( rA) rB E ( rB)       measured in percentage terms, as is the expected value. The variance is also called the sec- ond central moment around the mean, with the expected return itself being the first moment. Although the variance measures the average squared deviation from the expected value, it does not provide a full description of risk. To see why, consider the two probability dis- tributions for rates of return on a portfolio, in Figure 6A.1. A and B are probability distributions with identical expected values and variances. The graphs show that the variances are identical because probability distribution B is the mirror image of A. What is the principal difference between A and B? A is characterized by more likely but small losses and less likely but extreme gains. This pattern is reversed in B. The difference is important. When we talk about risk, we really mean "bad surprises." The bad surprises in A, although they are more likely, are small (and limited) in magnitude. The bad surprises in B are more likely to be extreme. A risk-averse investor will prefer A to B on these grounds; hence it is worthwhile to quantify this characteristic. The asymmetry of a distrib- ution is called skewness, which we measure by the third central moment, given by   n M3 Pr(s)[r(s) E(r)]3 s 1   Cubing the deviations from the expected value preserves their signs, which allows us to distinguish good from bad surprises. Because this procedure gives greater weight to larger deviations, it causes the "long tail" of the distribution to dominate the measure of skewness. Thus the skewness of the distribution will be positive for a right-skewed distribution such as A and negative for a left-skewed distribution such as B. The asymmetry is a relevant characteristic, although it is not as important as the magnitude of the