a line because investments show a direct riskÐreward rela-tionship. You may recall from your economics classes that only one tangency point will be possible between this kind of curve and a straight line. The spot where the tangency occurs is called the market portfolio, which has a special significance. The market port-folio represents ownership in all traded assets in the economy, so this portfolio provides maximum diversification. You can locate your optimal portfolio on this line by owning LG10-3 asset pricingThe process of directly specifying the relationship between required return and risk.capital asset pricing model (CAPM)An asset pricing theory based on a beta, a measure of market risk.capital market line (CML)The line on a graph of return and risk (standard deviation) from the risk-free rate through the market portfolio.market portfolioIn theory, the market port-folio is the combination of securities that places the portfolio on the efficient frontier and on a line tan-gent from the risk-free rate. In practice, the S&P 500 Index is used to proxy for the market portfolio.TIME OUT 10-1 Describe the similarities between computing average return and expected return. Also, describe the similarities between expected return risk and historical risk.   10-2 Why would people take risks by investing their hard-earned money?  TABLE 10.1 The Realized Average Annual Risk Premium for StocksRealized risk premiums were very different in each decade. The recent decade even had a negative risk premium!Source: S&P 500 Index and T-bill rate data.1950 to 20151950 to 19591960 to 19691970 to 19791980 to 19891990 to 19992000 to 20092010 to 2015Risk premium8.2%18.8%4.7%1.2%9.3%14.1%Ð1.8%13.4%Final PDF to printer

336 part five Risk and Returncor91411_ch10_330-361.indd 336 01/13/17 11:59 AMvarious combinations of the risk-free security and the market portfolio. If most of your money is invested in the market portfolio, then you will have a portfolio on the line that lies just to the left of the market portfolio dot in the graph. If you own just a little of the market portfolio and hold mostly risk-free securities, then your portfolio will lie on the line near the risk-free security dot. For your investments to lie on the line to the right of the market portfolio, you would have to invest all your money in the market portfolio, then borrow more money at the risk-free rate and invest these additional funds in the mar-ket portfolio. Borrowing money to invest is known as using financial leverage. Using financial leverage increases the overall risk of the portfolio, which is illustrated in this figure as a higher standard deviation.Notice that if you had a portfolio on the efficient frontier (labeled Òold portfolioÓ), you could do better. Instead of owning the old portfolio, you can put some of your money in the market portfolio and some in the risk-free security to obtain the Ònew portfolio.Ó See how the new portfolio dominates that old one? It carries the same risk level, but offers a higher return. In fact, notice that the line drawn between the risk-free investment and the market portfolio dominates all of the efficient frontier portfolios (except the market portfolio itself). All portfolio allocations between the risk-free security and the mar-ket portfolio constitute the capital market line. All investors should want to locate their portfolios on the CML, rather than the efficient frontier. Portfolios on the CML offer the highest expected return for any level of desired risk, which the investor controls by deciding how much of the market portfolio and how much of the risk-free asset to hold. financial leverageThe extent to which debt securities are used by a firm.Risk (Standard Deviation)Expected ReturnOld portfolioRfMNew portfolioCapital market lineRisk (Standard Deviation)Expected ReturnEfficient frontierPanel A: The Efficient FrontierPanel B: Add a Risk-Free Asset and Do Even BetterFIGURE 10.1Maximizing Expected ReturnIn MPT, investors want to be on the efficient frontier (Panel A) because it gives them the highest expected return for each level of risk. However, after adding a risk-less asset (Panel B), investors can then get portfolios on the straight line (shown), which offers a higher expected return for each level of risk than the efficient frontier.Final PDF to printer

chapter 10 Estimating Risk and Return 337cor91411_ch10_330-361.indd 337 01/13/17 11:59 AMRisk-averse investors can put more of their money in T-bills and less into the market portfolio. Investors willing to take on higher risk for larger returns can put more of their money in the market portfolio.Beta, a Measure of Market RiskThe CML demonstrates that the market portfolio is crucial. Indeed, its return less the risk-free rate represents the expected average market risk premium. The market portfolio features no firm-specific risk; all such risk is diversified away. So the market portfolio carries only market risk. Thus the market portfolioÕs risk factor allows us to compute a measure of firm-specific risk for any individual stock or portfolio. We can now examine the question posed at the beginning of this section: ÒHow much of MattelÕs total risk is attributable to market risk?Ó The standard deviation of returns includes all of Mattel stockÕs riskÑit quantifies how much the stock price rises and falls. The market risk por-tion will rise and fall along with the market portfolio. If we subtract the market risk por-tion from the total risk measure, weÕre left with firm-specific risk. This part of risk rises and falls in ways unrelated to market changes.Remember that portfolio theory describes a measureÑcorrelationÑthat measures how two stocks move together through time. Instead of measuring how any two stocks or portfolios move together, we now want to know how a stock or portfolio moves relative to market portfolio movements. This measure is known as beta(β). Beta measures the comovement between a stock and the market portfolio.If MattelÕs total risk level is measured by its standard deviation, σMattel, then we can find the portion of this risk that is attributable to the market in general by multiplying MattelÕs total risk by its correlation with the market portfolio, σMattel × ρMattel, Market. The beta com-putation is scaled so that the market portfolio itself has a beta of one. The scaling is done by dividing by standard deviation of the market portfolio: σMattel × ρMattel, Market Ö σMarket.1 Stocks with betas larger than one are considered riskier than the market portfolio, while betas of less then one indicate lower risk. Mattel has a beta of 0.65, meaning that Mattel has low sensitivity to market risk. When the market portfolio moves, you can expect Mat-tel stock to move in the same direction. Technically, you should expect MattelÕs realized risk premium to be 35 percent less than the realized market risk premium.Table 10.2 shows the beta for each of the 30 companies in the Dow Jones Industrial Average. Investors consider many of these companies high risk, like Du Pont (β = 2.01) and Disney (1.56). These firmsÕ stocks carry high market risk because the demand for their products is very sensitive to the overall economyÕs strength. Investors consider other com-panies safe bets with low risk, like Walmart (0.19), Verizon (0.47), and McDonaldÕs (0.56). Many lower-beta firms sell consumer goods that we consider the necessities of life, which we will buy whether the economy is in recession or expansion. The demand for these prod-ucts is price inelastic and not sensitive to economic conditions. Some companies have nearly the same risk as the market portfolio, like Pfizer (1.02), Microsoft (1.02), and Intel (1.02).The Security Market LineBeta indicates the market risk that each stock represents to investors. So the higher the beta, the higher the risk premium investors will demand to undertake that securityÕs market risk. Since beta sums up precisely what investors want to know about risk, we often replace the standard deviation risk measure shown in Figure 10.1 with beta. Figure 10.2 shows required return versus beta risk. We call the line in this figure the security market line (SML), which illustrates how required return relates to risk at any particular time, all else held equal. The SML also shows the market portfolioÕs risk premium or any stockÕs risk premium.When a stock like General Electric carries a beta greater than one, then its risk pre-mium must be larger than the market risk premium. A stock like Johnson & Johnson LG10-4 beta (β)A measure of the sensitiv-ity of a stock or portfolio to market risk.LG10-3 1A mathematically equivalent equation for beta is β = cov(Rs, RM)/var (RM), where cov() is the covariance between the stock and market portfolio returns, and var() is the variance of the market portfolio.security market line (SML)Similar to the capital market line except risk is charac-terized by beta instead of standard deviation.Final PDF to printer

338 part five Risk and Returncor91411_ch10_330-361.indd 338 01/13/17 11:59 AMcarries a lower beta than does the overall market; therefore Johnson & Johnson would offer a lower risk premium to investors.We can use the SML to show the relationship between risk and return for any stock or portfolio. To precisely quantify this relationship, we need the equation for the SML. The equation of any line can be defined as y = b + mx, where b is the intercept and m is the slope. In this case, the y-axis is required return and the x-axis is beta. The intercept is Rf. You may remember that the slope is the Òrise over runÓ between two points on the line. The rise between the risk-free security and the market portfolio is RM − Rf and the run is 1 − 0. Substituting into the line equation results in the CAPM: Expected return = Risk-free rate + Beta × Market risk premium =  R f  + β( R M  −  R f ) (10-4)TABLE 10.2 Dow Jones Industrial Average Stock BetasData Source: Yahoo! Finance, March 2, 2016CompanyBetaCompanyBeta3M Company1.08Intel1.02American Express1.21Johnson & Johnson0.89Apple1.35JPMorgan Chase1.20Boeing1.36McDonaldÕs0.56Caterpillar1.09Merck0.75Cisco Systems1.18Microsoft1.02Chevron1.17Nike0.63Coca-Cola0.77Pfizer1.02Disney1.56Procter & Gamble0.66Du Pont de Nemours2.01Travelers1.22Exxon Mobil0.92United Technologies1.18General Electric1.22UnitedHealth Group0.62Goldman Sachs1.35Verizon Communications0.47Home Depot0.96Visa1.06IBM0.66Walmart Stores0.19BetaRequired Return (%)RfRMM1Security market line1.2General ElectricRGEGeneral Electricrisk premiumMarket risk premiumFIGURE 10.2The Security Market Line Uses Beta as the Risk MeasureGeneral Electric has higher risk than the overall stock market, so it should require a higher return.Final PDF to printer

chapter 10 Estimating Risk and Return 339cor91411_ch10_330-361.indd 339 01/13/17 11:59 AMSo, we have determined a way to estimate any stockÕs required return once we have determined its beta. Consider this: We expect the market portfolio to earn 12 percent and T-bill yields are 5 percent. Then General ElectricÕs required return, with a β =1.22, is 5% + 1.22 × (12% − 5%) = 13.54 percent. Table 10.3 shows the 30 Dow Jones Industrial Average stocksÕ required return, using these same market and risk-free rate assumptions. Higher-risk companies have higher betas, and thus require higher returns.TABLE 10.3 Required Returns for DJIA StocksHigher beta stocks require higher expected returns.Assumptions: market return = 12% and risk-free rate = 5%.Source: Yahoo! Finance, March 2, 2016.CompanyRequired ReturnCompanyRequired Return3M Company12.56%Intel12.14%American Express13.47 Johnson & Johnson11.23Apple14.45 JPMorgan Chase13.40Boeing14.52 McDonaldÕs 8.92Caterpillar12.63 Merck10.25Cisco Systems13.26 Microsoft12.14Chevron13.19 Nike9.41Coca-Cola10.39 Pfizer12.14Disney15.92 Proctor & Gamble9.62Du Pont de Nemours19.07 Travelers13.54Exxon Mobil11.44 United Technologies13.26General Electric13.54 UnitedHealth Group9.34Goldman Sachs14.45 Verizon Communications8.29Home Depot11.72 Visa12.42IBM9.62Walmart Stores6.33EXAMPLE 10-2CAPM and Under- or Overvalued StockSay that you are a corporate CFO. You know that the risk-free rate is currently 4.5 percent and you expect the market to earn 11 percent this year. Through your own analysis of the firm, you think it will earn a 13.5 percent return this year. If the beta of the company is 1.2, should you consider the firm undervalued or overvalued?SOLUTION: You can compute shareholdersÕ required return with CAPM as 4.5% + 1.2 × (11% − 4.5%) = 12.3%. Since you think the firm will actually earn more than this required return, the firm appears to be currently undervalued. That is, its price must rise more then predicted by CAPM to obtain the return you estimated in your original analysis.Similar to Problems 10-7, 10-8, 10-19, 10-20, Self-Test Problem 3For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.LG10-3 PORTFOLIO BETA As you might expect, a stock portfolioÕs beta is the weighted average of the portfolio stocksÕ betas.The portfolio beta equation resembles equation 9-7, which gives the return of a portfolio: β p = Sum of the beta of each stock × Its weight in the portfolio = ( w 1  ×  β 1 ) + ( w 2  ×  β 2 ) + ( w 3  ×  β 3 ) + á á á + ( w n  ×  β n ) =  ∑ j=1 n w j β j (10-5)portfolio betaThe combination of the individual company betas in an investorÕs portfolio.Final PDF to printer

340 part five Risk and Returncor91411_ch10_330-361.indd 340 01/13/17 11:59 AMWith this equation, you can easily determine whether adding a particular stock to the portfolio will increase or decrease the portfolioÕs total market risk. If you add a stock with a higher beta than the existing portfolio, then the new portfolio will carry higher market risk than the old one did. Although we can find the effects on total portfolio risk of adding particular stocks using beta, the same is not necessarily true if we use standard deviations as our risk measure. The new stock, however risky, might have low correlations with the other stocks in the portfolioÑoffsetting (negative) correlations would reduce total risk.Finding BetaThe CAPM is an elegant explanation that relates the return you should require for taking on various levels of market risk. Although CAPM provides many practical applications, you need a companyÕs beta to use those applications. Where or how can you obtain a beta? You have two ways. First, given the returns of the company and the market port-folio, you can compute the beta yourself. Second, you can find the beta that others have computed through financial information data providers.Many financial outlets publish company betas. Websites that provide company betas for free include MSN Money and Yahoo! Finance, to name just a couple. For example, in March 2016, the beta these websites listed for Disney were: MSN Money (1.41) and Yahoo! Finance (1.56). Note that these reported betas have some differences. To know why differences might arise, consider how you would go about gathering information and computing beta yourself.To compute your own beta, first obtain historical returns for the company of interest and of the market portfolio. Then run a regression of the company return as the dependent variable and the market portfolio return as the independent variable. The resulting market portfolio return coefficient is beta. Many important questions may come to mind. First, what do you use as the market portfolio? People typically use a major stock index like the S&P 500 Index to proxy for the market portfolio. Second, what time frame should you use? You can use daily, weekly, monthly, or even annual returns. Using monthly returns is the most common. How long a time series is needed? As you will recall, statistical estimates become more reliable and valid as more data are used. But you will have to weigh those statistical advantages against the fact that companies change their business enterprises and thus their risk levels over time. Using data from too long ago reflects risks that may no longer apply. Generally speaking, using time series data of three to five years is common. Whatever decisions you make to address these questions, be consistent by making the same decisions for all the company betas you compute. Table 10.4 shows the spreadsheet of a stockÕs beta calculation. In this case, monthly returns from five years are used for the stock return and a market index. The SLOPE() function of the spreadsheet directly computes the regression coefficient of interest. The beta estimation using the spreadsheet function is 0.83.LG10-4 Portfolio BetaYou have a portfolio consisting of 20 percent Boeing stock (β = 1.04), 40 percent Hewlett- Packard stock (β = 1.54), and 40 percent McDonaldÕs stock (β = 0.34). How much market risk does the portfolio have?SOLUTION: Compute a beta for the portfolio. Using equation 10-5, the portfolio beta is 0.2 × 1.04 + 0.4 × 1.54 + 0.4 × 0.34 = 0.96. Note that this portfolio carries 4 percent less market risk than the general market does.Similar to Problems 10-11, 10-12, 10-21, 10-22, 10-27, 10-28, Self-Test Problem 2EXAMPLE 10-3For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.LG10-4 Final PDF to printer

chapter 10 Estimating Risk and Return 341cor91411_ch10_330-361.indd 341 01/13/17 11:59 AMConcerns about BetaConsider the estimation choices just mentioned. Say you estimate a firmÕs beta using monthly data for five years and the Dow Jones Industrial Average return as the market portfolio. Suppose that the result is a beta of 1.3. Then you try again using weekly returns for three years and the return from the S&P 500 Index as the market portfolioÕs yield, resulting in a beta of 0.9. These estimates are quite different and would create a large varia-tion in required return if you plugged them into the CAPM. So, which is the more accurate estimate? Unfortunately, we may not be able to determine which is most representative, or Òtrue.Ó In general, you may estimate a little different beta using different market portfolio proxies, different return intervals (like monthly returns versus annual returns), and differ-ent time periods. Problem 10-31 at the end of this chapter explores these differences.In addition to these estimation problems, a company can change its risk level, and thus its beta, by changing the way it operates within its business, by expanding into new busi-nesses, and/or by changing its debt load. So even if beta is an accurate measure of what the firmÕs risk level was in the past, does it apply to the future? BetaÕs applicability will depend on the firmÕs future plans.Both financial managers and investors share these concerns about beta. In the end, betaÕs usefulness depends on its reliability. Unfortunately, betaÕs empirical record is not as good as we would like. We should expect that companies with high betas yield higher The spreadsheet function SLOPE() finds the statistical relationship between a stockÕs return and the market return. Considering these monthly returns for a stock and a market index, the beta of this stock is 0.83.ABCDE1DateStock ReturnMarket Return2Apr−4.13%−1.01%  3Mar0.843.60  beta =4Feb−0.46 1.11  =SLOPE(B2:B60,C2:C60) =0.835Jan5.835.04  6Dec−0.47 0.71  7Nov8.230.28  8Oct−8.43 −1.98  9Sep2.442.42  10Aug6.421.98  11Jul2.171.26  12Jun7.253.96  13May−8.19 −6.27  14Apr14.51 −0.75  15Mar12.70 3.13  16Feb−7.59 4.06  17Jan12.33 4.36  18Dec−9.98 0.85  19Nov−9.94 −0.51  20Oct−1.26 10.77  21Sep0.46−7.18  22Aug−3.28 −5.68  49May−3.14 5.31  50Apr9.649.39  51Mar13.35 8.54  52Feb10.15 −10.99    53Jan14.70 −8.57  54Dec20.09 0.78  55Nov−25.40  −7.48  56Oct−21.33  −16.94    57Sep−9.96 −9.08  58Aug5.861.22  59Jul4.10−0.99  60Jun−10.16  −8.60  TABLE 10.4 Compute Beta Using a SpreadsheetFinal PDF to printer

chapter 10 Estimating Risk and Return 343cor91411_ch10_330-361.indd 343 01/13/17 11:59 AM10.3 ∙ Capital Market EfficiencyThe risk and return relationship rests on an underlying assumption that stock prices are generally ÒcorrectÓÑthey are not predictably too high or too low. Imagine having a sys-tem that identified undervalued stocks with low risks (i.e., relatively high returns with a low beta). Because those stocks are undervalued, they will earn you a high return, on average, as their stock prices rise to their correct value. Note that the CAPMÕs risk-return relationship would be incorrect. You would be consistently getting high returns with low risk. On the other hand, if you consistently picked overvalued stocks, you wouldnÕt be earning enough return to compensate you for the risks you are taking. Investors move their money to the best alternatives by selling overvalued stocks and buying undervalued stocks. This causes the prices of the overvalued stocks to drop and the prices of the under-valued stocks to rise until both stocksÕ returns stand more in line with their riskiness. Thus, the riskÐreturn relationship relies on the idea that prices are generally accurate.What conditions are necessary for an efficient market? Efficient, or perfectly com-petitive, markets feature ¥ Many buyers and sellers. ¥ No prohibitively high barriers to entry. ¥ Free and readily available information available to all participants. ¥ Low trading or transaction costs.Are these conditions met for the U.S. stock market? Certainly millions of stock inves-tors trade every day, buying and selling securities. With discount brokers and online traders, the costs to trade are fairly minimal and present no real barriers to enter the mar-ket. Information is increasingly accessible from many sources and trading philosophies, and commission costs and bidÐask spreads have steadily declined. With millions of the larger companiesÕ shares (say the S&P 500) of stock trading every day, the U.S. stock exchanges appear to meet efficiency conditions. But other segments of the market, like those exchanges that trade in penny stocks, feature very thin trading. The prices of these very small companiesÕ stock may not be fair and these equities may be manipulated in fraudulent scams. In the 1970s and 1980s, penny stock king Meyer Blinder and his firm Blinder-Robinson was known as Òblind Õem and rob ÕemÓ as they practiced penny stock price manipulation to rob many small investors of their entire investments in these small markets. These days, penny stock price manipulation is typically conducted through e-mail and Web posting scams.Efficient Market HypothesisOur concept of market efficiency provides a good framework for understanding how stock prices change over time. This theory is described in the efficient market hypothesis (EMH), which states that security prices fully reflect all available information. At any point in time, the price for any stock or bond reflects the collective wisdom of market participants about the companyÕs future prospects. Security prices change as new infor-mation becomes available. Since we cannot predict whether new information about a company will be good news or bad news, we cannot predict whether its stock price will go up or go down. This makes short-term stock-price movements unpredictable. But in the longer run, stock prices will adjust to their proper level as market participants gather and digest all available information.The EMH brings us to the question of what type of information is embedded within current stock prices. Segmenting information into three categories leads to the three basic levels of market efficiency, described as: 1. Weak-form efficiencyÑcurrent prices reflect all information derived from trading. This stock market information generally includes current and past stock prices and trading volume.LG10-5 efficient marketA securities market in which prices fully reflect avail-able information on each security.penny stocksThe stocks of small compa-nies that are priced below $1 per share.efficient market hypothesis (EMH)A theory that describes what types of information are reflected in current stock prices.Final PDF to printer

344 part five Risk and Returncor91411_ch10_330-361.indd 344 01/13/17 11:59 AM 2. Semistrong-form efficiencyÑcurrent prices reflect all public information. This includes all information that has already been revealed to the public, like financial statements, news, analyst opinions, and so on. 3. Strong-form efficiencyÑcurrent prices reflect all information. In addition to pub-lic information, prices reflect the privately held information that has not yet been released to the public, but may be known to some people, like managers, accoun-tants, auditors, and so on.Each of the EMHÕs three forms rests on different assumptions regarding the extent of information that is incorporated into stock prices at any point in time. A fourth possibilityÑthat markets may not be efficient and prices may not reflect all the informa-tion known about a companyÑalso arises.The weak-form efficiency level involves the lowest information hurdle, stating that stock prices reflect all past price and trading volume activity. If true, this level of effi-ciency would have important ramifications. A segment of the investment industry uses price and volume charts to make investment timing decisions. Technical analysis has a large following and its own vocabulary of patterns and trends (resistance, support, break-out, momentum, etc.). If the market is at least weak-form efficient, then prices already reflect this information and these activities would not result in useful predictions about future price changes, and thus would be a waste of time. Indeed, the people who make the most money from price charting services are the people who sell the services, not the investors who buy and use those services.The semistrong-form efficiency level assumes that stock prices include all public information. Notice that past stock prices and volumes are publicly available information, so this level includes the weak form as a subset. Important investment implications arise if markets are efficient to public information. Many investors conduct security analysis in which they obtain financial data and other public information to assess whether a companyÕs stock is undervalued or overvalued. But in a semistrong-form efficient market, stock prices already reflect this information and are thus Òcorrect.Ó Using only public information, you would not be able to determine whether a stock is misvalued because that information is already reflected in the price.If prices reflect all public information, then those prices will react as traders hear new (or private) information. Consider a company that announces surprisingly good quarterly profits. Traders and investors will have factored the old profit expectations into the stock price. As they incorporate the new information, the stock price will quickly rise to a new and accurate price as shown in the solid black line in Figure 10.3. Note that the stock price was $35 before the announcement and $40 immediately following. If you tried to buy the stock after hearing the news, then you would have bought at $40 and not received any benefit of the good quarterly profit news. On the other hand, if the market is not sem-istrong-form efficient, then the price might react quickly, but not accurately. The dashed red line shows a reaction in a non-semistrong efficient market where the price continues to drift up well after the announcement. This gradual drift to the ÒcorrectÓ price indicates that the market initially underreacted to the news. In this case, you could have bought the stock after the announcement and still earned a profit. The dashed blue line shows an overreaction to the firmÕs better-than-expected profits announcement. If markets either consistently underreact or consistently overreact to announcements that would change stock prices (earnings, stock split, dividend, etc.), then we would believe that the market is not semistrong efficient.The strong-form market efficiency level presents the highest hurdle to test market reac-tion to information. The strong-form level includes information considered by the weak-form, the semistrong-form, as well as privately known information. People within firms, like CEOs and CFOs, know information that has not yet been released to the public. They may trade on this privately held, or insider, information and their trading may cause stock prices to change as it reflects that private information. In this way, stock prices could public informationThe set of information that has been publicly released. Public information includes data on past stock prices and volume, financial state-ments, corporate news, analyst opinions, etc.privately held informationThe set of information that has not been released to the public but is known by few individuals, likely com-pany insiders.Final PDF to printer

chapter 10 Estimating Risk and Return 345cor91411_ch10_330-361.indd 345 01/13/17 11:59 AMreflect even privately known information. Note that the firm managers, accountants, and auditors know several days in advance that a firm has earned unexpectedly high quarterly profits. If the stock price already incorporated this closely held private knowledge, then the big price reaction shown in Figure 10.3 would not occur.So, is the stock market efficient? If it is, at what level? This has been a hotly debated topic for decades and continues to be. It is not likely that the market is strong-form effi-cient. Since insider trading is punished, insider information must be valuable. However, much evidence suggests that the market could be weak-form or semistrong-form efficient. Of course, we also have evidence that the market is not efficient at any of the three levels. We will explore this more in the following section.Behavioral FinanceThe argument for the market being efficient works as follows: Many individual and professional investors constantly look for mispriced stocks. If they find a stock that is undervalued, they will buy it and drive up its price until itÕs correctly priced. Likewise, investors would sell an overpriced stock, driving down its price until itÕs correctly valued. With so many investors looking for market Òmistakes,Ó itÕs unlikely that any mispriced stock opportunities will be left in the market.The argument against the market being efficient is equally convincing. The market comprises many people transacting with one another. When someone makes trading decisions influenced by emotion or psychological bias, those decisions may not seem rational. When many people fall under such influences, their trading decisions may actu-ally drive stock prices away from the correct price as emotion carries the traders away from rationality. For example, many people believe that investors were Òirrationally exuberantÓ about technology stocks in the late 1990sÑand that their buying excitement drove prices to an artificially high level. In 2000, the excitement wore off and tech stock prices plummeted. Whenever a set of stock prices go unnaturally high and subsequently crash down, the market experiences what we call a stock market bubble.In the past couple of decades, finance researchers have studied behavioral finance and found that people often behave in ways that are very likely Òirrational.Ó At times, investors appear to be too optimistic, as though they are looking through rose- colored glasses. At other times they appear to be too pessimistic. Common investment deci-sions arenÕt necessarily optimal ones, which flies in the face of the economistÕs expec-tation of rational economic actors. Perhaps, then, capital markets donÕt represent perfectly competitive or efficient markets if buyers and sellers do not always make rational choices.stock market bubbleInvestor enthusiasm causes an inflated bull market that drives prices too high, end-ing in a dramatic collapse in prices.behavioral financeThe study of the cognitive processes and biases asso-ciated with making financial and economic decisions.FIGURE 10.3Potential Price Reaction to a Good News AnnouncementStock prices react quickly to news, but do they react accurately?303234363840424446Stock Price ($)Price reaction to newsIndicates an overreactionIndicates an underreactionFinal PDF to printer

346 part five Risk and Returncor91411_ch10_330-361.indd 346 01/13/17 11:59 AMIt may take many biased investors to move a stockÕs price enough that it would be con-sidered a pricing mistake. However, the important decisions in a company are typically made by just one CEO or a management team. Thus, their biases can have a direct impact on decisions involving hundreds of millions, or even billions of dollars. In other words, the contribution of behavioral finance to economic decision making is likely to be even more important in corporate behavior than market behavior. For example, consider the psycho-logical concept of overconfidence. One of the most pervasive biases, overconfidence describes a tendency for people to overestimate the accuracy of their knowledge and under-estimate the risks of a decision. These problems can adversely affect important decisions of investment (i.e., acquiring other firms) and financing (i.e., issuing new stock or bonds).10.4 ∙ Implications for Financial ManagersFinancial managers must understand the crucial relationship between risk and return for several reasons. First, while the relationship between risk and return is demonstrated here using the capital markets, it equally applies to many business decisions. A firmÕs prod-uct mix, marketing campaign combination, and research and development programs all entail risk and potential rewards. Being able to understand and characterize these decisions within a risk and return framework can help managers make better decisions. In addition, managers must understand what return their stockholders require at various times of firm operations. After all, a firm must receive enough revenue from its variously risky activities to pay its business and debt costs and reward the owners (the stockholders). Managers must thus include the return to shareholders when they analyze new business opportunities.Firms and capital markets also interact directly. For example, a good understanding of market efficiency helps managers understand how their stock prices will react to differ-ent types of decisions (like dividend changes) and news announcements (like unexpect-edly high or low profitability). In fact, many managers own company stock and are thus compensated through programs that rely on the stock price, like restricted stock and executive stock options. Companies also periodically issue (sell) additional shares of stock to raise more capital, and these sales depend upon market efficiency assumptions. The firm would not want to sell additional shares if the stock price is too low (i.e., under-valued). They would want to sell more shares at any time that they thought their shares are overvalued. Other times, firms repurchase (buy back) shares of stock. The firm might want to do this if its shares were undervalued, but not if its shares were overvalued. Of course, valuation is not an issue if security markets are efficient.Using the Constant-Growth Model for Required ReturnFor decades, financial managers have used the CAPM to compute shareholdersÕ required return. Given recent concerns about betaÕs limitations, many see the CAPM as a less useful model for calculating appropriate returns. Some have turned instead to another model useful for computing required returnÑthe constant-growth model discussed in Chapter 8. We can arrange the terms of that model as i = Dividend yield + Constant growth = D 1 ___ P 0  + g (10-6)overconfidenceOverconfidence is used to describe three psycho-logical observations. First, people are miscalibrated on understanding the preci-sion of their knowledge. Second, people have a tendency to underestimate risks, and third, people tend to believe that they are bet-ter than average at tasks they are familiar with.TIME OUT 10-5 Can the market be semistrong-form efficient but not weak-form efficient? Explain.   10-6 If the market usually overreacts to bad news announcements, what would your return be like if you bought after you heard the bad news?  LG10-6 restricted stockA special type of stock that is not transferable from the current holder to others until specific conditions are satisfied.executive stock optionsSpecial rights given to cor-porate executives to buy a specific number of shares of the company stock at a fixed price during a specific period of time.LG10-7 Final PDF to printer

348 part five Risk and Returncor91411_ch10_330-361.indd 348 01/13/17 11:59 AMFinancial managers need an estimate of their shareholdersÕ required return in order to make appropriate decisions about their companiesÕ future growth. Good financial man-agers will compute shareholdersÕ required return using as many methods as they can to determine the most realistic value possible.Required ReturnConsider that the required returns for 3M, Home Depot, and Hewlett-Packard are 12.56 percent, 12.07 percent, and 15.78 percent, respectively. These expectations may seem quite far apart, considering that all three firms are in the DJIA and are leaders in their market sectors. Use the following information to compute the constant-growth model estimate of the required return:Expected DividendCurrent PriceAnalyst Growth Estimate3M Company$2.54$105.7010.4%Home Depot1.5670.1014.5Hewlett-Packard0.5322.00 0.25SOLUTION: You can now use equation 10-6 to find each companyÕs required return as 3M required return =  ( $2.54 Ö $105.70 )  + 0.104 = 12.80%Home Depot required return =  ( $1.56 Ö $70.10 )  + 0.145 = 16.73%Hewlett-Packard required return =  ( $0.53 Ö $22.00 )  + 0.0025 = 2.66% The 3M estimates using CAPM and the constant-growth rate model are similar. The constant-growth rate model estimate is more than 4 percent higher than the CAPM estimate for Home Depot, but far lower for Hewlett-Packard.Similar to Problems 10-15, 10-16, 10-29, 10-30, Self-Test Problem 3EXAMPLE 10-4For interactive versions of this example, log in to Connect or go to mhhe.com/Cornett4e.LG10-7 TIME OUT 10-7 Why is the shareholdersÕ required return important to corporate managers?  viewpoints REVISITEDBusiness Application SolutionYou need to determine the firmÕs level of market risk. If you can obtain a beta, then you can make a required return estimate using CAPM. To assess the result, you can use the constant-growth model to check the CAPM estimated required return for comparisonÕs sake.If you find the beta of the firm to be 1.8, assume a market return of 11 percent, and note a 5 percent T-bill rate, the CAPM computations would be 5% + 1.8 ×  ( 11% − 5% )  = 15.8 percent Final PDF to printer

chapter 10 Estimating Risk and Return 349cor91411_ch10_330-361.indd 349 01/13/17 11:59 AMThe firm will pay a $0.50 dividend next year and the current stock price is $32. Managers believe the company will grow at 13 percent per year for the foreseeable future. The constant-growth model computation gives $0.50 Ö $32 + 0.13 = 0.1456, or 14.56 percent You can now take these estimates to the team.Personal Application SolutionYou are investing 57.1 percent (= $200 Ö $350) of your monthly contribution in stocks. You are also contributing 28.6 percent in bonds and 14.3 percent into a money market account. The diversified stock portfolio has a beta of 1. The long-term bond portfolio has a beta of 0.18. By definition, the money market account is risk-free and thus has a beta of zero.The beta of this portfolio is therefore 0.571 ×  ( 1 )  + 0.286 ×  ( 0.18 )  + 0.143 ×  ( 0 )  = 0.62 With a portfolio beta of 0.62, a market return of 11 percent, and a risk-free rate of 5 percent, you can expect a return of 5% + 0.62 ×  ( 11% − 5% )  = 8.72 percent If you want a higher expected return, you will have to take more risk. You can do that by contributing a higher proportion of your funds to the stock portfolio.summary of learning goalsIn this chapter, we explored the theory and application of expected return. As an incentive to take market risk, inves-tors require a commensurate return. We developed more precise specifications of the risk and required return rela-tionship here via the CAPM and then discussed whether the underlying assumptions of the CAPM hold well enough in reality for CAPM required return estimates to give realistic insight into what investors really expect. However, people often think about risk differently from how it is captured by traditional statistical measures, which can lead to misconceptions.Compute forward-looking expected return and risk. A firmÕs stock return performance relates closely to the strength of the economy. We can compute expected return and risk using the probabilities of various good and bad economic states occurring in the future as predicted by macroeconomists.Understand risk premiums. Investors will take on risk if they are given positive risk premiums. The risk premium of the stock market itself is defined as the market return minus the risk-free rate. The market risk premium provides a basis for us to understand the rewards for taking risk. Any particular stockÕs risk premium will be jointly determined by the market risk premium and the stockÕs sensitivity to market risk.Know and apply the capital asset pricing model (CAPM). Adding a risk-free security to any portfolio along the efficient frontier gives the investor a higher required return. Investors should own LG10-1LG10-2LG10-3combinations of the market portfolio and the risk-free security. As we change the amounts of the market portfolio and risk-free securities that investors may choose according to their risk preferences, we derive the security market line. The security market lineÕs equation is known as CAPM, which specifies a direct relationship between required return and market risk. Any stockÕs required return comprises the risk-free rate plus the stockÕs risk premium. That risk premium is determined by the amount of market risk to which the stock is subject, as measured by beta.Calculate and apply beta, a measure of market risk. We can use a stockÕs standard deviation to measure a stockÕs volatility. The market only rewards investors for taking on the portion of risk or volatility that arises due to general, economywide volatility, as shown in the market portfolio. The market risk portion of total risk is scaled so that a beta of one represents the LG10-4Final PDF to printer

350cor91411_ch10_330-361.indd 350 01/13/17 11:59 AMrisk of the overall stock market. A beta of 0.5 means that the stock exhibits only half of the overall stock market risk, while a beta of 2 means that the stock exhibits twice the risk that the overall market shows. A riskless securityÑsuch as a U.S. Treasury billÑhas a zero beta. We can compute betas using past stock returns and the returns from a market portfolio proxy, like the S&P 500 Index. Many financial publications and financial websites also provide their own beta estimates for particular stocks.Differentiate the levels of market efficiency and their implications. Financial risk-reward relationships rely upon the assumption that stock market prices are generally Òright,Ó given known company information. Various levels of the efficient market hypothesis (EMH) are characterized by the information types that stock prices reflect. The weak-form level of market efficiency states that stock prices incorporate all trading information, like past prices and trading volume. The semistrong-form efficiency level states that current stock prices reflect all public information. Note that publicly known information includes the weak-form efficiency information and financial statements, analyst opinions, news, etc. Information that is not publicly known, but that is known by some corporate officers and other insiders, is called privately held information. The strong-form market efficiency level of the EMH claims that stock LG 10-5prices incorporate all information, public and private. Note that all U.S. stock exchanges forbid corporate officers and other people privy to closely held information from profiting from such informationÑan activity known as insider trading. The fourth possibility of the EMH is that stock prices are not efficient and thus are not always correct. If this is the case, investors can profit from mispricings.Calculate and explain investorsÕ required return and risk. Financial managersÑand all managers, for that matterÑmust have a firm grasp upon the trade-off between risk and return. This trade-off arises in many business decisions involving product mix, marketing campaigns, and research and development. Financial managers in particular must understand the return that shareholders require from the firm when they analyze new business opportunities.Use the constant-growth model to compute required return. The constant-growth model provides a useful alternative to the CAPM for computing shareholdersÕ required return. This model requires only the current stock price, an estimate of next yearÕs dividends, and an estimate of the firmÕs growth rate. To make the best assessment of the required return, compute estimates from both the CAPM and the constant- growth model and compare them, judging which seems more in line with investorsÕ actual expectations.LG 10-6LG 10-7chapter equations 10-1 Expected return = ( p 1  ×  Return 1 ) + (p 2  ×  Return 2 ) ( p 3  ×  Return 3 ) + á á á + ( p s  ×  Return s ) =  ∑ j=1 s p j  ×  Return j 10-2 Standard deviation =  √ ________________________________ p 1  × ( Return 1  −  Expected return) 2  +  p 2 × ( Return 2  − Expected return)2 + á á á =  √ ______________________________ ∑ j=1 s p j  × ( Return j  −  Expected return) 2 10-3 Required return = Risk-free rate + Risk premium 10-4 Expected return = R f   + β( R M  −  R f ) 10-5 β ρ = ( w 1  ×  β 1 ) + ( w 2  ×  β 2 ) + ( w 3  ×  β 3 ) + á á á + ( w n  ×  β n ) = ∑ j=1 n w j β j 10-6 i = Dividend yield + Constant growth = D 1 ___ P 0 + g Final PDF to printer

351cor91411_ch10_330-361.indd 351 01/13/17 11:59 AMkey termsasset pricing The process of directly specifying the rela-tionship between required return and risk. p. 335behavioral finance The study of the cognitive processes and biases associated with making financial and eco-nomic decisions. p. 345beta (β) A measure of the sensitivity of a stock or portfo-lio to market risk. p. 337capital asset pricing model (CAPM) An asset pricing theory based on a beta, a measure of market risk. p. 335capital market line (CML) The line on a graph of return and risk (standard deviation) from the risk-free rate through the market portfolio. p. 335efficient market A securities market in which prices fully reflect available information on each security. p. 343efficient market hypothesis (EMH) A theory that describes what types of information are reflected in cur-rent stock prices. p. 343executive stock options Special rights given to corpo-rate executives to buy a specific number of shares of the company stock at a fixed price during a specific period of time. p. 346expected return The average of the possible returns weighted by the likelihood of those returns occur – ring. p. 332financial leverage The extent to which debt securities are used by a firm. p. 336market portfolio In theory, the market portfolio is the combination of securities that places the portfolio on the efficient frontier and on a line tangent from the risk-free rate. In practice, the S&P 500 Index is used to proxy for the market portfolio. p. 335market risk premium The return on the market portfolio minus the risk-free rate. Risk premiums for specific firms are based on the market risk premium. p. 334overconfidence Overconfidence is used to describe three psychological observations. First, people are miscali-brated on understanding the precision of their knowledge. Second, people have a tendency to underestimate risks, and third, people tend to believe that they are better than average at tasks they are familiar with. p. 346penny stocks The stocks of small companies that are priced below $1 per share. p. 343portfolio beta The combination of the individual com-pany betas in an investorÕs portfolio. p. 339privately held information The set of information that has not been released to the public but is known by few individuals, likely company insiders. p. 344probability The likelihood of occurrence. p. 332probability distribution The set of probabilities for all possible occurrences. p. 332public information The set of information that has been publicly released. Public information includes data on past stock prices and volume, financial statements, cor-porate news, analyst opinions, etc. p. 344required return The level of total return needed to be compensated for the risk taken. It is made up of a risk-free rate and a risk premium. p. 334restricted stock A special type of stock that is not trans-ferable from the current holder to others until specific conditions are satisfied. p. 346risk premium The portion of the required return that represents the reward for taking risk. p. 334security market line (SML) Similar to the capital mar-ket line except risk is characterized by beta instead of standard deviation. p. 337stock market bubble Investor enthusiasm causes an inflated bull market that drives prices too high, ending in a dramatic collapse in prices. p. 345self-test problems with solutions1 Expected Return and Risk An economist has determined that the probability of the economy being in various states is shown in the following table:Economic StateProbabilityReturnFast growth0.13 40%Slow growth0.42 15No growth0.25 5Recession0.17 −15Depression0.03−30LG10-1Final PDF to printer

352cor91411_ch10_330-361.indd 352 01/13/17 11:59 AMYou have added the return that your firm will achieve in each economic state. Given this information, you can compute the expected return and risk of the firm.  Solution:Use equations 10-1 and 10-2 to complete the following table:EconomyProbabilityReturnP × ReturnDeviation Deviation2× PFast growth0.13 40%5.20% 30.70%942.49122.52Slow growth0.42 156.30 5.7032.4913.65No growth0.25 51.25 −4.3018.494.62Recession0.17−15−2.55 −24.30590.49100.38Depression0.03−30−0.90 −39.301544.4946.33Sum =1−9.30287.51Square root =16.96%The expected return for the firm is 9.3 percent and the standard deviation risk is 16.96 percent.2 Portfolio Beta and Required Return You have a stock portfolio that consists of the following positions:SharesPriceBetaApple Inc. 50$89.002.40Fiserv100 55.001.34Monster Worldwide150 52.002.37Ross Stores200 34.001.27Whole Foods100 51.001.66The beta of each stock is also shown. What is the portfolio beta? If the market return is expected to be 12 percent and the risk-free rate is 4 percent, what is the required return of the portfolio?  Solution:To compute the portfolio beta, you must first calculate the portfolio weights for each stock. The position of each stock is denoted by the number of shares multiplied by the price of the stock. Adding all of the positions results in a total portfolio value of $29,650. The portion that each stock represents in the portfolio is shown as its weight and is computed by dividing each position by the total portfolio value. Once the weights are known, then equation 10-5 can be used. The last column shows the computations for the portfolio beta.SharePricePositionWeightBetaBeta W × BetaApple Inc.50$89.00$4,4500.152.400.36Fiserv10055.00 5,5000.191.340.25Monster Worldwide15052.00 7,8000.262.370.62Ross Stores20034.00 6,8000.231.270.29Whole Foods100 51.00 5,1000.171.660.29Sum =$29,6501.001.81The beta of this portfolio is 1.81. This is a high-risk portfolio. You can now use the CAPM to compute the required return of the portfolio as4% + 18.1 × (12% Ð 4%) = 18.47 percentLG10-3, 10-4Final PDF to printer

353cor91411_ch10_330-361.indd 353 01/13/17 11:59 AM3 Required Return Compute the required return for three stocks: Molson Coors, Hilton Hotels, and Tribune Co. To be thorough, compute required return using both the CAPM and the constant-growth model.For the CAPM analysis, see the following market risk information: Molson Coors (β = 0.37), Hilton Hotels (β = 1.51), and Tribune (β = 0.46). Assume that the risk-free rate is 4.5 percent and the market risk premium is 6 percent.For the constant-growth model, the stock price, dividend, and growth information is PriceDividendGrowth RateMolson Coors$50.05$1.209.0%Hilton Hotels36.700.1615.0Tribune30.700.7611.0Solution:Start by calculating the required return using CAPM. Note that it was the market risk premium that was given instead of the market return. Since the market risk premium is what goes in the parenthesis of the equation, the results are Molson Coors: 4.5% + 0.37 × (6%) = 6.72% Hilton Hotel: 4.5% + 1.51 × (6%) = 13.56% Tribune: 4.5% + 0.46 × (6%) = 7.26% The required returns for Molson Coors and for Tribune seem a little low. So you should also compute the required return using the constant-growth model: Molson Coors: ($1.20 Ö $50.05) + 0.09 = 11.40% Hilton Hotel: ($0.16 Ö $36.70) + 0.15 = 15.44% Tribune: ($0.76 Ö $30.65) + 0.11 = 13.48% These estimates for the required return seem much better for Molson Coors and Tribune, but the Hilton Hotels estimate may be a little high.LG10-4, 10-7questions 1. Consider an asset that provides the same return no matter what economic state occurs. What would be the standard deviation (or risk) of this asset? Explain. (LG10-1) 2. Why is expected return considered Òforward- lookingÓ? What are the challenges for practitioners to utilize expected return? (LG10-1) 3. In 2000, the S&P 500 Index earned −9.1 percent while the T-bill yield was 5.9 percent. Does this mean the market risk premium was negative? Explain. (LG10-2) 4. How might the magnitude of the market risk premium impact peopleÕs desire to buy stocks? (LG10-2) 5. Describe how adding a risk-free security to modern portfolio theory allows investors to do better than the efficient frontier. (LG10-3) 6. Show on a graph like Figure 10.2 where a stock with a beta of 1.3 would be located on the security market line. Then show where that stock would be located if it is undervalued. (LG10-3) 7. Consider that you have three stocks in your portfolio and wish to add a fourth. You want to know if the fourth stock will make the portfolio riskier or less risky. Compare and contrast how this would be assessed using standard deviation versus market risk (beta) as the measure of risk. (LG10-3) 8. Describe how different allocations between the risk-free security and the market portfolio can achieve any level of market risk desired. Give examples of a portfolio from a person who is very risk averse and a portfolio for someone who is not so averse to tak-ing risk. (LG10-3)Final PDF to printer

354cor91411_ch10_330-361.indd 354 01/13/17 11:59 AM 9. Cisco Systems has a beta of 1.25. Does this mean that you should expect Cisco to earn a return 25 percent higher than the S&P 500 Index return? Explain. (LG10-4) 10. Note from Table 10.2 that some technology- oriented firms (Apple) in the Dow Jones Industrial Average have high market risk while others (Intel and Verizon) have low market risk. How do you explain this? (LG10-4) 11. Find a beta estimate from three different sources for General Electric (GE). Compare these three values. Why might they be different? (LG10-4) 12. If you were to compute beta yourself, what choices would you make regarding the market portfolio, the holding period for the returns (daily, weekly, etc.), and the number of returns? Justify your choices. (LG10-4) 13. Explain how the concept of a positive riskÐreturn relationship breaks down if you can systematically find stocks that are overvalued and undervalued. (LG10-5) 14. Determine what level of market efficiency each event is consistent with the following: (LG10-5) a. Immediately after an earnings announcement the stock price jumps and then stays at the new level.  b. The CEO buys 50,000 shares of his company and the stock price does not change.  c. The stock price immediately jumps when a stock split is announced, but then retraces half of the gain over the next day.  d. An investor analyzes company quarterly and annual balance sheets and income statements looking for undervalued stocks. The investor earns about the same return as the S&P 500 Index.  15. Why do most investment scams conducted over the Internet and e-mail involve penny stocks instead of S&P 500 Index stocks? (LG10-5) 16. Describe a stock market bubble. Can a bubble occur in a single stock? (LG10-5) 17. If stock prices are not strong-form efficient, what might be the price reaction to a firm announcing a stock buyback? Explain. (LG10-6) 18. Compare and contrast the assumptions that need to be made to compute a required return using CAPM and the constant-growth model. (LG10-7) 19. How should you handle a case where required return computations from CAPM and the constant-growth model are very different? (LG10-7)problems 10-1 Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns: (LG10-1)Economic StateProbabilityReturnFast growth0.3 40%Slow growth0.4 10Recession0.3−25 10-2 Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns: (LG10-1)Economic StateProbabilityReturnFast growth0.2 35%Slow growth0.6 10Recession0.2−30 10-3 Required Return If the risk-free rate is 3 percent and the risk premium is 5 percent, what is the required return? (LG10-2) 10-4 Required Return If the risk-free rate is 4 percent and the risk premium is 6 percent, what is the required return? (LG10-2)basic problemsFinal PDF to printer

355cor91411_ch10_330-361.indd 355 01/13/17 11:59 AM 10-5 Risk Premium The average annual return on the S&P 500 Index from 1986 to 1995 was 15.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these 10 years? (LG10-2) 10-6 Risk Premium The average annual return on the S&P 500 Index from 1996 to 2005 was 10.8 percent. The average annual T-bill yield during the same period was 3.6 percent. What was the market risk premium during these 10 years? (LG10-2) 10-7 CAPM Required Return Hastings Entertainment has a beta of 0.65. If the mar-ket return is expected to be 11 percent and the risk-free rate is 4 percent, what is HastingsÕ required return? (LG10-3) 10-8 CAPM Required Return Nanometrics, Inc., has a beta of 3.15. If the market return is expected to be 10 percent and the risk-free rate is 3.5 percent, what is NanometricsÕ required return? (LG10-3) 10-9 Company Risk Premium Netflix, Inc., has a beta of 3.61. If the market return is expected to be 13 percent and the risk-free rate is 3 percent, what is NetflixÕs risk premium? (LG10-3) 10-10 Company Risk Premium Paycheck, Inc., has a beta of 0.94. If the market return is expected to be 11 percent and the risk-free rate is 3 percent, what is PaychecksÕ risk premium? (LG10-3) 10-11 Portfolio Beta You have a portfolio with a beta of 1.35. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 5 percent in a stock with a beta of 0.78? (LG10-3) 10-12 Portfolio Beta You have a portfolio with a beta of 1.1. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 15 percent in a stock with a beta of 0.5? (LG10-3) 10-13 Stock Market Bubble The NASDAQ stock market bubble peaked at 4,816 in 2000. Two and a half years later it had fallen to 1,000. What was the percentage decline? (LG10-5) 10-14 Stock Market Bubble The Japanese stock market bubble peaked at 38,916 in 1989. Two and a half years later it had fallen to 15,900. What was the percentage decline? (LG10-5) 10-15 Required Return Paccars current stock price is $48.20 and it is likely to pay a $0.80 dividend next year. Since analysts estimate Paccar will have an 8.8 percent growth rate, what is its required return? (LG10-7) 10-16 Required Return Universal Forests current stock price is $57.50 and it is likely to pay a $0.26 dividend next year. Since analysts estimate Universal Forest will have a 9.5 percent growth rate, what is its required return? (LG10-7) 10-17 Expected Return Risk For the same economic state probability distribu-tion in problem 10-1, determine the standard deviation of the expected return. (LG10-1)Economic StateProbabilityReturnFast growth0.3 40%Slow growth0.410Recession0.3−25intermediate problemsFinal PDF to printer

356cor91411_ch10_330-361.indd 356 01/13/17 11:59 AM 10-18 Expected Return Risk For the same economic state probability distribution in problem 10-2, determine the standard deviation of the expected return. (LG10-1)Economic StateProbabilityReturnFast growth0.2 35%Slow growth0.6 10Recession0.2 −30 10-19 Undervalued/Overvalued Stock A manager believes his firm will earn a 14 percent return next year. His firm has a beta of 1.5, the expected return on the market is 12 percent, and the risk-free rate is 4 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is undervalued or overvalued. (LG10-3) 10-20 Undervalued/Overvalued Stock A manager believes his firm will earn a 14 percent return next year. His firm has a beta of 1.2, the expected return on the market is 11 percent, and the risk-free rate is 5 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is undervalued or overvalued. (LG10-3) 10-21 Portfolio Beta You own $10,000 of Olympic Steel stock that has a beta of 2.2. You also own $7,000 of Rent-a-Center (beta = 1.5) and $8,000 of Lincoln Edu-cational (beta = 0.5). What is the beta of your portfolio? (LG10-3) 10-22 Portfolio Beta You own $7,000 of Human Genome stock that has a beta of 3.5. You also own $8,000 of Frozen Food Express (beta = 1.6) and $10,000 of Molecular Devices (beta = 0.4). What is the beta of your portfolio? (LG10-3) 10-23 Expected Return and Risk Compute the expected return and standard devia-tion given these four economic states, their likelihoods, and the potential returns: (LG10-1)Economic StateProbabilityReturnFast growth0.30 60%Slow growth0.50 13Recession0.15−15Depression0.05−45 10-24 Expected Return and Risk Compute the expected return and standard devia-tion given these four economic states, their likelihoods, and the potential returns: (LG10-1)Economic StateProbabilityReturnFast growth0.25 50%Slow growth0.55 11Recession0.15−15Depression0.05−50 10-25 Risk Premiums You own $10,000 of Dennys Corp. stock that has a beta of 2.9. You also own $15,000 of Qwest Communications (beta = 1.5) and $5,000 of Southwest Airlines (beta = 0.7). Assume that the market return will be 11.5 per-cent and the risk-free rate is 4.5 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? (LG10-3)advanced problemsFinal PDF to printer

357cor91411_ch10_330-361.indd 357 01/13/17 11:59 AM 10-26 Risk Premiums You own $15,000 of Opsware, Inc., stock that has a beta of 3.8. You also own $10,000 of Lowes Companies (beta = 1.6) and $10,000 of New York Times (beta = 0.8). Assume that the market return will be 12 percent and the risk-free rate is 6 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? (LG10-3) 10-27 Portfolio Beta and Required Return You hold the positions in the following table. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio? (LG10-3)PriceSharesBetaAmazon.com$40.801003.8Family Dollar Stores 30.101501.2McKesson Corp. 57.40750.4Schering-Plough Corp. 23.802000.5 10-28 Portfolio Beta and Required Return You hold the positions in the following table. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio? (LG10-3)PriceSharesBetaAdvanced Micro Devices$ 14.703004.2FedEx Corp.120.00 501.1Microsoft28.901000.7Sara Lee Corp.17.251500.5 10-29 Required Return Using the information in the table, compute the required return for each company using both CAPM and the constant-growth model. Compare and discuss the results. Assume that the market portfolio will earn 12 percent and the risk-free rate is 3.5 percent. (LG10-3, LG10-7)PriceUpcoming DividendGrowthBetaUS Bancorp$36.55$1.6010.0%1.8Praxair64.751.1211.02.4Eastman Kodak24.951.004.50.5 10-30 Required Return Using the information in the table, compute the required return for each company using both CAPM and the constant-growth model. Compare and discuss the results. Assume that the market portfolio will earn 11 percent and the risk-free rate is 4 percent. (LG10-3, LG10-7)PriceUpcoming DividendGrowthBetaEstee Lauder$47.40$0.6011.7%0.75Kimco Realty52.101.548.01.3Nordstrom5.250.5014.62.2 10-31 Spreadsheet Problem As discussed in the text, beta estimates for one firm will vary depending on various factors such as the time over which the estimation is conducted, the market portfolio proxy, and the return intervals. You will demon-strate this variation using returns for Microsoft. a. Using all 45 monthly returns for Microsoft and the two stock market indexes, compute MicrosoftÕs beta using the S&P 500 Index as the market proxy. Then compute the beta using the NASDAQ index as the market portfolio proxy. Compare the two beta estimates.Final PDF to printer

358cor91411_ch10_330-361.indd 358 01/13/17 11:59 AM b. Now estimate the beta using only the most recent 30 monthly returns and the S&P 500 Index. Compare the beta estimate to the estimate in part (a) when using the S&P 500 Index and all 45 monthly returns. c. Estimate MicrosoftÕs beta using the following quarterly returns. Compare the estimate to the ones from parts (a) and (b).ABCDEFGHIJKL1DateMSFTS&P500NASDAQDateMSFTS&P500NASDAQDateMSFTS&P500NASDAQ2Jan 2016−6.98%−0.41%−1.21%Oct 20142.47%2.45%3.47%Jul 20135.64−3.13%−1.01%3Dec 2015−0.70 −5.07 −7.86 Sep 20141.27 2.32 3.06 Jun 2013−7.824.95 6.56 4Nov 20152.08 −1.75 −1.98 Aug 20142.05 −1.55 −1.90 May 2013−1.03−1.50 −1.52 5Oct 20153.94 0.05 1.09 Jul 20145.92 3.77 4.82 Apr 20136.182.08 3.82 6Sep 201518.93 8.30 9.38 Jun 20143.50 −1.51 −0.87 Mar 201315.691.81%1.88%7Aug 20151.70 −2.64 −3.27 May 20141.86 1.91 3.90 Feb 20132.913.60 3.40 8Jul 2015−6.19 −6.26 −6.86 Apr 20142.05 2.10 3.11 Jan 20132.111.11 0.57 9Jun 20155.78 1.97 2.84 Mar 2014−1.44 0.62%−2.01 Dec 20122.775.04 4.06 10May 2015−5.78 −2.10 −1.64 Feb 20147.00 0.69 −2.53 Nov 20120.340.71 0.31 11Apr 2015−3.03 1.05 2.60 Jan 20142.00 4.31 4.98 Oct 2012−5.960.28 1.11 12Mar 201519.63 0.85 0.83 Dec 20131.15 −3.56 −1.74 Sep 2012−4.10−1.98 −4.46 13Feb 2015−7.27 −1.74 −1.26 Nov 2013−1.89 2.36 2.87 Aug 2012−3.442.42 1.61 14Jan 20159.31 5.49 7.08 Oct 20138.50 2.80 3.58 Jul 20125.271.98 4.34 15Dec 2014−13.02 −3.10 −2.13 Sep 20136.40 4.46 3.93 Jun 2012−3.661.26 0.15 16Nov 2014−2.84 −0.42 −1.16 Aug 2013−0.36 2.97 5.06 May 20124.803.96 3.81 ABC1DateMSFTS&P5002Q4 201525.31%  1.05%3Q3 20150.91−6.944Q2 20159.29−0.235Q1 2015−11.84   0.446Q4 20140.83 4.397Q3 201411.87  0.628Q2 20142.45 4.699Q1 201410.39  1.3010Q4 201313.26  9.9211Q3 2013−2.97  4.6912Q2 201313.02  1.9313Q1 20138.0010.0314Q4 2012−9.51 −1.0115Q3 2012−2.07  5.7616Q2 2012−4.55 −3.29 10-32 Spreadsheet Problem Build a spreadsheet that automatically computes the expected market return and risk for different assumptions about the state of the economy. a. First, create a spreadsheet like the one shown below and compute the expected return and standard deviation.ABC1State of EconomyProbability of StateExpected Market Return2Fast growth0.1335%3Slow growth0.4217%4No growth0.25 3%5Recession0.18−15% 6Depression0.02−30% 78Sum =1.009Expected return =10Standard deviation =Final PDF to printer

359cor91411_ch10_330-361.indd 359 01/13/17 11:59 AM b. Compute the expected return and risk for the following two scenarios:  ABC1State of EconomyProbability of StateExpected Market Return2Fast growth0.1330%3Slow growth0.3315%4No growth0.30 2%5Recession0.20−18% 6Depression0.04−25% ABC1State of EconomyProbability of StateExpected Market Return2Fast growth0.1540%3Slow growth0.35 18  4No growth0.3445Recession0.15−20  6Depression0.01−35  research it! Find a BetaUsing beta as a risk measure has been fully integrated into corporate finance and the investment industry. You can obtain a beta for most companies at many financial websites. Sites that list a beta include MSN Money (in the Company Report section), Yahoo! Finance (in the Key Statistics section), and Zacks (follow the Detailed Quote link). Obtain the beta for your favorite company from several different websites. Are the values you obtain similar? If they are not, why might they be different? (moneycentral.msn.com, finance.yahoo.com, www.zacks.com)integrated mini-case: DisneyÕs BetaWhen you go on the Web to find a firmÕs beta, you do not know how recently it was computed, what index was used as a proxy for the market portfolio, or which time series of returns the calculations used. Earlier in this chapter, it was shown that when we went on the Web to find a beta for Disney, we found the following: MSN Money (1.41) and Yahoo! Finance (1.56).An alternative is to compute beta yourself. A common estimation procedure is to use 60 months of return data and to use the S&P 500 Index as the market portfolio. You can obtain price data for a company and for the S&P 500 Index free from websites like Yahoo! Finance. Using monthly prices, you can compute the monthly returns, as (Pn − Pn − 1) Ö Pn − 1. Below are 60 monthly returns for Disney and the S&P 500 Index. You can use these returns to compute DisneyÕs beta. A spreadsheet, like Excel, can run a regression (go to Tool menu, select Data Analysis, and then Regression). Select Disney returns as the y variable and S&P 500 Index return as the x variable. The coefficient for the x variable is the beta estimate. The regression will provide all the statistical information you might like. However, if you only want beta, you can simply use the SLOPE function in Excel. Or you may have learned to run a regression using statistical software.Final PDF to printer

360cor91411_ch10_330-361.indd 360 01/13/17 11:59 AMABCDEFGHI1DateDisneyS&P500DateDisneyS&P500DateDisneyS&P5002Feb 16−0.31%−0.41%Jun 142.06%1.91%Oct 12−6.04%−1.98%3Jan 16−8.81 −5.07 May 145.89 2.10 Sep 125.68 2.42 4Dec 15−7.39 −1.75 Apr 14−0.91 0.62 Aug 120.67 1.98 5Nov 15−0.24 0.05 Mar 14−0.92 0.69 Jul 121.32 1.26 6Oct 1511.29 8.30 Feb 1411.29 4.31 Jun 126.10 3.96 7Sep 150.31 −2.64 Jan 14−4.96 −3.56 May 126.03 −6.27 8Aug 15−15.10 −6.26 Dec 139.64 2.36 Apr 12−1.53 −0.75 9Jul 155.75 1.97 Nov 132.84 2.80 Mar 124.26 3.13 10Jun 153.42 −2.10 Oct 136.36 4.46 Feb 127.94 4.06 11May 151.52 1.05 Sep 136.02 2.97 Jan 123.73 4.36 12Apr 153.65 0.85 Aug 13−5.91 −3.13 Dec 116.36 0.85 13Mar 150.78 −1.74 Jul 132.38 4.95 Nov 112.78 −0.51 14Feb 1514.42 5.49 Jun 130.11 −1.50 Oct 1115.65 10.77 15Jan 15−3.43 −3.10 May 130.38 2.08 Sep 11−11.45 −7.18 16Dec 143.11 −0.42 Apr 1310.63 1.81 Aug 11−11.81 −5.68 17Nov 141.24 2.45 Mar 134.05 3.60 Jul 11−1.08 −2.15 18Oct 142.64 2.32 Feb 131.32 1.11 Jun 11−6.22 −1.83 19Sep 14−0.95 −1.55 Jan 138.21 5.04 May 11−3.41 −1.35 20Aug 144.66 3.77 Dec 121.80 0.71 Apr 110.02 2.85 21Jul 140.16 −1.51 Nov 121.10 0.28 Mar 11−1.49 −0.10  a. Compute DisneyÕs beta using the listed returns. b. Compare your estimate with the ones found on the Web as listed. c. How different will the required returns be using these betas? Compute required return using each beta (assume that the risk-free rate is 5 percent and the market return will be 12 percent).ANSWERS TO TIME OUT 10-1 Average return is computed using the simple average of historical returns. The expected return is a forward-looking return. However, it is computed using a weighted average (the probabilities) of returns. The returns used in the various economic stages are usually chosen from historical knowledge of how the firm performs in each stage. Thus, both measures use an average of historical returns in one way or another. The historical risk and expected risk are both measured using standard deviation and his-torical knowledge of returns as well. 10-2 Many people are willing to take market risk because over time they expect to earn a risk premium. This risk premium allows them to build their wealth significantly more than just investing in the risk-free asset. However, because risk is involved, these peo-ple should have a long-term focus and recognize that they can lose money in the short term. 10-3 For every point on the efficient frontier (except the market portfolio), you can form a portfolio that has the same level of risk but a higher expected return through a combi-nation of the market portfolio and the risk-free asset. Thus, the capital market line has a better riskÐreturn trade-off because it has a higher return at every level of risk. 10-4 In early 2016, oil prices had fallen a lot. Thus, the relatively low beta values of Chevron (1.17) and Exxon Mobil (0.92) seem too low for the risk these firms are experiencing. Procter & Gamble is a diversified firm selling consumer goods that are purchased in good economies and bad. Therefore, its low beta of 0.66 seems reasonable. Du Pont is a chemical firm that seems to be highly tied to the success of the economy, so its very high beta of 2.01 seems too high. Apple has a beta of 1.35. Given that it is driven by the growth of new products and innovations within existing products, the risk seems high and this beta seems appropriate. Final PDF to printer

361cor91411_ch10_330-361.indd 361 01/13/17 11:59 AM 10-5 No. Weak-form efficiency is a subset of semistrong-form efficiency. Information about market prices and volumes is public and is thus included in the broader definition of public information in the semistrong-form efficiency hypothesis. Therefore, if a market is semistrong-form efficient, it is also weak-form efficient, by definition. 10-6 Consider a case when the market consistently overreacted to bad news announce-ments. This means that prices would fall too far after the announcement and eventu-ally partially rebound. If this scenario was predictable, an investor could make money by buying stocks after bad news and capturing the price bounce. 10-7 Consider that you obtained money from the bank and had to pay an 8 percent interest rate. If you invested that money in a project that returned 5 percent to you, then you would not be earning enough to pay back the bank. You need to earn more than 8 percent on your business project in order to be successful. Corporate man-agers are using the shareholdersÕ equity capital and need to know what return they r

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