Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? b) Find A as a function of w.
Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? b) Find A as a function of w.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.9P
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Consider the following portfolio choice problem. The investor has initial wealth w and
utility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has net
real return of zero. There is also a risky asset with a random net return that has only
two possible returns, R1 with probability 1 − q and R0 with probability q. We assume
R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is
invested in the safe asset.
a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?
b) Find A as a function of w.
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