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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.9P

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