Stocks versus Bonds: Explaining the Equity Risk Premium

From the 19th century through the mid-20th century, the dividend yield (dividends/price) and earnings yield (earnings/price) on stocks generally exceeded the yield on long-term U.S. government bonds, usually by a substantial margin. Since the mid-20th century, however, the situation has radically changed. In addressing this situation, I argue that the difference between stock yields and bond yields is driven by the long-run difference in volatility between stocks and bonds. This model fits 1871–1998 data extremely well. Moreover, it explains the currently low stock market dividend and earnings yields. Many authors have found that although both stock yields forecast stock returns, they generally have more forecasting power for long horizons. I found, using data up to May 1998, that the portion of dividend and earnings yields explained by the model presented here has predictive power only over the long term whereas the portion not explained by the model has power largely over the short term. This article examines the relationship between stock and bond yields and, by extension, the relationship between stock and bond market returns (or the equity risk premium).The dividend yield on the S&P 500 Index has long been examined as a measure of stock market value. For instance, the well-known Gordon model expresses a stock price (or a stock market's price) as the discounted value of a perpetually growing dividend stream. Based on the Gordon model, the expected return on stocks equals the dividend yield (that is, dividends to price, D/P) in Year 0 plus the annual growth rate of dividends in perpetuity. Thus, if growth is constant, changes in D/P are exactly the changes in expected (or required) return. Numerous empirical studies have found that the dividend yield on the market portfolio of stocks has forecasting power for aggregate stock market returns and that this power increases as forecasting horizon lengthens.The market earnings yield (earnings to price or E/P) represents how much investors are willing to pay for a given dollar of earnings. E/P and D/P are linked by the payout ratio, dividends to earnings, which represents how much of current earnings is being passed directly to shareholders through dividends. Numerous studies have found that the market E/P has power to forecast the aggregate market return.Under certain assumptions, a bond's yield to maturity will equal the nominal holding-period return on the bond. As with equity yields, the inverse of the bond yield can be thought of as a price paid for the bond's cash flows (coupon payments and repayment of principal). When the yield is low (high), the price paid for the bond's cash flow is high (low). Research has shown that bond yield levels have power to predict future bond returns.The hypothesis of the study reported is that the yield stocks must provide in relation to bonds is driven by the experience of each generation of investors with each asset class. Defining a generation as 20 years, I found that stocks must provide relatively more yield (and expected return) versus bonds when for the preceding 20 years they were relatively more volatile.The article goes on to address the observation of many authors, economists, and market strategists that dividend and earnings yields on stocks as of May 1998 were, by historical standards, shockingly low. I found that today's low stock yields are predicted by the model presented in the article and, therefore, are not shocking.Finally, I decomposed stock yields into a fitted portion (stock yields explained by the model) and a residual portion (stock yields not explained by the model). I found that the residual portion forecasts primarily short-term returns and the fitted portion forecasts long-term returns only. These results point to approximately average short-term stock returns in the future but below-average long-term stock returns. These results run counter to certain popular arguments that the world is undergoing a one-time change that is driving equity risk premiums to zero and that, as this change continues, stock prices are set to soar.