Portfolio Problem:

An 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 a 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. 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 the risk preferences of this investor, are they risk-averse, risk-neutral, 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, , invested in the risky asset. How does change with wealth?

e) Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?