Econ 156
Fall 2002

Final Exam (150 minutes)
Answer all 20 questions, leaving tedious calculations undone. The test ends promptly at 4:30.

1. When a child loses a baby tooth, an old U.S. tradition is for the tooth to be put under the child’s pillow, so that the tooth fairy will leave money for it. A survey by a Northwestern University professor indicates that the tooth fairy paid an average of 12 cents for a tooth in 1900 and $1 for a tooth in 1987. The consumer price index was 25 in 1900 and 340 in 1987.

2. In November 1988, 2-year Treasury zeros had 8 1/2 percent interest rates while 30-year Treasury zeros had 9 percent interest rates. An article in The Wall Street Journal began: “Why would anyone buy 30-year Treasury bonds right now when they can earn nearly the same returns on short-term issues that aren’t as susceptible to price decline?”

3. A computer program identified these three portfolios as being on the Markowitz frontier. Carefully explain why there must be an error in this program.

4. A 1985 article on John Neff, a highly respected managing partner of Wellington Management Company, gives this example of market irrationality:

Neff cites the example of two companies, one expected to grow at 8 percent and the other expected to grow at 15 percent. Both have the same total return–because an 8 percent grower typically pays a [dividend] yield of 7 percent while the 15 percent grower pays little or no yield. Yet the fast grower usually sells at a much higher [price-earnings] multiple. “Now does that make sense?” asks Neff with exasperation. “The market gives away yield. It’s just damn stupid.”

To investigate the rationality of such data, consider these 3 hypothetical companies:

For each firm, assume a 15 percent required return and use the constant-growth model to determine the plowback rate, growth rate, price, dividend yield, and price/earnings ratio. What are the shareholder rates of return for these three companies?

5. Many savings and loan associations have short-term deposits and long-term mortgages. Will their net worth (the market value of their assets minus the market value of their liabilities) decline if interest rates go up or if they go down? Explain which of the following actions are appropriate and which are inappropriate if they want to reduce the extent to which their net worth is affected by unexpected changes in interest rates:

6. Mr. Smith is currently 55 years old. The Social Security Administration estimates that Mr. Smith will receive $1,791 in monthly Social Security benefits if he begins collecting benefits at age 66 and $2,407 in monthly benefits if he begins collecting benefits at age 70. (Each of these estimates is in 2000 dollars; Social Security benefits are fully indexed for inflation. Either way, he will continue working and this will not reduce his benefits.) Identify the biggest error in this answer to the question of whether Mr. Smith should begin receiving Social Security benefits at age 66 or 70:

Suppose Mr. Smith lives to age n. He should choose 66 or 70, depending on which of these present values is larger, where R is his monthly real required rate of return:

7. In November 1984, Professor Stephen Figlewski was quoted in the New York Times as saying that stock index futures are so new and complex that the market is not yet dominated by arbitragers and other professionals, and is consequently not yet efficient:

Clearly explain the logic behind the professor’s formula. If, in the example, the index future were selling for 104, how could you make a safe profit by taking advantage of this mispricing?

8. Explain why you either agree or disagree with this CAPM advice: “If the market was expected to rise, an investor should increase the R-square of the portfolio. If the market was expected to decline, a portfolio with a low R-square would be appropriate.”

9. Firm ABC has n1 shares outstanding, a market price per share of $10, and earnings per share E1. Firm XYZ has n2 shares outstanding, a market price per share of $20, and earnings per share E2. The firms will merge with firm ABC giving each XYZ shareholder two shares of newly issued ABC stock for each share of XYZ stock they owned. For example, a person who holds 1000 shares of XZY will receive 2000 newly issued shares of ABC, and the XYZ stock will disappear. If the combined earnings of the merged company are equal to the sum of the earnings of the separate companies, show the necessary and sufficient condition for ABC’s earnings per share to increase.

10. A new faculty member has to decide whether to rent or buy a house to live in. This professor expects to live in the house for the rest of her life. The monthly rent is $3,000 and includes heat, electricity, and all utilities. The house costs $400,000 and: (a) with a $100,000 down payment, the monthly mortgage payments are $2201.29 on a 30-year 8% mortgage; (b) the monthly taxes, insurance, utilities, and maintenance are $1,000. Thus she is better off renting. Identify two extremely important errors in this analysis (other than ignoring the tax deductibility of certain expenses).

11. “Insurance companies tend to be leveraged at between 10 and 20 to 1 for life companies and 4 or 5 to 1 for casualty companies.” If you were assigned to estimate the leverage ratio for a company, which of these data would you use and how: sales, before-tax profits, after-tax profits, assets, liabilities, net worth, or stock price?

12. The Fama bond strategy is based on the assumption that the implicit forward rates embedded in the term structure are worthless as predictors of future interest rates. Instead the best predictor of future interest rates is current interest rates. Here are the current interest rates on 1, 2, 3 year zeros: 4%, 7%, 8%. If the interest rates one year from now on 1, 2, and 3 year zeros are 4%, 7%, 8%, which investment will be more profitable for the coming year; the purchase of a 1, 2, or 3 year zero?

13. A professor noted that businesses are advised to gauge projects by discounting the dollar cash flow by nominal interest rates or, equivalently, by discounting the real cash flow by real interest rates. He argued that the latter course simplifies matters because real cash flow are easier to forecast than nominal flows (which depend on unknown rates of inflation) and real interest rates are approximately equal to zero. As evidence, he cited the fact that during the years 1948—1978, the average value of the long-term AAA corporate bond rate was approximately equal to the average value of the annual rate of inflation. Why might you, as your business’s chief financial officer, hesitate to follow the professor’s advice?

14. Explain why you either agree or disagree: “Mean-variance analysis is fine on paper, but it assumes an efficient stock market and there is plenty of evidence of bubbles and busts that cause stock prices to be irrationally high or low.”

15. The federal government’s budget is calculated on a cash flow basis. In 1987, several borrowers prepaid their loans from the federal Export-Import Bank, reducing the Bank’s 1987 budget deficit by $1.5 billion.

16. Show the profit picture (as a function of the stock price at expiration) for this butterfly strategy: simultaneously buy one call option with an exercise price of $100, sell two calls with an exercise price of $110, and buy one call with an exercise price of $120.

17. Mean-variance analysis was recently used to assess the opportunities available for investors dividing all of their wealth among these three asset classes: 1-year T-bills, 20-year Treasury zeros, and an S&P 500 index fund. The analyst assumed that the investments will be made for one year with no adjustment during the year. Explain the major conceptual error in this argument: “We should not assume that T-bills are safe, since their returns vary from year to year. From 1962—2001, the return on 1-year T-bills had a mean of 6.2% and a standard deviation of 2.4%.”

18. Explain why you either agree or disagree: “This project’s internal rate of return (IRR) is 10%; this means that its NPV is positive if the required rate of return is less than 10%.”

19. A certain closed-end mutual fund began by issuing 1 million shares at a price of $10 each, using the $10 million raised to purchase securities. The value of the securities owned by this fund have risen to $15 million, giving a net asset value of $15 per share, while the fund’s shares trade on the New York Stock Exchange at only $12 a share.

20. In December 2001, GE Chairman Jeff Immelt told a group of Wall Street analysts that, “We give investors a chance to sleep at night knowing that you’re going to get consistency and visibility and, over every economic cycle, performance that surpasses the S&P 500.” [Melanie Warner, “Can GE light Up the Market Again?,” Fortune, November 11, 2002, p. 110.] What would an efficient-market believer say about Immelt’s prediction that GE stock will always surpass the S&P 500?