Answer to Question #106988 in Economics for Peace Adah

Question

Consider the decision problem of investing an amount of wealth W into a risky asset with return

0.1 with probability p
R=
−0.05with probability 1−p


and into a risk-less asset with risk-free interest rate r=2%. You are a risk averse investor with utility function
U(WT)=10+ln(WT)

where WT is the amount of wealth at the end of the investment.


a) Find the optimal allocation in risky and risk-less assets as a function of
the probability p and the initial amount of wealth W invested.
b) Compute the optimal allocation for a probability value p=0.5.
c) What is the lower bound of the probability p for investing a positive
share into the risky asset?
d) What is the lower bound of p for starting to borrow money at the risk-
less interest rate and invest an amount larger than W in the risky
asset?

Answer 1

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