Geometric vs. Arithmetic

The estimated equity returns (9.37%) and equity risk premiums (3.97%) are geometric averages. The arithmetic average is often used in portfolio optimization. There are several ways to convert the geometric average into an arithmetic average. One method is to assume the returns are independently log-normally distributed over time. Then the arithmetic and geometric roughly follows the following relationship:

deviation of equity returns is 19.67%. Since almost all the variation in equity returns is from the equity risk premium (rather than the risk free rate), we need to add 1.93% to the geometric equity risk premium

estimate to convert into arithmetic. R_A = R_G +1.93% . Adding the 1.93 percent to the geometric estimate,

the arithmetic average equity risk premium is estimated to be 5.90% for the earnings model.

¹⁴ Stock Market Returns in the Long Run

To summarize, the long-term supply of equity return is estimated to be 9.37% (6.09% after inflation) conditional on the historical average risk free rate. The supply side equity risk premium is estimated to be 3.97% geometrically and 5.90% arithmetically.¹³

IV. CONCLUSIONS

We adopt a supply side approach to estimate the forward looking long-term sustainable equity returns and equity risk premium. We analyze historical equity returns by decomposing returns into factors commonly used to describe the aggregate equity market and overall economic productivity. These factors include inflation, earnings, dividends, price-to-earnings ratio, dividend-payout ratio, book value, return on equity, and GDP per capita. We examine each factor and its relationship with the long-term supply side framework. We forecast the equity risk premium through supply side models using historical information. A complete tabulation of all the numbers from all models is presented in Appendix. Contrary to several recent studies on equity risk premium that declare the forward looking equity risk premium to be close to zero or negative, we find the long-term supply of equity risk premium is only slightly lower than the straight historical estimate. The equity risk premium is estimated to be 3.97% in geometric terms and 5.90% on an arithmetic basis. This estimate is about 1.25% lower than the straight historical estimate. The differences between our estimates and the ones provided by several other recent studies are principally due to the inappropriate assumptions used, which violate the Miller and Modigliani Theorem. Also our models interpret the current high P/E ratios as the market forecasting high future growth, rather than a low discount rate or an overvaluation. Our estimate is in line with both the historical supply measures of the public corporations (i.e., earnings) and the overall economic productivity (GDP per capita).

Our estimate of the equity risk premium is far closer to the historical premium than being zero or negative. This implies that stocks are expected to outperform bonds over the long run. For long-term investors, such as pension funds or individuals saving for retirement, stocks should continue to one of the

favored asset classes in their diversified portfolios. Due to our lowered equity risk premium estimate

¹⁵ Stock Market Returns in the Long Run

(compared to historical performance), some investors should lower their equity allocations and/or

increase their savings rate to meet future liabilities.

¹⁶ Stock Market Returns in the Long Run

Date: 2016-01-14; view: 637