Under each, Yahoo has a significant amount of information, available by clicking in the various tabs shown in the left-hand margin. For example, you can look up the beta of a security by clicking on "Key Statistics" for that security. The Beta is listed at the top of the "Trading Information" box, under "Stock Price History" off to the right-hand side of the page that appears once you click on "Key Statistics."
Write down the betas for the securities listed above. Do the sizes of these betas make sense to you knowing what you know about each of these companies?
Problem 2:
You have an idea for a new product that will generate future cash flows that are correlated with general market conditions (i.e., when the economy is doing well, the cash flows will be usually higher than average and when the economy is slumping, the cash flows will usually be below average). In particular, you have estimated that the correlation in the cash flow returns from your new product and the return on the market is .75. You have also estimated that the standard deviation of the return on your new product is .15 (15%). The current estimate of the standard deviation of market returns is .20 (20%). The risk-free rate is .02. You have also estimated that after the first year, your new product will produce $150,000 in cash flow (at the end of the year) on average; beyond that, you expect that the average cash flow will grow 3% per year indefinitely.
1. Based on a market risk premium of .07 (7%) and the data above, what is the present value of the expected stream of future cash flows from your new product. First calculate the beta of the new project and the required rate of return given that beta. Using the present value of a growing perpetuity formula, calculate the present value of the stream of growing cash flows.
2. If it costs $4,000,000 to develop and implement this new product, do you want to go forward and spend the $4,000,000?
3. Sensitivity Analysis: Do you want to go forward if the growth rate in the average cash flow is only .01 (1%)? What if the market risk premium is only .06 (6%)?
Problem 3:
Consider the following information on three securities.
Security E(return) Variance () Beta ()
A.1135 .04841.15
B.05.0625 .25
C.0775.0225.75
Correlations (e.g., the entry in the B row and C column is the correlation coefficient between B and C).
ABC
A1.00.169.847
B.1691.00.162
C.847.1621.00
A fourth security is risk-free Treasury STRIPS (i.e., zero coupon bonds) that mature in exactly one year with an effective annualized yield of 1%. The return on a board-based portfolio (i.e., the market) is expected to be .10 (10%) over the next year; its standard deviation is .18 (18%).
Questions:
1. Based on the information provided above, what should be the expected returns for A, B, and C according to CAPM? If you believe CAPM is correct, which securities do you want to favor and which securities do you want to shy away from?
2. If you form a portfolio using $10,000 invested in A and $10,000 invested in B (i.e., a portfolio with 50% in A and 50% in B), what is the expected return on that portfolio given the data above? What is the beta of that portfolio? Using the beta of the portfolio, what does CAPM imply the expected return on the portfolio should be? How does that compare to that predicted by the data above?
3. What portfolio of A and B will give you a portfolio that has the same beta as security C? That is, solve for the weight on A (denoted wA) and (1-wA) on B such that the portfolio beta is .75. What is the expected return on this portfolio using the data in the table above? How does that compare to the expected return for security C shown in the table? If they are different, you should short the one with the low expected return (by shorting you are borrowing at this low expected rate) and use the proceeds to buy (i.e., invest in) the one with the high expected return. By doing so, you earn the spread between the two rates, without having to invest any of your own money.
4. Consider what happens to prices and returns if you (and a bunch of other people) execute the strategy you identified above. Given the pressure on prices given the above trades, will the expected returns on the various securities move in a direction that makes them more consistent with CAPM or less consistent with CAPM?
5. To think about: Notice that Security B has a low beta but a high variance. What does this imply with respect to the amount of idiosyncratic volatility B has? (Hint: Recall that the beta measures the slope of the relationship between the return on B and the return on the market. B's systematic volatility is the amount of variation in B's return that is due to variation in the market return. In fact, mathematically, the amount of variance in B's return due to the variation in the market return is , where is the beta of B and is the variance of the market. The difference between this measure of systematic variance and the total variance of the return on B (in the above data, that total variance is .0625) is the variance that is due to "idiosyncratic" variation. What is the amount of idiosyncratic variation in B's returns?) What is the amount of idiosyncratic variance in A and C? According to the table of correlation coefficients, B has relatively low correlation with both A and C, but A and C are fairly highly correlated. Does the amount of idiosyncratic variance in B relative to that in A and C explain the magnitudes of the differences in correlations between the 3 securities?