## O rr

To carry out the CAPM approach, we need to estimate the three factors that determine the CAPM line: the risk-free rate, the market risk premium, and the systematic risk (beta). The balance of this section describes a recommended approach for estimating each.

### Determining the Risk-Free Rate

Hypothetically, the risk-free rate is the return on a security or portfolio of securities that has no default risk and is completely uncorrelated with returns on anything else in the economy. In theory, the best estimate of the risk-free rate would be the return on a zero-beta portfolio, constructed of long and short positions in equities in a way that produces the minimum variance zero-beta portfolio. Because of the cost and complexity of constructing minimum variance zero-beta portfolios, they are not practical for estimating the risk-free rate.

We have three reasonable alternatives that use government securities: the rate for Treasury bills, the rate for 10-year Treasury bonds, and the rate Exhibit 10.3 The Capital Asset Pricing Model

for 30-year Treasury bonds. We recommend using a 10-year Treasury-bond rate for several reasons:7

• It is a long-term rate that usually comes close to matching the duration of the cash flow of the company being valued. Since the current Treasury-bill rate is a short-term rate, it does not match duration properly. If we were to use short-term rates, the appropriate choice would be the short-term rates that are expected to apply in each future period, not today's short-term interest rate. The 10-year rate is a geometric weighted average estimate of the expected short-term Treasury-bill rates.

• The 10-year rate approximates the duration of the stock market index portfolio—for example, the S&P 500—and its use is therefore consistent with the betas and market risk premiums estimated relative to these market portfolios.8

• The 10-year rate is less susceptible to two problems involved in using a longer-term rate, such as the 30-year Treasury-bond rate. Its price is less sensitive to unexpected changes in inflation, and so has a smaller beta than the 30-year rate. Also, the liquidity premium built into 10-year rates may be slightly lower than that of 30-year bonds. These are technical details, with a minor impact in normal circumstances. But they do argue for using a 10-year bond rate.9

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