Calculate the investor expected utility

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Reference no: EM132187854

Question - The asset-market economy

Suppose there are two assets available to investors: a risk-free asset with a price of p₁ = 1 and that pays R_f with certainty at date 1, and a risky asset with a price of p₂ = 1 and that pays R^- at date 1, where R^- is normally distributed with mean R^- and variance σ². An expected utility maximizer with von Neumann-Morgenstern utility function u(c) = -e-^αc and date 0 wealth of w holds a portfolio of these two assets. For simplicity, we will allow consumption at date 1 to take negative values.

(a) Calculate the investor's expected utility if she holds a proportion x of her date 0 wealth in the risky asset.

(b) What level of x maximizes her expected utility?

(d) Now suppose that the investor also has normally-distributed labor income L^- at date 1, with mean L^-, variance θ², and covariance with the risky asset's payoff equal to ρσθ. That is, her date 1 consumption equals the sum of her portfolio payoff and her labor income. Derive the expected utility maximizing portfolio x and discuss how it is affected by labor income.

Reference no: EM132187854

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