ANSWER E PLEASE ONLY 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. c) Does the investor put more or less of his portfolio into the risky asset as his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How does α change with wealth? e) Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
ANSWER E PLEASE ONLY
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.
c) Does the investor put more or less of his portfolio into the risky asset
as his wealth increases?
d) Now find the share of wealth, α, invested in the risky asset. How does
α change with wealth?
e) Calculate relative risk aversion for this investor. How does relative
risk aversion depend on wealth?
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