Consider an investor who must decide how much of his initial wealth w to put into a risky asset. Let the amount invested in risky asset be denoted by . The risky asset can have any of the positive or negative rates of return ri with probabilities pi (i=1,2,,n). The investor also has an option of investing in a riskless asset that gives back a total of 1 for every dollar invested.

1. Find out the condition under which a risk averse individual will abstain from investing in the risky asset. Interpret it.

Suppose now that the risk averse investor does invest a part of their wealth in risky asset (i.e., assume an interior solution). Prove that under DARA( Decreasing Absolute Risk Aversion ), risky asset is a normal good.

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