1. Explain the error in this assertion: "If the yield curve were a crystal ball, all economists would be billionaires." [S. L. Mintz, Dana Dakin, and Thomas Willison, Beyond Wall Street: The Art of Investing, New York: John Wiley & Sons, 1998, p. 151.]

2. Explain the error in this assertion: "[John Burr] Williams had declared that the price of a security rests on the expected stream of future dividends, adjusted by the effect of inflation that makes one dollar received tomorrow worth less than a dollar already in an investor's pocket--the so-called 'dividend discount' model." [S. L. Mintz, Dana Dakin, and Thomas Willison, Beyond Wall Street: The Art of Investing, New York: John Wiley & Sons, 1998, p. 68.]

3. 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, said that investors should, "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." To illustrate this point, he 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 percent coupons over horizons of 1 to 25 years under three scenarios: interest rates rise to 10 percent, interest rates stay at 8 percent, and interest rates fall to 6 percent.
     a. For a horizon of 25 years, which of these three scenarios gives the highest terminal value?
     b. For a horizon of 1 year, which of these three scenarios gives the highest terminal value?
     c. For what horizon is the terminal value the same for all three scenarios?

4. Answer this question posed by The Wall Street Journal: "Which is less damaging [to your portfolio], inflation of 50% or a 50% drop in your portfolio's value?" [Jonathan Clements, "Confused by Investing? Maybe It's the New Math," The Wall Street Journal, February 20, 1996.]

5. The Federal Home Loan Bank System says that one of the advantages of Freddie Mac to savings and loan associations is that, "When interest rates are rising, lenders can sell off their older, low-interest loans and reinvest in mortgages at higher interest rates." What is the implicit assumption? ["A Guide to the Federal Home Loan Bank System," FHLB System Publication Corporation, March 1987, p. 59.]

6. Critically evaluate this argument by a legendary mutual fund manager: "The p/e ratio can be thought of as the number of years it will take the company to earn back the amount of your initial investment--assuming of course that the company's earnings stay constant....If you buy shares in a company selling at two times earnings (a p/e of 2), you will earn back your initial investment in two years, but in a company selling at 40 times earnings (a p/e of 40) it would take forty years to accomplish the same thing." [Peter Lynch, One Up on Wall Street, New York: Simon and Schuster, 1989, p. 164]

7. (From Brealey/Meyers) Here are recent financial data on Pisa Construction Company:

stock price = $40
number of shares = 10,000
book value = $500,000
market value = $400,000
return on investment = 8 percent
earnings per share = $4

          Pisa has not performed spectacularly to date. However, it wishes to issue new shares to obtain $80,000 to finance expansion into a promising market. Pisa's financial advisers think a stock issue is a poor choice because "sale of a stock at a price below book value per share can only depress the stock price and decrease shareholder wealth." To prove this point, they construct the following example: "Suppose 2000 new shares are issued at $40 and the proceeds invested. Then

     Thus, EPS declines, book value per share declines, and share price will decline proportionately to $38.70. Evaluate this argument.

8. What is the implicit rate of return that has been omitted from this 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 compound interest arithmetic. An investment that produces a profit of 257% in 6 1/2 years (i.e., $100 grows to $357) has an [implicit] rate of return of [x] %, not the 39.5% as quoted by Herbage. The 39.5% was evidently arrived at by dividing 257% by 6 1/2 years. This calculation goes beyond the limits of reasonable puffery, certainly does not conform to U.S. financial advertising practice...and is totally without significance.

9. Explain the error(s) in this newspaper column:

Thomas M. Poor, manager of the Scudder Short-term Bond Fund in Boston, suggests that you focus on a volatility index known as “duration.” This is a calculation in which you determine the present value of a bond’s future interest payments and principal repayment. Sound complicated? It is. Suffice it that bond funds with lower duration numbers are less volatile. According to Poor, money market funds have a duration of zero, while a portfolio filled with 30-year Treasury bonds would have a duration of 10.

10. Here is an excerpt from a recent article:

Stock buybacks, long a favorite tool for pleasing investors, could be developing some unpleasant side effects.
   The surge of announced buybacks since the fall has come at the same time that corporate America is issuing record amounts of debt. Some analysts now worry that with profits and sales flat, companies may find themselves ill prepared for an economic downturn. [Greg Ip, "Was Wave of Stock Buybacks a Bad Idea?," The Wall Street Journal, February 22, 1999.]