Econ 156
Fall 2002

Final Exam Answers

1. The real value is equal to the nominal value divided by the price level.

2. Remember that the market will set prices so that someone is willing to hold these bonds.

3. If the returns on Portfolios 1 and 3 are perfectly positively correlated, the opportunity locus between the two portfolios would be straight line. One point on the line would be halfway between these two portfolios with an expected return of 10% and a standard deviation of 13%. This is to the left of Portfolio 2–the same expected return with a lower standard deviation! If the returns from Portfolios 1 and 3 are not perfectly positively correlated, then the opportunity locus is curved to the left. Thus Portfolio 2 cannot be on the Markowitz frontier:

4. Here are the calculations:

The price-earnings ratios are higher for the low-yield, high-growth stocks than for the high-yield, low-growth stock because the high profit rates fuel high growth rates, which require high prices to keep the return at 15%. All three stocks are priced to give shareholders a 15% return.

5. They will lose money if interest rates go up.

6. The present values should be in the same year:

7. Figlewski is describing the no-arbitrage equilibrium in the textbook’s Equation 5, which is based on a stock index’s cost of carry–the lost interest minus the dividend yield. In the numerical example, ownership of the stocks in the index costs 10% in lost interest, but earns 4% in dividends, a net cost of 6%. Therefore, if the index is at 100, the futures contract (which postpones the payment of cash for the index stocks) is worth 106. If the futures price is below 106, say at 104, a pension fund owning the stocks in the index could increase its profits by selling the stocks in the index and buying index futures. The 100 it receives for selling these stocks can be invested to earn 10; at the futures expiration date with the index at P, it makes a profit of P-104, for a total profit of 10 + P - 104 = P - 94. If the pension fund held on to the stock, it receives dividends of 4 plus capital gains of P-100, for a total profit of 4 + P - 100 = P - 96, 2 less than with the arbitrage strategy.

Here is another way to think of it. If the pension fund held on to the stock, it receives dividends of 4. If it sells the stocks for 100, the 100 it receives can be invested in T-bills to earn 10; at the futures expiration date, the fund is implicitly able to buy back the stocks at 104, a loss of 4. Its net profit 10 - 4 = 6 is 2 more than the dividends of 4 it would have received by holding onto the stocks.

8. If the investor were confident that the market were going to increase, a high-beta portfolio would be appropriate. High R-squared would also be nice, since the investor could then be confident that firm-specific risk has been diversified away, but a high beta is paramount. A high R-squared with a low or negative beta would be exactly the wrong portfolio.

9. Total earnings will be n1*E1 + n2*E2, total shares will be n1 + 2*n2. Earnings per share will increase iff (n1*E1 + n2*E2)/(n1 + 2*n2) > E1 or (n1*E1 + n2*E2) > (n1 + 2*n2)E1 implies E2 > 2*E1, since this is the necessary and sufficient conditions for P1/E1 > P2/E2

10. This analysis ignores these important points: the $100,000 down payment has an opportunity cost; the monthly mortgage payments include principal as well as interest; the mortgage payments will stop after 30 years, but the rent will not; and the rent and some expenses will grow over time.

11. The appropriate leverage estimate is the ratio of the firm’s assets to its net worth.

12. The 2-year zero does best. Let all the current prices be $1, so that the maturation value of the 1-year zero is 1.04, the maturation value of the 2-year zero is 1.07², and the maturation value of the 3-year zero is 1.08³. One year from now,

13. In deciding between investing in a project or corporate bonds, the appropriate real required return for the project depends on the real rates of return available now on corporate bonds, not some average of past returns.

14. Mean-variance analysis doesn’t assume efficient stock markets. It can be used during bubbles and busts, with investors setting the values of mean, standard deviations, and correlation coefficients to reflect beliefs.

15. This is very similar to home mortgages from a savings and loan association.

a. They prepaid early because they could borrow elsewhere at lower interest rates.

b. These prepayments reduced the Export-Import Bank’s cash-flow deficit because it brought in more cash, ignoring the fact that it also diminished future cash flow.

c. Since these were presumably high-interest loans, the Export-Import Bank was made worse off by their prepayment.

16. Here is the profit picture (as a function of the stock price at expiration) for this butterfly strategy:

17. For a horizon of one-year, the purchase of a one-year T-bill is a perfectly safe investment, with a rate of return equal to the current rate of return on a one-year T-bill.

18. The IRR is that discount rate for which the NPV = 0; it is not necessarily true that the NPV is positive if the required rate of return R is less than the IRR. Consider, for example, a project (like the classroom discussion of the Dallas Cowboys’ sale of luxury boxes) that pays $1,000,000 immediately and costs $100,000 every year thereafter. The IRR is 10%, but the NPV is negative for R less than 10%; the future expenses are less burdensome with high interest rates.

19. Remember that Tobin’s q is the market value divided by replacement cost.

20. The efficient market theory says that stocks do unusually well or poorly because of unpredictable events. Unless GE stock were especially risky, there is no logical reason why it would be priced in an efficient market to consistently give a higher return than the average stock.