# Risky Assets

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Suppose that there is one safe and one risky asset and that the investor has initial wealth . Investing in the risky asset yields the total (principal plus interest) of x(1+r), where r is a random variable with density f(r), r where < 0 < . The safe asset pays zero interest. The investor's final random wealth is Assume that , i.e., that short sales and borrowing at the riskless rate of interest to invest in the risky asset are not allowed. The risk averse von Neumann-Morgenstern investor chooses x to maximize . Prove that if the investor's measure of absolute risk aversion is a decreasing function of w, the wealthier investor will hold more of the risky asset.

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