Stocks versus Bonds: Explaining the Equity Risk Premium
Clifford S. Asness
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.
he dividend yield on the S&P 500 Index has long been examined as a measure of stock market value. For instance, the wellknown Gordon growth model expresses a stock price (or a stock market’s price) as the discounted value of a perpetually growing dividend stream: D P = ------------- . R–G (1)
price dividends in Year 0 expected return annual growth rate of dividends in perpetuity Now, solving this equation for the expected return on stocks produces D R = --- + G. P (2)
where P = D= R = G=
Thus, if growth is constant, changes in dividends to price, D/P, are exactly changes in expected (or required) return. Empirically, studies by Fama and French (1988, 1989), Campbell and Shiller (1998), and others, 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. Clifford S. Asness is president and managing principal at AQR Capital Management, LLC. 96
The market earnings yield or earnings to price, E/P (the inverse of the commonly tracked P/E), 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 are being passed directly to shareholders through dividends. Studies by Sorenson and Arnott (1988), Cole, Helwege, and Laster (1996), Lander, Orphanides, and Douvogiannis (1997), Campbell and Shiller (1998), and others, have found that the market E/P has power to forecast the aggregate market return. Under certain assumptions, a bond’s yield-tomaturity, Y, will equal the nominal holding-period return on the bond.1 Like the equity yields examined here, 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). Bernstein (1997), Ilmanen (1995), Bogle (1995), and others, have shown that bond yield levels (unadjusted or adjusted for the level of inflation or short-term interest rates) have power to predict future bond returns. This article examines the relationship between stock and bond yields and, by extension, the relationship between stock and bond market returns (the difference between stock and bond expected returns is commonly called the equity risk premium). I hypothesize that the relative yield stocks must provide versus bonds today is
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Stocks versus Bonds driven by the experience of each generation of investors with each asset class. The article also addresses the observation of many authors, economists, and market strategists that today’s dividend and earnings yields on stocks are, by historical standards, shockingly low. I find they are not. Finally, I report the...
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Stocks versus Bonds
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