to the expected profit that is attributable to the risk of the prospect.   Y E(W) - WCE $100,000 $86,681.87 $13,318.13   This investor views $86,681.87 for certain as being equal in utility value as $100,000 at risk. Therefore, she would be indifferent between the two.       CONCEPT C H E C K ☞ QUESTION B.1 Suppose the utility function is U(W) W . a. What is the utility level at wealth levels $50,000 and $150,000? b. What is expected utility if p still equals .5? c. What is the certainty equivalent of the risky prospect? d. Does this utility function also display risk aversion? e. Does this utility function display more or less risk aversion than the log utility function?     Does revealed behavior of investors demonstrate risk aversion? Looking at prices and past rates of return in financial markets, we can answer with a resounding "yes." With re- markable consistency, riskier bonds are sold at lower prices than are safer ones with other- wise similar characteristics. Riskier stocks also have provided higher average rates of II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           182 PART II Portfolio Theory     return over long periods of time than less risky assets such as T-bills. For example, over the 1926 to 1999 period, the average rate of return on the S&P 500 portfolio exceeded the T-bill return by about 9% per year. It is abundantly clear from financial data that the average, or representative, investor ex- hibits substantial risk aversion. For readers who recognize that financial assets are priced to compensate for risk by providing a risk premium and at the same time feel the urge for some gambling, we have a constructive recommendation: Direct your gambling impulse to investment in financial markets. As Von Neumann once said, "The stock market is a casino with the odds in your favor." A small risk-seeking investment may provide all the excite- ment you want with a positive expected return to boot!