Consider the asset pricing relation (5.6). Prove that the covariance between the return on the market portfolio

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Consider the asset pricing relation (5.6). Prove that the covariance between the return on the market portfolio and the stochastic discount factor \(\delta \mathbf{u}_{1}^{\prime}\left(\tilde{x}^{m}\right) / \mathbf{u}_{0}^{\prime}\left(x_{0}^{m}\right)\) is negative. Deduce that the risk premium \(\mathbb{E}\left[\tilde{r}^{m}\right]-r_{f}\) of the market portfolio is positive.

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