1. Here is an excerpt from a letter to the editor of Barron's:

I read with interest your tale of woe about Caprimex and the IMAC Currency Hedge Fund. In addition to having computer problems, Alex Herbage also cannot do interest arithmetic. An investment that produces a profit of 257% in 6 1/2 years (i.e., $100 grows to $357) has a rate of return of [x]%, not the 39.5% as quoted by Herbage....This calculation goes beyond the limits of reasonably puffery...and is certainly without significance.

   

   a. How was the 39.5% calculated?

   b. What is the correct rate of return (which has been omitted from the above excerpt)?

2. The owner of a Washington, D.C. real-estate firm said that an equation basic to real estate is

total interest paid = (principal) (interest rate per year) (number of years)

   a. Explain why the total interest paid on a $100,000 conventional 30-year mortgage at 10 percent is not ($100,000) (10%) (30 years) = $300,000.

   b. Is the actual total interest larger or smaller than $300,000?

3. In 1986, a Wall Street Journal reporter told how he had been tempted to refinance his 25-year, 13.25% $55,000 mortgage at 9 to 10%, but had been dissuaded by the $3,500 to $4,000 he would have had to pay in points and other closing costs. Critically evaluate his logic:

With, say, a saving of $100 a month in principal and interest payments, I would pocket $36,000 over 30 years [net of closing costs], I thought at first. Not so. Since I have only 22 1/2 years left on my existing contract and if I convert it to 25 or 30 years to keep my payments low, I discovered that I could end up paying more total dollars in the long run.

4. The following is a 1987 analysis of municipal bond prices:

Demand for the bonds of states, cities and public authorities, which offer tax-exempt interest payments, has been tremendous. So many have rushed to buy what bond houses advertise as the last tax shelter of the middle class that customary price differentials between tax-exempt and taxable bonds have narrowed. Crowd psychology rather than economics is at work.

5. In a credit swap, Omaha Second Federal Bank might swap $20 million in farm loans for $20 million in oil loans from Houston Third and Long Bank. How can such a swap be mutually beneficial if all of these loans are denominated in dollars, tied to the one-year T-bill rate, have equal maturities, and have equal default risk?

6. "Last week alone, more than two dozen companies announced programs to repurchase their stock, while announced merger and acquisition activity is a record $588 billion so far this year. The aim in both cases is identical: to boost shareholder value and add to investors' total return by boosting earnings per share and the stock price rather than dividends." [Suzanne McGee, "Bearish Yield: More Bark Than Bite," The Wall Street Journal, November 25, 1996.]

   a. Why might shareholders prefer stock repurchases to dividends?

   b. Why might merger and acquisition activity boost earnings per share and yet reduce the stock price?

7. Explain why you either agree or disagree with this reasoning by the director of research for the American Association of Individual Investors: "Certificates of Deposit, unless they are the large-denomination, negotiable type, have no market interest-rate risk because they are not traded and have no market price."

8. John Kenneth Galbraith once wrote that,

International currency stabilization will, however, only be possible when national economies are stable—when the industrial countries have succeeded in combining reasonably high employment with tolerably stable prices. Until then all talk of international currency reform will be in a vacuum and can safely be ignored except by those whose employment depends on the discussion.

9. The Dow P/E can be obtained by dividing the average price of the 30 Dow Industrial stocks by the average earnings of these 30 stocks. Since 1905, as far back as these data go, the Dow P/E has had a median value of 13.8, and 80% of the time has been between 7.4 and 23.0. The highest value was 931 in August of 1933. How do you explain this extraordinarily high value?

10. In 1996, Ian MacKinnon, Senior Vice President of the Vanguard Fixed Income Group said that, "With...a yield of just over 2% on the Standard & Poor's 500 Index and nearly 7% on ten-year Treasury bonds--that's a gap of 400 to 500 basis points a year that the stockholder has to hope to make up by price appreciation and dividend increases." If we let x be the annual price appreciation and y be the annual dividend increase, does the phrase "price appreciation and dividend increases" mean (a) x = y = 400-to-500 basis points, or (b) x + y = 400-to-500 basis points? Explain your reasoning.

11. On November 15, 1996, Warren Buffett's Berkshire Hathaway and the California Earthquake Authority reached an agreement that will take effect on April 1, 1997, in which

   1. The Authority will pay Hathaway $590 million immediately.

   2. If earthquakes that occur before March 31, 2001 causes homeowner claims against the Authority to exceed $7 billion, Hathaway will pay the next $1.5 billion in claims.

   An actuary for the Authority estimated that there is a 0.05 probability that earthquakes occurring during this time period would cause claims to exceed $7 billion.

   a. Ignoring the time value of money and assuming that Hathaway will either have to pay $1.5 billion or nothing, what is the expected value of Hathaway's profit from this deal?

   b. Explain why the two assumptions made at the beginning of Part (a) caused your expected value calculation to be either larger or smaller than the actual expected value.

   c. Why is it generally not a good idea to bet against Warren Buffett?

12. Regarding the deal described in the preceding exercise, a spokesman for the Authority said that the $590 premium was less than the interest that the authority would have paid over 4 years if it sold $1.5 billion in bonds to boost its resources for the possibility of a catastrophic quake.

   a. Use these figures to estimate the interest rate the Authority evidently would have had to pay on these bonds. Assume that these are zero-coupon bonds with all of the interest due at the end of four years.

   b. Explain why it is a huge mistake to compare these alternatives by comparing the interest on these bonds to the $590 million paid to Buffett.

13. For each of the 45 years 1950 -1994, researchers calculated the ratio of market value to book value for the S&P500 on January 1 of that year and the total return (dividends plus capital gains) on the S&P500 during that year. The years were then divided into two categories, depending on the beginning-of-year ratio of market value to book value:

Category 1: The 22 years with the highest ratios
Category 2: The 22 years with the lowest ratios

(The median year was discarded.) Finally, the average total return was calculated for the years in each category. One category had an average return of 19.8%, the other 6.0%. [Kevin Cole, Jean Helwege, and David Laster, "Stock Market Valuation Indicators: Is this Time Different?," Financial Analysts Journal, May/June 1996, pp. 56-64]

   a. According to fundamental analysis, assuming rational and efficient markets with stocks priced each year to give a constant return of say 10%, when would we expect to find market value greater than book value, and when would we expect to find market value lower than book value?

   b. According to contrarian logic, which of these two categories would we expect to have the higher average return, and which would we expect to have the lower average return?

14. On February 28, 1994, Tudor Investment Company established a married-put position by purchasing shares of stock worth $350 million and buying put options that would expire in two weeks for an identical number of shares. (Tudor was later fined by the SEC for a technical violation of trading rules as it tried to undo this married-put position; Tudor had not done a married-put transaction in the stock market before this and, as of September 1996, has done none since.) Describe the wager implicit in a married-put position.

15. In a November 1996 analysis of the long surge in stock prices, Bankers Trust economist John Williams was quoted as saying,

When I look at the economy now [with low unemployment and low inflation] I think, ‘It can’t get any better than this.’ That’s the good news and the bad news.

   a. Explain why low unemployment and low inflation are good news for the stock market.

   b. Explain what you think Williams meant by his bad-news comment.

16. In March 1987, a real estate columnist wrote that,

Everybody in the business was struck by the prices the Japanese paid for some trophy properties last year; for example, $610 million that Shuwa paid for the Exxon Building. Few remembered the plunge of the dollar against the yen that preceded these purchases. That decline of 55 percent in value in the preceding 16 months made U.S. property look especially cheap in Japanese eyes; applying that arithmetic to the prices paid means that Shuwa really laid out $274.5 million for the Exxon Building—less than what the seller would have gotten from an American institution.

        If you were advising Shuwa, would you have figured the cost of the Exxon building to be $610 million or $274.5 million? Explain.

17. Federally chartered savings-and-loan associations are allowed to swap variable-rate debts for fixed-rate ones, but are not allowed to swap fixed-rate debts for variable-rate ones. Why?

18. Many mutual funds are always 100 percent invested in stocks, believing that in a risk-averse world the average return from stocks will be larger than the average return from Treasury bills and other safe investments. Under what circumstances might such a mutual fund be virtually 100 percent certain of increasing its profits by selling some of its stocks and using the proceeds to buy Treasury bills and stock-index futures?

19. In his November 11, 1996 "Weekly Economic Analysis," Ed Yardeni listed four possible surprises (none of which he considers likely) that could affect financial markets. For each surprise, explain whether the occurrence would be bullish or bearish for stocks and bonds, by writing "bull" or "bear" in the appropriate column.

		stocks	bonds
a.	Stop the mania. The Fed raises interest rates to stop stock market speculation.
b.	Global synchronized boom. Worldwide increase in economic growth and inflation causes the major central banks to raise interest rates.
c.	Worker backlash. Workers are mad as hell and they aren’t going to take it anymore, forcing employers to increase pay and benefits.
d.	Punk profits. If inflation remains low and economic growth slows early next year, then corporate profits could be very weak.

20. Harvard University has 3% of its $8.6 billion endowment in wheat futures, oil futures, and other commodities-related investments. The Wall Street Journal noted that, "Commodity futures prices are volatile and tied to unpredictable patterns in politics or the weather. Most universities prefer blue-chip stocks." An outside consultant criticized Harvard's investment, arguing that because "it's a higher-risk asset," any investment in commodities futures "should be based on one's risk tolerance." However, the CEO of Harvard Management Company justified this investment by arguing that, "Commodities have zero or negative correlation" to stocks and bonds.
   Consider a stylized model in which there are three assets--stocks, commodity futures, and T-bills--with the following characteristics: