1. Suppose there are n risky assets with normally distributed payoffs , and no risk-free asset....

 

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1. Suppose there are n risky assets with normally distributed payoffs , and no risk-free asset. Assume all investors have CARA utility and no labor income. Define a to be the aggregate absolute risk aversion defined by 1 α = Σi_₁ (1/a₂)* Let 7 = (₁,...,n) denote the vector of supplies of the n risky assets. Let denote the mean and Σ the covariance matrix of the vector X = (₁,...,n)' of asset payoffs. Assume Σ is nonsingular. There is no consumption at date 0. Show that the vector p = γ(μ - «Σ7) is an equilibrium price vector for any > 0. Hint: Solve each investor's portfolio choice problem subject to the budget constraint p'0 = Who. Next show that the markets clear, using the budget constaints to eliminate the Lagrangian multipliers. 1. Suppose there are n risky assets with normally distributed payoffs , and no risk-free asset. Assume all investors have CARA utility and no labor income. Define a to be the aggregate absolute risk aversion defined by 1 α = Σi_₁ (1/a₂)* Let 7 = (₁,...,n) denote the vector of supplies of the n risky assets. Let denote the mean and Σ the covariance matrix of the vector X = (₁,...,n)' of asset payoffs. Assume Σ is nonsingular. There is no consumption at date 0. Show that the vector p = γ(μ - «Σ7) is an equilibrium price vector for any > 0. Hint: Solve each investor's portfolio choice problem subject to the budget constraint p'0 = Who. Next show that the markets clear, using the budget constaints to eliminate the Lagrangian multipliers.

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a Selection of risky Asset should be made on the bases of Coefficient of Variation CM ie H... View the full answer