Econ 156
Gary Smith
Fall 2009

Final Examination (150 minutes)

No calculators allowed; if calculations are needed, write the explicit equation(s). Do not write “Y = aX; solve for X.” You can write “100 = 10X; solve for X.” The price of extra time is 1 point/minute; e.g., if your test is handed in 5 minutes after the scheduled finish time, 5 points will be subtracted from your test score.

1

In 2008 an Englishman received £200 from an Australian tourist who had borrowed £5 from him 40 years earlier. The Australian figured that £200 was £5 for each year that had gone by since he borrowed £5. If the Englishman had made a £5 investment 40 years ago that was now worth £200, what was the rate of return?
   
2
 In the early 1980s, a tax lawyer gave a speech at Pomona College in which he stated that most leveraged buyouts were motivated by tax considerations. Suppose that Company 1 initially has $1 billion in assets and no debt and then borrows $500 million in order to acquire Company 2, which has $500 million in assets and no debt.
  a. What is Company 1’s new leverage ratio?
  b. Why might this leveraged buyout be motivated by tax considerations?
   
3
 After the U.S. stock market fell more than 50% between October 2008 and March 2009, Mr. Jones told his investment manager to sell all his stocks and then to get back into the stock market after the economic recession had ended. What flaw do you see in this strategy?
   
4

In December 2008, Henry Blodget wrote this

Consider, for instance, the late 1950s, when a tried-and-true ‘sell signal’ started flashing on Wall Street. For the first time in years, stock prices had risen so high that the dividend yield on stocks had fallen below the coupon yield on bonds. To anyone who had been around for a while, this seemed ridiculous: stocks are riskier than bonds, so a rational buyer must be paid more to own them. Wise, experienced investors sold their stocks and waited for the obvious mispricing to correct itself. They’re still waiting.
  a. What does Blodget mean by “a rational buyer must be paid more to own them”?
  b. What rational reason is there for an investor to believe that he will get a better long-run return from stocks than from bonds if the dividend yield is less than the coupon yield?
c. What does Blodget mean by “They’re still waiting”?
   
5
 The prime rate is generally above the Treasury-bill rate. Why? If a U.S. corporation borrows from a bank at a floating interest rate that is linked to the prime rate and then swaps this loan for one indexed to the Treasury-bill rate, is this an implicit wager that the spread between prime rate and the Treasury-bill rate will widen or narrow?
   
6
 Bernie Madoff told investors he was earning 15% a year, year after year, using a “split-strike conversion” strategy which involves the purchase of stock and the simultaneous purchase of out-of-the-money put options and the sale of out-of-the-money call options. He used the S&P 100 index, but we can illustrate with Apple stock. On November 27, 2009, Apple stock closed at 200.59, while January 16, 2010 put options with an exercise price of 190 closed at 5.20 and January 16, 2010 call options with an exercise price of 210 closed at 5.90. Draw the profit picture for a split-strike conversion strategy as a function of the price of Apple stock on January 16, 2010.
   
7
 A study by Margaret Hwang, Keil, and Smith found that stocks with the most optimistic earnings forecasts generally underperform those with the most pessimistic forecasts. How would you explain this finding?
   
8
 ABC has 200 million shares outstanding with a current market price of $10 per share; XYZ has 100 million shares outstanding with a current market price of $8 per share. ABC offers to acquire XYZ by giving all XYZ shareholders 1 share of newly issued ABC stock for each share of XYZ stock they hold. After the announcement of this offer, ABC’s stock price falls to $9.50 and XYZ’s stock price rises to $9.00. Suppose that an arbitrager buys 100,000 shares of XYZ at $9.00 and sells 100,000 shares of ABC stock short at $9.50. (Neglect taxes, interest, and commissions.)
a. What will the arbitrager’s profit be if the merger goes through as planned?
b. If the Conservation of Value applies, what would the price of ABC stock have been if the merger had happened immediately after it had been announced?
   
9
 Consider these three S&P 500 contracts, all with the same expiration date: a futures contract with a price F, a call option with a price Pc and an exercise price E, and a put option with a price Pp and an exercise price E.
a. Use these three contracts to construct a perfect hedge that had a fixed payoff on the expiration date, no matter what the value of the S&P 500 on that date.
b. How exactly should F be related to E, Pc, and Pp in an efficient market?
   
10

Shown below are 5 assets, the Markowitz Frontier, and CAPM’s Market portfolio. Among Assets 2, 3, and 4, which asset has the highest beta coefficient and which has the lowest beta coefficient? Explain your reasoning.
   
11
 In November of 1996, The Wall Street Journal reported that the Strong Discovery Fund “was undone by a late 1995 bet that the U.S. economy was sliding into recession and ... moved 40% of the aggressive-growth fund’s assets into long-term zero-coupon Treasury bonds and watched those highly volatile instruments get creamed when the economy … perked up.”
a. Why are these Treasury bonds so volatile?
b. Why did a perky economy cream this investment?
   
12 “Target-payout funds” are investment companies that guarantee that the annual distribution to the fund’s shareholders will exceed a specified minimum amount, for example 7 percent of assets. If the dividends and realized capital gains on the investment company’s portfolio are less than this minimum amount, the company sells some of its portfolio in order to make the target payout. A 1992 Shearson Lehman report called the yields for target-payout funds “illusionary” and “artificially high.”
Use a numerical example to explain why a 7 percent target payout does not guarantee that the fund’s investors will get at least a 7 percent return on their investment.
   
13

Answer this question: “I’m 66 and recently retired, with $300,000 in a 401(k) plus a military pension of $3,000 a month. My wife, 48, earns $87,000 a year. Should I take the $24,000 in my company pension fund as a lump sum and roll it into an IRA or my 401(k), or take an annuity of $122 a month until my death, then for the rest of my wife’s life?”

T.M., Waldorf, MD
   
14

Shown below is a graph of R-squared for the equation B = a + bS + e, where B is the monthly return for the Lehman Aggregate Bond Index and S is the monthly return for the S&P500.
  a. Provide a logical explanation for the empirical fact that R-squared is sometimes near 0% and sometimes near 40%.
  b. When R-squared is 0.36, do you think that R is equal to +0.6 or -0.6?
c. This figure was used to support an argument for either: (a) adding bonds to a stock portfolio, or (b) excluding bonds from a stock portfolio. Which and why?
   
15 For each of the following pairs, identify the asset with the longer duration: (Assume that each is priced to give a 10% required return)
  a. a stock with a dividend that will always equal $1 or a stock with a dividend that is currently $1 and will grow by 5% a year.
  b. a stock with a dividend that is currently $2 and will grow by 3% a year or a stock with a dividend that is currently $1 and will grow by 5% a year.
c. a consol bond with a $10 quarterly coupon a no-growth stock that will pay a $5 quarterly dividend forever.
   
16 In 1996 Morningstar, an independent mutual fund rating service, began rating mutual funds on their annual performance, even though in 1995 Morningstar’s president said that was “the dumbest thing imaginable.” What do you suppose he meant by this?
   
17

Here the current interest rates on Treasury zeros. According to the Expectations Hypothesis, what is the market’s anticipated interest rate on 5-year Treasury zeros 3 years from now (at the time of the next Presidential election)?

Maturity (years)
 
Yield (%)
1
  
0.21
2
  
0.42
3
  
1.17
4
  
1.63
5
  
2.12
6
  
2.52
7
  
2.84
8
  
3.13
9
  
3.35
10
  
3.66
   
18 Mr. Jones is a new investment manager who wants to use modern portfolio theory to manage his clients’ money. He is starting with three asset classes (1-year Treasury bills, 20-year Treasury zeros, and a Vanguard stock index fund) and wants to identify the Markowitz frontier for a 1-year investment horizon. He collected annual data over the past 20 years on the interest rate B on 1-year Treasury bills, the interest rate Z on 20-year Treasury zeros, and the annual price change S in the S&P 500. He then calculated the historical means, standard deviations, and correlations as a staring point, to be adjusted based on current market conditions. Explains his mistakes:
  a. He estimated the mean stock return from the average value of S.
  b. He estimated the correlation between Treasury-zeros and stocks from the correlation between Z and S.
c. He estimated the Treasury-bill standard deviation from the standard deviation of B.
   
19 “Once again [the Olsons] crunched a few numbers. This time they decided to rent—and they're saving a bundle. For $2,350 a month, they have a four-bedroom, 2,100-square-foot home. If they were to purchase that same home today for $700,000 (the going rate for a similar home in the neighborhood), the monthly payment on a 30-year, $630,000 mortgage at 6.1% would run them more than $3,800.” What numbers would you crunch?
   
20 What is the value of Tobin’s q for an open-end mutual fund?