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.

1. What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?

2. Find A as a function of w.

3. Does the investor put more or less of his portfolio into the risky asset as his wealth increases?

4.Now find the share of wealth, , invested in the risky asset. How does change with wealth?

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