in Mr. Friers average return over the five-year pe- riod will affect final wealth by a factor of (1 .1342)5 .487, meaning that final wealth will be less than one-half of its expected value. This is a larger impact than the 30% one- year swing. Ms. Mavin is wrong: Time diversification does not reduce risk. Although it is true that the per year average rate of return has a smaller standard deviation for a longer time hori- zon, it also is true that the uncertainty compounds over a greater number of years. Unfor- tunately, this latter effect dominates in the sense that the total return becomes more uncertain the longer the investment horizon. Figures 8C.1 and 8C.2 show the fallacy of time diversification. They represent simu- lated returns to a stock investment and show the range of possible outcomes. Although the confidence band around the expected rate of return on the investment narrows with invest- ment life, the confidence band around the final portfolio value widens. Again, the coin-toss analogy is helpful. Think of each years investment return as one flip of the coin. After many years, the average number of heads approaches 50%, but the possible deviation of total heads from one-half the number of flips still will be growing. II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill Companies, 2001           256 PART II Portfolio Theory     Figure 8C.2 Dollar returns on common stocks. Simulated distributions of nominal wealth index for the period 2000-2017 (year-end 1999 equals 1.00).     Wealth   50         10