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. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
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. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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.
Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
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