Compare the expected returns that you computed for each security with the published 52-week change

This week, the discussion will examine your individual risk tolerance through a survey on Investment Risk Tolerance Assessment. Then, you will select investments that closely match your Risk Tolerance. In addition, you will analyze both Sam’s and Martin’s Risk Tolerance and select an investment for each of them that matches their individual risk tolerance.

Before you begin, be sure to review the following narrated lecture:
Risk and return data and the capital asset pricing model, the Cap M.
In the last unit, you learned how to estimate the required return of an investment using the dividend growth model. Remember, you sold four are in the equation. This model had the assumption that the dividends would grow at a constant rate. As you will recall, we could not use this model for companies that did not pay a dividend.
In this unit, we will learn another method for computing the required return on a common stock. It is called the Capital Asset Pricing Model, or Cap M. This model was developed in the 1960s and was largely credited to William Sharpe, who won a Nobel Prize for his contribution in nineteen ninety. The Cap M uses statistical analysis to relate the risk of an individual stock to its expected return. The premise is that investors must be compensated for the time value of money and the risk of undertaking the investment is not necessary for a company to pay dividends in order to use this model.
The return of the stock abbreviated are subscripts stock is the rate of return that an investor can expect from an individual security over the next period.
Free rate, abbreviated R subscript RF is the return an investor can expect if there is no risk of losing the investment. In other words, the investment is completely safe. The rate on short term Treasury bills called T bills is usually considered to be a good representative of the risk free rate because these investments are relatively free from any risk of default.
Turn of the market abbreviated R subscript M, the return on the market as a whole is generally approximated using the historical return on the S&P 500 stock index. The beta coefficient, abbreviated as a Script B is a measure of riskiness of the stock relative to the riskiness of the market. Before we can discuss this measure in detail. However, we must first learn about different types of risk and some other ways of measuring it.
Types of risk, systematic and unsystematic, the true risk of an investment comes from the events that cannot be predicted. These surprises come in two different forms. Systematic risk is the risk that affects a large number of companies. It has a widespread effect on the market as a whole. Examples would include announcements about the economy or inflation. Unsystematic risk affects a single company or just a small number of companies within the same category. For example, an employee strike of one oil company is likely to affect that company and perhaps its suppliers and customers, but is not likely to affect the market of a whole or even other companies. Therefore, the expected return of any stock will include both a systematic component and an unsystematic component.
Variance and standard deviation. One of the most common ways to express the volatility of a stock is to measure the variance of the actual returns as compared with the expected return variance measures, the mathematical dispersion of the actual returns around the expected return in this chart. We see that the actual return, the blue line fluctuates both above and below the expected return. The red line. If we take the distances above and below, the expected return represented by the black lines, squared them, add them up, then average them, we get the variance for their return. In other words, we know the average of the squared differences between the actual return and the expected return. If we take the square root of that, we get the standard deviation, which gives us the information in the same unit of measure, which is a percent. In this case, it represents how far from normal or how far from the expected return the actual returns are. In this example, the standard deviation is three point seven percent. This tells us that the actual return will fluctuate by approximately three point seven percent above and below the expected return.
Covariance and correlation, well, the variance and standard deviation from the previous slide measures the variability of a single stock, the covariance and the correlation measure the relationship of one stock to another. Covariance and correlation measure how two stocks move in tandem together. Covariance tells us whether or not they are related and correlation tells us the degree to which they are related. A positive covariance means that the stocks move in the same direction. A negative covariance means that they move opposite to each other. Correlation when the prices of two securities move in a similar direction, they are positively correlated. The closer this relationship is to a positive one, the more closely the movement of these stocks is related. For example, if oil prices per barrel increase, we are likely to also see an increase in gas prices at the pump. When the prices of two securities do not move together, the securities are not correlated. The correlation coefficient in this case is zero. And finally, if the stocks appear to move opposite one another, then they are negatively correlated. The closer the correlation coefficient is to negative one, the more opposite the stock movements are.
Beta, now, finally, we can discuss beta, as we mentioned earlier, beta is a measure of volatility. It is a measure of the systematic risk of a security in comparison to the market as a whole. It represents the tendency of a securities returns to respond to swings in the market. It’s calculated using this formula, the covariance of the stock return and the market return is divided by the variance of the market returns or an easier way is you can look beta up in the financial pages. If beta equals one, the security will move with the market, if there is less than one, it means that it is less volatile than the market as a whole. If beta is greater than one, then it is more volatile than the market.
Now, let’s put it all together, using the cap and model, we can compute the required return for IBM stock if we know a couple of things. First, we must know the going rate on the Treasury. Short term Treasury bills. This approximates the risk free return. That’s our subscript, R.F.. The beta coefficient of the stock, we can look IBM stock up and find its beta on Yahoo! Finance, dotcom and the return of the S&P five hundred. This is traditionally used to approximate the return of the market. That’s our subscript M.
Let’s assume that the risk free rate is point zero, six percent, Beda is point eight six and the return of the S&P is nine point four three percent. Here’s what our calculation looks like. Our result is eight point one nine percent. This means that IBM must return eight percent in order to compensate its investors for putting money in their stock instead of investing it elsewhere.
Stock portfolios and risk tolerance. Now, suppose that an investor wants to make an investment in a portfolio of stocks, that means more than one. How then does the investor choose the best combination of securities to hold? Well, remember when we discussed systematic and unsystematic risk when creating the optimal portfolio? The general assumption is that investors want the highest return for the least amount of risk. In a perfect world, that would mean that all the unsystematic and systematic risk would be eliminated by carefully choosing the stocks in the portfolio such that when some stocks go down, others will go up, thereby offsetting the risk. This is called portfolio diversification. However, in practice, it’s not really possible to completely eliminate systematic risk. Therefore, since it’s not possible to eliminate all the risk and investor must decide how much undiversified, viable risk he or she is comfortable risk. This is called risk tolerance.
Let’s use a two stock portfolio to illustrate, let’s assume that I will invest an equal amount of money in each stock such that 50 percent of my investment is in each security. Let’s also say that I’m very risk tolerant investor and I’m comfortable with taking on twice as much risk as the overall market. This would mean that I would look to create a portfolio that had an overall beta of two to compute this as simply take the weighted average of the stock Spader’s and their expected returns. Here is an example using Kraft Foods and Seagate Technologies. As you can see, Kraft has a beta of one point one buy. This stock represents 50 percent of my total dollar investment and therefore contributes half of the risk to the portfolio. Additionally, the expected return that I have computed using the cap m suggests that I will have a return of ten point five four percent. However, when I take the weighted average contribution of this stock to my portfolio, we see that it will only contribute approximately five point to seven percent to my overall expected return. If we repeat this calculation with Seagate stock, we see that it will contribute a bit of one point five in risk and a nine point six nine percent in return. Finally, we add the results together and we see that the low risk of the Kraft stock offsets the high risk of the Seagate stock. Together, the portfolio will have a beta of about two and we will have an expected return of just under 15 percent.

Instructions:
For this discussion, please complete the following tasks:
1. Select a publicly-traded company.
2. Go to (https://finance.yahoo.com/?guccounter=1). Enter the company’s stock symbol in the “Get Quotes” box. If you do not know the stock symbol, you can enter the company’s name in the search tool.
3. Search for the company’s Beta on the Summary page. Make a note of this number.
4. Next, go to the Historical data page and note the last closing price. Then scroll all the way to the very bottom and note the closing price for 1 year ago. Using these two numbers, calculate the 1-yr actual return for the stock. Use this formula: (yesterday’s price – last year’s price)/last year’s price. For example: (62.15 – 59.05)/59.05 = 5.24%
5. Next, click on Markets at the top of the page. Click on S&P500. Then navigate to the Historical data page and retrieve the last close price and the close 1-yr ago. Compute the actual change for the market using the same formula as above.
6. Next, go to Treasury.gov (https://home.treasury.gov/). and search for information on US Treasury Bills. There should be 3-month, 6-month, 2-year, etc. These are found toward the bottom of the home page in an area called Data Center. Select the 6-month rate, and make a note of this number.
7. Using the information above (the stock’s Beta, the rate on the 6-month Treasury, and the 52-week return for the S&P 500) compute the required rate of return for your stock. In other words, plug these numbers into the CAPM model.
8. Use the CAPM to determine the expected return of this additional stock.
9. Click to download the discussion table (Risk and Return Table.docx , attached). Compute the weighted average risk and return for your portfolio.
10. Save your completed table.

Directions:
In your original post, answer the following:
First, copy and paste your tables.
1. Compare the expected returns that you computed for each security with the published 52-week change. What do you notice? Are these stocks performing as well as expected?
2. How do these returns compare with the market return of the last year?
3. How did the overall risk and return change when you added the stocks together in a portfolio?
4. What was the outcome of the risk tolerance questionnaire? Were you an aggressive, moderate, or risk-averse investor? Did the portfolio you created match your risk tolerance? If so, how? If not, what would you do to make the portfolio a better match?

Please follow the instructions and complete the directions. When doing the written portion in the directions, please use the questions as headers and answer below. Please insert the completed table from the instructions in the Word document according to the directions.

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