return, in equilibrium, on the capitalization-weighted global equity market in excess of the riskless asset. Since the CAPM is a one-period model, it requires the arithmetic mean return on the market minus the current yield over one period. To apply this in the real world, we must define what is meant by one period. Because we are analyzing an equilibrium concept, we require a fairly long horizon, say five to 30 years. We can think of this as the investment horizon over which investors make strategic decisions on how much market risk to take. The investment horizon is required to measure the riskless return, as (nominally) riskless securities exist for one day out to 30 years. In this chapter, we take the U.S. 10-year government bond as the proxy for the riskless asset in the United States. Consistent with past research and current practice, we report all mean return estimates using geometric averaging.1 HISTORICAL PERSPECTIVE Roger Ibbotson and Rex Sinquefield (1976) conducted the first major analysis on equity returns using data from the Center for Research in Securities Prices at the University of Chicago. At that time, they estimated that the ERP in the United States since 1926 was 5.1 percent. They derived this from the total nominal annualized equity return of 8.5 percent, inflation of 2.4 percent, and a real risk-free return of 1.0 percent (on long-term government bonds). When Ibbotson and Peng Chen update the data to 2000, the real risk-free return is somewhat higher at 2.05 percent but the ERP is very similar at 5.24 percent. Of this premium, 1.25 percent per year is explained by expansion of price-earnings multiples since 1976, shown in Figure 5.1. If we postulate that this P/E expansion was a one-time event, not a secular trend or a bubble that will reverse, their adjusted ERP estimate is approximately 4 percent. Using a slightly longer data set starting in 1872, Eugene Fama and Kenneth French (2002) reach similar conclusions. Over their sample, they estimate the ERP at 5.57 percent. Fama and French conclude that the secular rise in P/E ratios since 1951 is likely to have been a one-time event and conclude the ERP estimate from 1872 to 1951 is more representative of future expectations. Their ERP estimate for this earlier window is 4.40 percent. These results are effectively averages over many possible regimes. From a more dynamic perspective, Jagannathan, McGrattan, and Scherbina (2000) look at the long-run equity premium in the United States and conclude that it has fallen. They apply a version of the Gordon growth model to different historical time periods and conclude that the long-run experience studied by Ibbotson, Fama and French, and others includes distinct regimes. On the basis of their analysis, they conclude that the U.S. equity premium averaged around 700 basis points during the period 1926 through 1970, and closer to 70 basis points after that. !In the CAPM, the market risk premium is the arithmetic expected return over the investment horizon, but converting arithmetic to geometric returns is straightforward using the following approximation: R o = Kanth - V2var(K).