1. Babe Ruth was paid $80,000 in 1931; Chili Davis will be paid $1.75 million in 1993. The consumer price index was 15.2 in 1931 and will be about 147 in 1993. Which of these two salaries is higher in real terms? What would Davis' 1993 salary be if he were paid an amount with the same purchasing power as Ruth's 1931 salary?

2. A store advertises that if a customer borrows money to buy a major appliance, no interest is charged for 6 months and no payments are due for 6 months. What is the effective interest rate if $1,000 is borrowed and, after the initial 6-month grace period, 18% annual interest is charged and the loan is paid off in 24 equal monthly installments?

3. A "seven-and-seven loan" has an interest rate that is 7 percentage points over the prime rate and initial fees that are equal to 7% of the size of the loan. If the prime rate is 10%, what is the effective interest rate on a seven-and-seven 10-year loan with amortized monthly payments? Explain why the effective interest rate would be higher or lower if this were a 5-year loan.

4. A certain bond pays $1,100 one year from now and $1,331 three years from now. At a 10% yield to maturity, the price is $2,000 and the duration is 2 years. Without doing any calculations, if, in addition to $1,100 one year from now and $1,331 three years from now, this bond pays $1,100 two years from now, will the price be higher or lower? Will the duration be higher or lower?

5. A home buyer will obtain a $150,000 conventional amortized mortgage at 9%, and must choose between a 15-year and 30-year mortgage. Without doing any calculations,

   a. Which loan has the higher monthly payments?

   b. Which loan has the higher unpaid balance after 1 year?

   c. Which loan has the higher total payments?

   d. If the mortgage is paid off after 5 years, which loan's stream of payments (including the unpaid balance after 5 years) has the higher present value at a 9% required return?

6. Of the thousands of securities that exist, here are the expected returns and standard deviations for two securities:

7. A June 1992 article in The Wall Street Journal began,

At first glance, “premium bonds” may sound like a mad investment scheme straight out of a Marx Brothers movie: The investor pays even more for a bond than its face value.

8. Explain the logic behind Louis Rukeyser's observation that, "Almost invariably, the higher the yield [the ratio of a stock's dividend to its price] the lower the growth [of dividends]."

9. A 1989 newspaper article about the stock market was titled, "Even the Experts Disagree on the Market's Direction." How can the stock market be efficient if even the experts can't agree on whether stock prices are going higher or lower?

10. Here is an international bank's balance sheet, with all assets and liabilities valued in U.S. dollars:

   a. Will this bank's net worth increase or decrease if the dollar and the mark both appreciate by 50% relative to the pound?

   b. To reduce the exposure of its net worth to fluctuations in the value of the mark relative to the pound and the dollar, should this bank swap some of its mark-denominated liabilities for pound-denominated liabilities, or vice versa?

11. The table below shows a bank's balance sheet with all entries in millions of dollars and the parenthetical data showing the face value and the current interest rate. The interest rate on reserves is fixed at 0%; the interest rates on the variable-rate loans and deposits are adjusted weekly, depending on the prevailing interest rate on 1-year Treasury-bills.

   a. What is this bank's degree of leverage?

   b. Will this bank's net worth (calculated as the difference between the present value of its assets and liabilities) increase or decrease if all interest rates unexpectedly increase by one percentage point?

   c. If this bank wants to insulate its net worth from changes in interest rates, should it sell some of its 6-year zeros and use the proceeds to buy 1-year zeros or to buy 10-year zeros?

12. A senior vice-president of the bank in Exercise 12 suggests that, instead of selling some of its 6-year zeros, this bank can protect its net worth from interest-rate fluctuations by buying or selling bond puts, bond calls, and bond futures. Which of these should the bank buy and which should it sell to hedge its net worth against interest-rate risk?

   Alternatively, to reduce the effects of interest-rate changes on its net worth, should this bank swap some of the payments that will be due on its 2-year zeros for variable-rate payments, or should it swap variable-rate payments for fixed-rate payments?

13. Suppose that the term structure is upward sloping and that there is an inexplicably wide spread between the yields to maturity on 20-year Treasury bonds with 4% coupons and 20-year Treasury bonds with 8% coupons. If a securities dealer wants to bet that the spread will narrow, should the dealer buy 20-year bonds with 4% coupons or 20-year bonds with 8% coupons? How can the dealer hedge its position, so that it is betting just on the spread narrowing and not on a general movement in interest rates?

14. Most option contracts expire in less than a year. Long-term Equity Anticipation Securities ("Leaps") are special call and put options with expiration dates of up to three years. In June of 1992, a Wall Street Journal staff reporter argued that because Leaps are relatively new and thinly traded options, they are often mispriced. As an example, the Journal's staff reporter cited Waste Management Corporation, whose stock was selling then for $35 5/8 while a call option with a striking price of $40 and an expiration date in January of 1994 sold for $3 7/8. The reporter suggested that instead of spending 100($35 5/8) = $3,562.50 for 100 shares of Waste Management, an investor could buy 100 Waste Management call options for 100($3 7/8) = $387.50 and invest the remaining $3,562.50 † $387.50 = $3,175.00 in Treasury notes with a 4.85% yield to maturity that expire in January of 1994, the same time as the call options.
   Use a graph to compare the dollar profits from the following three strategies for various possible prices of Waste Management stock on the expiration date in January of 1994. For simplicity, assume that the Treasury notes are zeros with 1 year and 7 months to maturity and ignore any dividends on the Waste Management stock (the dividends were, in fact, $0.52 per share in 1992). Also ignore taxes and commissions.

   a. buy 100 shares of Waste Management at $35 5/8 per share.

   b. invest $3,562.50 in January 1994 Treasury notes with a 4.85% yield.

   c. buy 100 Waste Management call options and invest $3,175.00 in Treasury notes with a 4.85% yield.

   Under which, if any, circumstances, is the option strategy (c) less profitable than either of the other strategies?

15. Explain why the following explanation of a stock's beta coefficient is misleading:

This is the ratio of the variability in the return of the common stock of the firm to the variability in the average return on the common stocks of all firms.... A beta coefficient of 1 means that the variability in returns on the common stock of the firm is the same as the variability in the returns on all stocks.
[Dominick Salvatore, Microeconomics, New York: HarperCollins, 1991, p. 513.]

16. In 1990 the U.S. government sold 40-year bonds to help finance the thrift-industry bailout. The Wall Street Journal observed that many of these bonds were bought by dealers and stripped to create 40-year zero-coupon bonds, and that, "As trading vehicles, 40-year zeros can be lethal or lucrative depending upon an investor's ability to successfully time interest-rate moves." Use duration to estimate the percentage change in the price of a 40-year zero if its yield increases from 10% to 11%, and if its yield falls from 10% to 9%. Calculate the exact percentage changes and compare these with your duration-based estimates.

17. The University of Iowa had a futures market for the 1992 Democratic presidential nomination, with six types of shares--one for each of five candidates (Jerry Brown, Bill Clinton, Tom Harkin, Bob Kerrey, and Paul Tsongas) and one for the "rest of field." Each share is worth $1 if the designated person becomes the Democratic nominee and is worth nothing otherwise. If, for example, someone buys 500 Jerry Brown shares at 2¢ a share, then on the day that the Democratic Party chooses its nominee, the owner of these 500 shares pays $0.02(500) = $10 to the person who sold these futures and in return receives either $500 or $0 from the seller, depending on whether Jerry Brown is the nominee.

    a. On February 10, 1992, the day of the Iowa caucuses, Bill Clinton futures closed at 45.5¢, down 10¢ from the day before. For what probability of Clinton becoming the Democratic nominee did those who paid 45.5¢ for Clinton futures have a positive expected return?

    b. Are presidential futures prices determined by expectations or by the cost of carry?

    c. Why must the market prices of the six types of shares add up to $1? Give a numerical example to illustrate your reasoning.

18. In his keynote address to the American Association of Individual Investors' National Meeting for Investment Education, John C. Bogle, chief executive officer of the Vanguard family of mutual funds, gave five rules for selecting a bond fund:

   1. "Consider the 'interest rate risk' that bonds carry--not only risk to principal but also risk to income."

   2. "Consider the impact of income yield and principal change on total return in light of the length of time that you expect to own the investment."

   3. "Consider investment quality. Quality risk is the risk that a bond will be unable to meet its specified interest coupon and, at maturity, to repay its principal."

   4. "Consider prepayment and currency risks."

   5. "Consider the taxability of interest payments."

   In regard to Rule 1, explain the difference between principal risk and income risk. Do long-term or short-term bonds have relatively more income risk?

19. To illustrate the second rule cited in Exercise 18, Bogle presented a graph showing the terminal value (the market value of the bond plus the value of the reinvested coupons) for a 25-year Treasury bond with 8% coupons over horizons of 1 to 25 years under three scenarios: interest rates rise to 10%, interest rates stay at 8%, and interest rates fall to 6%.

    a. For a 25-year horizon, which of these three scenarios gives the highest terminal value?

    b. For a 1-year horizon, which of these three scenarios gives the highest terminal value?

    c. For what horizon is the terminal value the same for all three scenarios?

20. Regarding Bogle's third, fourth, and fifth rules given in Exercise 18,

    a. Do corporate, municipal, or Treasury bonds have the least quality risk? Why?

    b. Explain prepayment risk. Is prepayment more likely to occur after interest rates rise or fall?

    c. Explain currency risk. What kind of event would be bad news?

    d. Do corporate, municipal, or Treasury bonds have the most favorable tax treatment?