The slides from Lecture 5 give the following general relation for the risk premi

Question

The slides from Lecture 5 give the following general relation for the risk premium on a security with return ri: E(ri - rf) = - Cov(mrs,ri) / E(mrs) where mrs is the marginal rate of substitution between current and future consumption. It is given by mrs = gamma u'(c1) / u'(c0) The CAPM predicts that risk premia are proportional to the covariance of a security with the market portfolio's return, rm: E (ri - rf) = lambda Cov (ri, rm) Suppose that a representative investor holds a portfolio of the riskless asset and the market. Suppose, further, that this investor has quadratic utility, so that u(c) = alpha + theta c2. Demonstrate algebraically that the CAPM relationship above must hold.

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