Introduction and Investment Strategies
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Requirements: Steps to all questions
MASTER OF SCIENCE IN FINANCE (MSF)
ONLINE PROGRAM
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Unit 1: Introduction and Investment Strategies
Review and Preview Exercises
These exercises are both a review of material you have seen and a preview of the material we will cover in this class. This assignment is to be done individually, but you may discuss this with your classmates. This assignment should be written up and turned in before the Live Session. Don’t lose any sleep over these problems, although some may show up on a future quiz or exam. We will go over these in class.
You are planning on how much you need to save for retirement. You expect to live for 30 years in retirement and would like to spend $100,000 (in real terms) per year, while leaving a $1 million bequest to Georgetown when you die at the end of the 30th year. You are 35 years away from retirement. How much do you need to save at the end of each year if you earn 5% real (after-inflation) during your working years and 3% during your retirement years? Solve the problem in two different ways:
With a financial calculator
On a spreadsheet.
How much do your results change when you change your rate of return assumptions?
Hint: This is a two-step problem. First, calculate the present value of what you need to accumulate on your retirement date (Excel: PV) and then calculate the annual payment needed to get there (Excel: PMT).
Your uncle has saved diligently and is about to retire. He is 70 years old, widowed, and in good health (for now). He has no heirs other than you, but you don’t know whether he will leave anything to you or to some worthy charity. He has $2 million in assets and has just started collecting Social Security. Now that he knows that you studied investments at Georgetown, he is asking you for investment advice.
What do you need to know in order to provide appropriate advice?
How should he invest his portfolio?
How much can he spend each year?
How should he deal with the risk of outliving his assets?
The return last year for a hedge fund before fees was 10%. During the year, 90 day T-bills returned 2% and the overall market returned 8%. The portfolio had a beta of 1.4. Did the hedge fund do a good job? (HINT: Use the CAPM to determine the expected return given the amount of risk taken on.)
Fred is a disciplined day trader who believes in the old adage, “Don’t fight the market.” He feels that when he puts on a trade, if the market does not act as he predicts, then he has made a mistake. He should quickly exit his position to cut his losses. When he purchases a stock, he also puts in a stop loss order as part of his discipline. He has just purchased XYZ at $50, expecting it to rise. At the same time, he puts in a stop loss order at $49.
Under what conditions will the stop loss order be triggered?
What are the risks associated with Fred’s trading strategy?
A “news pending” trading halt occurs in XYZ when the last trade was at $50.03. The company announces a major recall of its main product. When the stock resumes trading, the first trade occurs at $40. What happens to Fred’s stop order?
You need to estimate the value of a company with the following characteristics:
Estimated EPS Next year: $2.50
Estimated EBITDA next year: $100 million
Total debt: $500 million
Excess cash: $100 million
Shares outstanding: 20 million
You have identified the following firms as comparables:
Using the median of the comparables, what is the estimated value per share using the P/E ratio method?
Using the median of the comparables, what is the estimated value per share using the EBITDA multiple method?
What is the price of a 10 year US Treasury STRIP that makes a single payment of $10,000 if the discount rate is 5% effective annual yield? (If you don’t recall what a Treasury STRIP is, check out . Google “US Treasury STRIP” for more details on strips.)
Why would anyone buy one of these?
Academic, Inc., has just issued a traditional 3-year 6% coupon bond that makes coupon payments twice a year at a price of 97. What is the yield to maturity on the bond?
Hint: Bonds are quoted as a percentage of face value. It doesn’t matter whether the face value of the bond is $100, $1000, or $1M – prices are still quoted as a percentage. Thus you do not need to know the par value of the bond, because the price is given as 97. The coupon payments (PMT) will be 3.00. The future value (FV) is just 100, (100% of the face value). If you are using a financial calculator, remember the sign convention that present and future values generally will have opposite signs.
The U.S. Treasury has issued a bond that matures on November 15, 2046. It pays an annual 2.875% interest in two semi-annual installments on February 15 and November 15 of each year. As of Friday, January 6, 2017, a bond dealer was quoting the bond as bid 97.4453 and asked 97.4766. The trade would settle on Monday, January 9, 2017.
a. Based on the ask price, what is the yield to maturity as of January 6, 2017 for a trade settling on January 9, 2017?
Hint: Use the Excel YIELD Function:
b. Based on the ask price and yield, what is the modified duration of the bond?
Hint: Use the MDURATION function in Excel.
c. If the yield increased by 1%, what would be the percentage change in the price of the bond using the basic duration model?
Hint: %change in price ≈ – Duration * Change in interest rates.
Perpetual Growth, Inc., has just paid a dividend of $2.00 per share. You expect the dividend to grow forever at a rate of 4% per year.
If you use a 10% discount rate, what is the value today of Perpetual Growth, Inc.?
Hint: this problem requires the growing perpetuity formula, also known as the constant growth form of the dividend discount model. This formula is a very useful “back-of-the-envelope” way to value predictable cash flows that are growing at a predictably constant rate indefinitely.
The formula is P = D1/(r-g). Google “growing perpetuity” for more details.
How much of the present value of the stock comes from dividends expected to be received within the next 5 years?
How much of the present value of the stock comes from dividends expected to be received within the next 10 years?
The M&M Growth Company has a return on equity of 10% per year, and the market uses a discount rate of 10%. Its earnings per share are expected to be $1.00 over the next year.
If the company has a dividend payout ratio of 50%, what is the sustainable growth rate?
HINT: The sustainable growth rate is the growth rate at which the company can grow using retained earnings without issuing new equity:
g = ROE*(1-dividend payout ratio)
If the company has a dividend payout ratio of 50%, what is the stock price today? [HINT: Use the constant growth form of the dividend discount model to calculate the growth rate of dividends.]
If instead, the company has a dividend payout ratio of 75%, what are the new sustainable growth rate and the new stock price? [HINT: Note that the change in dividend payout ratio also changes the sustainable growth rate that you would use for g in the formula.]
If instead, the company has a dividend payout ratio of 1%, what are the new sustainable growth rate and the new stock price?
You want to buy a house and wish to borrow $300,000.
What would the monthly payment be if the loan requires equal monthly payments for 30 years at an interest rate of 5% APR? Hint: The PMT function in Excel is useful for calculating loan payments.
What would your outstanding loan balance be immediately after you make your first payment?
At 5% APR, what is the present value of only the interest payments on the mortgage? Hint: The easiest way to do this is to create an amortization table that shows the principal and interest payments each month, and then use the NPV function to take the present value of the interest column. Here is what part of the amortization table might look like:
At 5% APR, what is the present value of only the principal payments on the mortgage?
At 5% APR, what is the present value of the interest and principal payments on the mortgage. (Hint: This is the sum of your answers to c and d.)
You expect equities to have a real (after inflation) return of 5% with a standard deviation of 20%, and you expect fixed income securities to have a real return of 2% with a standard deviation of 5%. Assume the correlation of equities and fixed income is 25%.
What is the expected return and risk (standard deviation) of a portfolio that is 60% equity and 40% fixed income?
Suppose that you can tolerate a maximum risk of 10%. What portfolio will provide that level of risk? What is its expected return?
Hints: The expected return of the portfolio is just the weighted average of the expected returns of the various assets.
The variance of the portfolio is just:
σ2 = w12 σ12 +w22σ22 + 2 w1w2σ1σ2ρ
where
wi = weight on asset i
σi = standard deviation of the expected return of asset i
ρ = correction between assets 1 and 2
If you have more than two risky assets, the variance of the portfolio is:
σ2 = wΣwT
where w = the vector of weights on the individual assets in the portfolio, Σ is the covariance matrix, and wT is the transpose of the weights on the individual assets. In order to do this in Excel, you should use the MMULT function for matrix multiplication.
Another hint: Use Solver in Excel. Solver can be found on the Data tab in the Excel ribbon. However, it is not normally loaded in the default installation. You may have to go to File then Options then Add-Ins to load Solver, which comes with Excel.
Track questions:
This hypothetical is for both tracks:
Your fax number is one digit different from that of a well-known investment bank. You receive a fax by mistake discussing the terms of a previously secret merger announcement between two public companies. It appears that the merger will be announced next Monday afternoon. It is likely that the stock of the target company will jump substantially when the news is announced.
U.S. law on insider trading is quite vague. (For an optional overview, you can check out Seitzinger, Michael V., Federal Securities Law: Insider Trading, Congressional Research Service, 2016 )
For the Institutional Asset Management Track:
You are employed in the research group of a hedge fund that often speculates on possible forthcoming mergers. Part of your job is to identify possible takeover candidates. Under the CFA Institute’s Standards of Professional Conduct Standard II-A, what is your responsibility? The Standards of Professional Conduct can be found at
For the Private Wealth Management Track:
You are employed in the Private Wealth Management group of a large prestigious institution and you are responsible for selecting investments for your clients. Under the CFP Code of Ethics and Standards of Professional Conduct, what is your responsibility? They can be found at
More hints for preview exercises
Many of these problems can be solved quickly using a financial calculator (or financial calculator smartphone app) or the financial functions in Excel. On a financial calculator, there are five time value of money keys:
N: Number of payments (e.g. 360 for a 30 year mortgage).
I/YR: Interest rate per year (APR on a loan)
PV: Present value. The present value today of a future payment or series of payments. The amount borrowed or the price today
PMT: The periodic payment made
FV: Future value, or amount left over at the end.
If you enter any four of these keys, the calculator figures out the fifth. Just make sure that you have the number of payments per year set properly, and that you specify whether payments are at the beginning or end of the period. Details vary across brands of calculators.
Useful Excel Functions:
NPER: Calculates how many payments need to be made
RATE: Calculates the interest rate implied in a series of payments.
PV: The present value today of a future payment or series of payments.
PMT: The periodic payment that needs to be made to achieve a given PV or FV
FV: The future value of a present value and a series of payments
PRICE Bond price
YIELD Yield to maturity on a bond.
MDURATION: Modified duration of a bond
Note that the calculators and spreadsheets have an arbitrary sign convention that generally assigns positive signs to cash inflows and negative signs to cash outflows. Thus, if you go to calculate a loan payment with the PMT function, and you input a positive number for the loan amount (PV), then it will return a negative sign with the payment amount.
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