Geometric versus Arithmetic Risk Premiums: Which is better?
The conventional wisdom is that the arithmetic mean is the better estimate. This is true if: • you consider each year to be a period (and the CAPM to be a one-period model) • annual returns in the stock and bond markets are serially uncorrelated As we move to longer time horizons, and as returns become more serially correlated (and empirical evidence suggests that they are), it is far better to use the geometric risk premium. In particular, when we use the risk premium to estimate the cost of equity to discount a cash flow in ten years, the single period in the CAPM is really ten years, and the appropriate returns are defined in geometric terms. In summary, the arithmetic mean is more appropriate to use if you are using the Treasury bill rate as your riskfree rate, have a short time horizon and want to estimate expected returns over that horizon. The geometric mean is more appropriate if you are using the Treasury bond rate as your riskfree rate, have a long time horizon and want to es
