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We are now prepared to introduce a more precise definition of risk aversion. An investor is said to be risk averse if his utility function is concave, which in turn means that the investor requires higher expected return to bear risk. Exhibit 1.1 displays the log function for various values of wealth. We can see that the level of utility increases but at a decreasing rate.

Alternatively, a risk-averse investor avoids taking risks with zero expected payoffs. That is, for risk-averse investors, , where is a zero mean random error that is independent from W.