or speculative prospects with positive risk premia. Loosely speak- ing, a risk-averse investor "penalizes" the expected rate of return of a risky portfolio by a certain percentage (or penalizes the expected profit by a dollar amount) to account for the risk involved. The greater the risk, the larger the penalty. One might wonder why we assume risk aversion as fundamental. We believe that most investors would accept this view from simple introspection, but we discuss the question more fully in Appendix B of this chapter. We can formalize the notion of a risk-penalty system. To do so, we will assume that each investor can assign a welfare, or utility, score to competing investment portfolios based on the expected return and risk of those portfolios. The utility score may be viewed as a means of ranking portfolios. Higher utility values are assigned to portfolios with more attractive risk-return profiles. Portfolios receive higher utility scores for higher expected returns and lower scores for higher volatility. Many particular "scoring" systems are legitimate. One reasonable function that is commonly employed by financial theorists and the AIMR (As- sociation of Investment Management and Research) assigns a portfolio with expected re- turn E(r) and variance of returns 2 the following utility score:   U E(r) .005A 2 (6.1)   where U is the utility value and A is an index of the investors risk aversion. The factor of .005 is a scaling convention that allows us to express the expected return and standard de- viation in equation 6.1 as percentages rather than decimals. II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           TIME FOR INVESTINGS FOUR-LETTER WORD       What four-letter word should pop into mind when the stock market takes a harrowing nose dive? No, not those. R-I-S-K. Risk is the potential for realizing low returns or even losing money, possibly preventing you from meeting im- portant objectives, like sending your kids to the college of their choice or having the retirement lifestyle you crave. But many financial advisers and other experts say that these days investors arent taking the idea of risk as seriously as they should, and they are overexposing themselves to stocks. "The market has been so good for years that investors no longer believe theres risk in investing," says Gary Schatsky, a financial adviser in New York. So before the market goes down and stays down, be sure that you understand your tolerance for risk and that your portfolio is designed to match it.