The CAPM Approach 231- Treasury bill rates are more volatile than are Treasury bond rates and, most experts
agree, more volatile than rs. - In theory, the CAPM is supposed to measure the expected return over a particular
holding period. When it is used to estimate the cost of equity for a project, the the-
oretically correct holding period is the life of the project. Since many projects have
long lives, the holding period for the CAPM also should be long. Therefore, the
rate on a long-term T-bond is a logical choice for the risk-free rate.
In light of the preceding discussion, we believe that the cost of common equity is
more closely related to Treasury bond rates than to T-bill rates. This leads us to favor
T-bonds as the base rate, or rRF, in a CAPM cost of equity analysis. T-bond rates can
be found in The Wall Street Journal or the Federal Reserve Bulletin. Generally, we use
the yield on a 10-year T-bond as the proxy for the risk-free rate.
Estimating the Market Risk Premium
The market risk premium, RPM, is the expected market return minus the risk-free
rate, rMrRF. It can be estimated on the basis of (1) historical data or (2) forward-
looking data.Historical Risk Premium A very complete and accurate historical risk premium
study, updated annually, is available for a fee from Ibbotson Associates, who examine
market data over long periods of time to find the average annual rates of return on
stocks, T-bills, T-bonds, and a set of high-grade corporate bonds.^8 For example, Table
6-1 summarizes some results from their 2001 study, which covers the period
1926–2000.
Table 6-1 shows that the historical risk premium of stocks over long-term T-bonds
is about 7.3 percent when using the arithmetic average and about 5.7 percent when us-
ing the geometric average. This leads to the question of which average to use. Keep in
mind that the logic behind using historical risk premiums to estimate the current risk
premium is the basic assumption that the future will resemble the past. If this assump-
tion is reasonable, then the annual arithmetic average is the theoretically correct pre-
dictor for next year’s risk premium. On the other hand, the geometric average is a bet-
ter predictor of the risk premium over a longer future interval, say, the next 20 years.
However, it is not at all clear that the future will be like the past. For example, the
choice of the beginning and ending periods can have a major effect on the calculated
risk premiums. Ibbotson Associates used the longest period available to them, but had
their data begun some years earlier or later, or ended earlier, their results would have
been very different. In fact, using data for the past 30 or 40 years, the arithmetic average
market risk premium has ranged from 5 to 6 percent, which is quite different than the
7.3 percent over the last 75 years. Note too that using periods as short as 5 to 10 years
can lead to bizarre results. Indeed, over many periods the Ibbotson data would indicate
negative risk premiums, which would lead to the conclusion that Treasury securities
have a higher required return than common stocks. That, of course, is contrary to both
financial theory and common sense. All this suggests that historical risk premiums
should be approached with caution. As one businessman muttered after listening to a
professor give a lecture on the CAPM, “Beware of academicians bearing gifts!”(^8) See Stocks, Bonds, Bills and Inflation: 2001 Yearbook (Chicago: Ibbotson Associates, 2001). Also, note that
Ibbotson now recommends using the T-bond rate as the proxy for the risk-free rate when using the CAPM.
Before 1988, Ibbotson recommended that T-bills be used.
To find the rate on a T-bond,
go to http://www.
federalreserve.gov.Select
”Research and Data,” then
select ”Statistics: Releases
and Historical Data.” Click
on the ”Daily Update” for
H.15, ”Selected Interest
Rates.”