Aug 25, 2009
Long-term government bonds outperformed the S&P 500 Index by 0.12% per year for the forty-year period ending March 2009. Does a negative risk premium for stocks vs. bonds over such a long period challenge conventional thinking about risk and return?

EFF/KRF: It is important to distinguish between the expected equity premium, which should be positive, and the realized premium, which is the expected premium plus the unexpected premium. Investing in stocks is risky because we do not know what the unexpected premium will be. 

Uncertainty about the average unexpected premium is smaller for longer investment horizons, so if we invest for many years the average unexpected premium will typically be close to zero. As a result, the premium of equities over bonds - the sum of the positive expected premium and the random unexpected premium - is likely to be positive over long investment horizons. But over any finite horizon, no matter how long, there is a positive probability that the premium will be negative. Without this long-term uncertainty, we would see simple arbitrage opportunities between stocks and bonds. Suppose, for example, we all know stocks will beat bonds over every forty year period. If stocks lose to bonds over the next 39 years, who would buy bonds in the 40th year? In fact, in that case we could make as much money as we want in the 40th year with no risk by simply shorting bonds and using the proceeds to invest in stocks.

Eugene F. Fama
The Robert R. McCormick Distinguished Service Professor of Finance at the University of Chicago Booth School of Business
Kenneth R. French
The Roth Family Distinguished Professor of Finance at the Tuck School of Business at Dartmouth College
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Eugene Fama and Ken French are members of the Board of Directors for and provide consulting services to Dimensional Fund Advisors LP.