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22 and for the risk-less one period bonds the relevant expression is 1=E, U'(C (5) U'(c) Where the gross rate of return on the riskless asset is by definition (6) with q,being the price of the bond.Since U(c)is assumed to be increasing,we can rewrite(3)as 1=BEM+R (7) where M is a strictly positive stochastic discount factor.This guarantees that the economy will be arbitrage free and the law of one-price holds.A little algebra shows that E(R)=R+Cov, [-U(C).R (8) E,(U'(c+1) The equity premium E(R)-R thus can be easily computed.Expected asset returns equal the risk-free rate plus a premium for bearing risk,which depends on the covariance of the asset returns with the marginal utility of consumption.Assets that co-vary positively with con- sumption-that is,they payoff in states when consumption is high and marginal utility is low- command a high premium since these assets "destabilize"consumption. The question we need to address is the following:is the magnitude of the covariance between the marginal utility of consumption large enough to justify the observed 6 percent eq- uity premium in U.S.equity markets?If not,how much of historic equity premium is a premium for bearing non-diversifiable aggregate risk. To address this issue,we present a variation on the framework used in our original paper on the equity premium.An advantage of our original approach was that we could easily test the22 and for the risk-less one period bonds the relevant expression is 1 1 = 1 ¢ ¢ Ï Ì Ó ¸ ˝ ˛ + bE + U c U c t R t t f t ( ) ( ) , (5) Where the gross rate of return on the riskless asset is by definition R q f t t , +1 = 1 (6) with qtbeing the price of the bond. Since U c( )is assumed to be increasing, we can rewrite (3) as 1 = bEM R t t et { } + + 1 1 , (7) where Mt +1is a strictly positive stochastic discount factor. This guarantees that the economy will be arbitrage free and the law of one-price holds. A little algebra shows that ER R Cov Uc R EU c t et f t t t et t t ( ) ( ), ( ( )) , , , + + + + + = + - ¢ ¢ Ï Ì Ó ¸ ˝ ˛ 1 1 1 1 1 (8) The equity premium ER R t et f t ( ) , +1 - , +1 thus can be easily computed. Expected asset returns equal the risk-free rate plus a premium for bearing risk, which depends on the covariance of the asset returns with the marginal utility of consumption. Assets that co-vary positively with con￾sumption – that is, they payoff in states when consumption is high and marginal utility is low – command a high premium since these assets “destabilize” consumption. The question we need to address is the following: is the magnitude of the covariance between the marginal utility of consumption large enough to justify the observed 6 percent eq￾uity premium in U.S. equity markets? If not, how much of historic equity premium is a premium for bearing non-diversifiable aggregate risk. To address this issue, we present a variation on the framework used in our original paper on the equity premium. An advantage of our original approach was that we could easily test the
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