taking the risk is measured by the first moment, which is the mean of the return distribution. Higher moments characterize the risk. Even moments provide in- formation on the likelihood of extreme values, and odd moments provide information on the asymmetry of the distribution. 2. Investorsrisk preferences can be characterized by their preferences for the various mo- ments of the distribution. The fundamental approximation theorem shows that when portfolios are revised often enough, and prices are continuous, the desirability of a port- folio can be measured by its mean and variance alone. 3. The rates of return on well-diversified portfolios for holding periods that are not too long can be approximated by a normal distribution. For short holding periods (e.g., up to one month), the normal distribution is a good approximation for the lognormal.     1. The Smartstock investment consulting group prepared the following scenario analysis for the end-of-year dividend and stock price of Klink Inc., which is selling now at $12 per share:     End-of-Year   Scenario Probability Dividend ($) Price ($)   1 .10 0 0 2 .20 0.25 2.00 3 .40 0.40 14.00 4 .25 0.60 20.00 5 .05 0.85 30.00 II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           178 PART II Portfolio Theory     Compute the rate of return for each scenario and a. The mean, median, and mode. b. The standard deviation and mean absolute deviation. c. The first moment, and the second and third moments around the mean. Is the proba- bility distribution of Klink stock positively skewed?     SOLUTIONS TO CONCEPT C H E C K S A.1. Investors appear to be more sensitive to extreme outcomes relative to moderate