The following table provides information on two risky stocks that you think, given some special information, are good investments.
Stock Expected Return Standard Deviation
A .15 .23
B .20 .18
The Covariance between these two stocks is -.001. The expected return on the market is .15 with a standard deviation of .15. The risk free rate is .03. You can borrow and lend at this risk free rate.
You have $1,000,000 to invest. Some of this you may put in risk free T-bills (with a return of 3%), with the remainder invested in a portfolio of the two stocks above. Consider a portfolio that has 50 percent of the amount you put at risk in Stock A, and 50 percent in Stock B. Call the portfolio that consists of Stock A and Stock B your risky portfolio. For this risky portfolio, answer the following questions.
a) What is the expected return for this risky portfolio?
b) What is the standard deviation of the return on this risky portfolio?
c) What is the Sharpe Ratio for this risky portfolio? Show your work below.
d) You have a choice between forming a total portfolio of risk free investments and either the risky portfolio above or the risky market portfolio. Which of the following risky portfolios would you prefer to hold in your total portfolio: (1) the above 50%/50% portfolio with Stock A and Stock B or (2) the market portfolio? Explain why.
You have estimated a market model (a regression of the return on each individual security excess of the risk free rate on the return on the market in excess of the risk free rate) and you have obtained the following estimates of the market betas of each of the above securities.
Stock Market Beta
A .8
B 1.2
According to CAPM, what should the expected returns on each of the two stocks equal?
Stock Expected Return (according to CAPM)
A
B
Does this explain why you prefer the portfolio you identified in b above? Why or why not?
2. Now is t = 0. What is the current (i.e., t = 0) value of a bond that pays $100 every year for 8 years, with the first payment at t = 5 (i.e., five years from now)? The effective annual discount rate is .10.
The stated annual interest rate is 10 percent. If interest is compounded semi-annually (i.e., twice a year), what is the periodic rate for 6 months? What is the effective annual rate?
Periodic 6-month rate =
Effective annual rate =
What is the current (i.e., t = 0) value of a bond that pays $200 every year for 5 years with the first payment being made at t = 1 (i.e., one year from now) if the stated annual interest rate is 10 percent, compounded semi-annually (i.e., twice a year)?
The effective annual interest rate is 12 percent. What is the effective six-month rate? That is, what effective rate over six months is such that if you were to get that rate over two six-month periods (i.e., a year) you would get a return of 12 percent?
Effective 6-month rate =
What is the current (i.e., t = 0) value of a bond that pays $100 every six months for 5 years (for a total of 10 payments) with the first payment occurring exactly six months from now if the effective annual discount rate is 10 percent?
3. Below is a set of current (t = 0) prices on a set of zero-coupon bonds. The face value on all of these bonds is $1000. The prices below are quoted per $1000 in face value. In answering the following questions, assume that you can buy fractions of a bond.
Bond Price
1-year zero 950
2-year zero 900
3-year zero 860
4-year zero 790
Also assume, for simplicity, that each of these bonds matures in exactly a multiple of a year from now (now = t = 0)
1. If you invested in a two-year bond and rolled over into a one-year bond at t = 2, what would the one-year yield at t = 2 have to be in order for you to be indifferent between that strategy and investing in the three-year bond at t = 0?
For the next set of questions, consider the following: You have $20,000 and want to make an investment that will allow you to have a down payment on a house in exactly two years. Consider the following two alternative strategies:
a. You can invest in the default-free 3-year zero-coupon bond and sell it after two years (t = 2).
b. You can invest in the default-free 2-year zero-coupon bond.
2. Consider the first strategy (i.e., strategy a) above.
a. If the forward rates implied by the bond price data above turns out to be the future rates that actually occur, what price (per $1000 in face value) will you get at t = 2 for the 3-year bonds you are buying at t = 0? That is, what is the price of these 3-year bonds in two years (at t = 2) from now (t = 0)?
b. If the forward rates implied by the bond price data above turns out to be the future rates that actually occur, what will be your holding period yield on the 3-year bond you are buying at t = 0? That is, what is the internal rate of return on the first strategy (i.e., strategy a.)?
c. If the forward rates implied by the bond price data above turns out to be the future rates that actually occur, how much money will you have at t = 2 under this first strategy (i.e., strategy a.)?
d. If it turns out that the one-year yield at t = 2 is 1 percentage point higher than the forward rate implied by the bond price date now (at t = 0), how much money will you have at t = 0 to use as a down payment?
e. If it turns out that the one-year yield at t = 2 is 1 percentage point lowerthan the forward rate implied by the bond price date now (at t = 0), how much money will you have at t = 2 to use as a down payment?
3. Now consider the second strategy (simply invest in the two-year zero coupon bond). How much money will you have at t = 2 to use a down payment? Does you answer depend upon what the one-year yields turn out to be at t = 2? Why or why not.
4. You currently work for a firm that has investment capital per share equal to $100. This firm currently enjoys an annual return on capital of 12 percent. The cash flows generated by this capital occur at the end of the year (or the beginning of the next year) and are risky. In fact, the beta of the cash flow is .9. The expected excess return on the market (i.e., E(RM) - RF) is 8 percent (i.e., E(RM) - RF = .08). The risk free rate is 4 percent (i.e., RF = .04).
Your firm currently has a policy of paying all cash flows out as a dividend. That is, its payout ratio is 100 percent (or equivalently, the plowback ratio is zero).
a. Given the current payout policy, what are the earnings per share for your firm?
b. What discount rate will the market apply to your cash flows if CAPM holds? (Note: The rest of the problem relies on the answer you get for this question. If you answer this question incorrectly but use this incorrect answer correctly in all subsequent questions, you will only be penalized on this question. If you are unable to get an answer for this question, make an assumption (e.g., r = .1) and use that in the subsequent questions.)
c. Given the kind of business your firm is in, you can expand and not have an appreciable change in your return on investment. If you retain 50 percent of earnings each year (and pay out the other 50 percent as a dividend) and grow the company, what will the new value of your firm be?
d. Under the 50 percent plowback policy, what is the present value of growth opportunities for your firm? That is, what is the difference between the price under the 50 percent payout rule versus the no growth price (with a 100 percent payout rule)?
5. Which of the following facts is/are inconsistent with CAPM but consistent with the weak form of the Efficient Market Hypothesis?
a. The strategy that buys securities with betas greater than 1.5 earns higher returns than the market on average.
b. Every time the market drops more than 3 percent in one day, the next day the return on a positive beta security is positive on average.
c. Every time the market drops more than 3 percent in one day, the next day the excess return on a positive beta security is negative on average.
d. Although there is no correlation between a securities idiosyncratic volatility and its beta (systematic risk), those securities with high idiosyncratic volatility have higher returns on average than those with low idiosyncratic volatility.
e. a. and b.
Which of the following is/are inconsistent with the weak form of market efficiency?
a. On average, when a firm announces a takeover, the stock price of the target firm jumps up on the announcement.
b. On average, when a firm announces a takeover, the stock price of the bidding firm falls on the announcement.
c. On average, when a firm announces it will raise its dividend, the stock price rises on the announcement.
d. On average, when a firm announces it will raise its dividend at the market open, the return from the close of the market that day to the close of the market the following day exceeds that predicted by CAPM.
e. None of the above.
6. You have an idea for a project. You have performed some analysis and predict that your project will generate the following average cash flows. It will cost you $1,000,000 in investment at t = 0. At t = 1 you will have to spend an additional $120,000. At t = 2 you will have a positive cash flow of $100,000. Thereafter, the expected cash flows will grow at a 3 percent rate every year forever.
These cash flows are risky and have the same risk as the types of projects that XZX Co. has. You have collected the following data on XZX Co. XZX Co. will pay a dividend only once a year. The next dividend is expected to be $2 per share and is expected to grow at 2 percent every year forever. The current price of XZX Co. is $25.
1. Given that investors who might invest in your project have the opportunity to invest in XZX Co., what is the opportunity cost of capital for you project?
2. Should you adopt your project?