Fundamentals of Investments, 5th edition
Jordan and Miller
A Brief History of Risk and Return
For both risk and return, increasing order is b, c, a, d. On average, the higher the risk of an investment, the higher is its expected return.
Since the price didn’t change, the capital gains yield was zero. If the total return was four percent, then the dividend yield must be four percent.
It is impossible to lose more than –100 percent of your investment. Therefore, return distributions are cut off on the lower tail at –100 percent; if returns were truly normally distributed, you could lose much more.
To calculate an arithmetic return, you simply sum the returns and divide by the number of returns. As such, arithmetic returns do not account for the effects of compounding. Geometric returns do account for the effects of compounding. As an investor, the more important return of an asset is the geometric return.
Blume’s formula uses the arithmetic and geometric returns along with the number of observations to approximate a holding period return. When predicting a holding period return, the arithmetic return will tend to be too high and the geometric return will tend to be too low. Blume’s formula statistically adjusts these returns for different holding period expected returns.
T-bill rates were highest in the early eighties since inflation at the time was relatively high. As we discuss in our chapter on interest rates, rates on T-bills will almost always be slightly higher than the rate of inflation.
Risk premiums are about the same whether or not we account for inflation. The reason is that risk premiums are the difference between two returns, so inflation essentially nets out.
Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns are smaller than pretax returns.
We have seen that T-bills barely kept up with inflation before taxes. After taxes, investors in T-bills actually lost ground (assuming anything other than a very low tax rate). Thus, an all T-bill strategy will probably lose money in real dollars for a taxable investor.
It is important not to lose sight of the fact that the results we have discussed cover over 70 years, well beyond the investing lifetime for most of us. There have been extended periods during which small stocks have done terribly. Thus, one reason most investors will choose not to pursue a 100 percent stock (particularly small-cap stocks) strategy is that many investors have relatively short horizons, and high volatility investments may be very inappropriate in such cases. There are other reasons, but we will defer discussion of these to later chapters.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.
Total dollar return = $988.00
Capital gains yield = 12.33%
Dividend yield = 1.21%
Total rate of return = 13.53%
Dollar return = –$2,790.00
Capital gains yield = –6.30%
Dividend yield = 1.21%
Total rate of return = –5.10%
average return = 5.8%, average risk premium = 2.0%
average return = 3.8%, average risk premium = 0%
average return = 12.3%, average risk premium = 8.5%
average return = 17.4%, average risk premium = 13.6%
Cherry average return = 9.20%
Straw average return = 13.80%
Stock A: RA = 9.80%
Var = 0.02077
Standard deviation = 0.1441 or 14.41%
Stock B: RB = 11.80%
Var = 0.01987
Standard deviation = 0.1410 or 14.10%
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