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Risk and Return

Earlier we looked at past returns on selected investments. The least risky investment was U.S. Treasury bills. Since the return on Treasury bills is fixed, it is unaffected by what happens to the market. Thus the beta of Treasury bills is zero. The most risky investment that we considered was the market portfolio of common stocks. This has average market risk: its beta is 1.0.

Wise investors don`t run risks just for fun. They are playing with real money and therefore require a higher return from the market portfolio than from Treasury bills. The difference between the return on the market and the interest rate on bills is termed the market risk premium. Over the past 73 years the average market risk premium has been just over 9 percent a year. Of course, there is plenty of scope for argument as to whether the past 73 years constitute a typical period, but we will just assume here that 9 percent is the normal risk premium, that is, the additional return that an investor could reasonably expect from investing in the stock market rather than Treasury bills.

In Figure 4.10a we plotted the risk and expected return from Treasury bills and the market portfolio. You can see that Treasury bills have a beta of zero and a risk-free return; we`ll assume that return is 5 percent. The market portfolio has a beta of 1.0 and an assumed expected return of 14 percent.3

Now, given these two benchmarks, what expected rate of return should an investor require from a stock or portfolio with a beta of .5? Halfway between, of course. Thus in Figure 4.10b we drew a straight line through the Treasury bill return and the expected market return and marked with an X the expected return for a beta of .5, that is, 9.5 percent. This includes a risk premium of 4.5 percent above the Treasury bill return of 5 percent.

You can calculate this return as follows: start with the difference between the expected market return rm and the Treasury bill rate rf. This is the expected market risk premium.

This formula states the basic risk Јreturn relationship called the capital asset pricing model, or CAPM. The CAPM has a simple interpretation:

The expected rates of return demanded by investors depend on two things: (1) compensation for the time value of money (the risk-free rate rf), and (2) a risk premium, which depends on beta and the market risk premium.

Note that the expected rate of return on an asset with = 1 is just the market return. With a risk-free rate of 5 percent and market risk premium of 9 percent,

WHY THE CAPM WORKS

The CAPM assumes that the stock market is dominated by well-diversified investors who are concerned only with market risk. That makes sense in a stock market where trading is dominated by large institutions and even small fry can diversify at very low cost.

How Would You Invest $1 Million?

Have you ever daydreamed about receiving a $1 million check, no strings attached, from an unknown benefactor? Let`s daydream about how you would invest it.

We have two good candidates: Treasury bills, which offer an absolutely safe return, and the market portfolio (possibly via the Vanguard index fund discussed earlier in this material). The market has generated superior returns on average, but those returns have fluctuated a lot. (Look back to Figure 3.15.) So your investment policy is going to depend on your tolerance for risk.

If you`re a cautious soul, you may invest only part of your money in the market portfolio and lend the remainder to the government by buying Treasury bills. Suppose that you invest 80 percent of your money in the market portfolio and lend out the other 20 percent to the government by buying U.S. Treasury bills. Then the beta of your portfolio will be a mixture of the beta of the market (Гвmarket = 1.0) and the beta of the T-bills

The fraction of funds that you invest in the market also affects your return. If you invest your entire million in the market portfolio, you earn the full market risk premium. But if you invest only 80 percent of your money in the market, you earn only 80 percent of the risk premium. The expected return on your portfolio is equal to the risk-free interest rate plus the expected risk premium:

CAPITAL ASSET PRICING MODEL (CAPM) Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

MARKET RISK PREMIUM Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.