Suppose you have the utility function u(,2) (k 2)2 where is the expected return on your portfolio, 2 is the portfolios variance, and k 0 is a constant Also suppose you invest a fraction of your wealth in the risk free asset with return rF, and the remaining fraction in the market portfolio (expected return M and variance M2) Determine the values of k for which you invest more than your wealth (and borrow risk free) and the values of k for which you invest less than your wealth (and lend risk free) in the market portfolio How would you define k And finally, given the definition of k, how does it fit with your answer above

Question: Suppose you have the utility function u(,2) = (k/2)2 where is the expected return on your portfolio, 2 is the portfolios variance, and

Suppose you have the utility function u(μ,σ2) = μ –(k/2)σ2 where μ is the expected return on your portfolio, σ2 is the portfolio’s variance, and k>0 is a constant. Also suppose you invest a fraction of your wealth in the risk free asset with return rF, and the remaining fraction in the market portfolio (expected return μM and variance σM2). Determine the values of k for which you invest more than your wealth (and borrow risk free) and the values of k for which you invest less than your wealth (and lend risk free) in the market portfolio.

How would you define k? And finally, given the definition of k, how does it fit with your answer above?

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