compounds and increases the expected future value. Once the time horizon is long enough, the tendency toward higher returns will increase even the worst-case scenarios. Table 30.5 illustrates this relationship by comparing historical real after-tax results for stocks and bonds. For short holding periods, the worst-case results of stocks were much worse than the worst-case results of bonds. For 10-year holding periods, however, the worst-case results for bonds were actually lower than the worst-case results for stocks. For 25-year horizons, the worst-case results for stocks had twice the wealth accumulation of bonds despite the greater volatility of stock returns.1 Investors should be sensitive to interim risk as well as terminal risk. For example, an investor with a 25-year horizon might look at the rightmost column in Table 30.5 and observe that there has never been a 25-year period in which stocks failed to produce real, after-tax wealth accumulation. The choice of stocks over bonds might seem obvious. But the investor should also consider whether he or she would have the tolerance for the interim risk. The results for the two- and three-year holding periods demonstrate that there were instances when the real value of a stock portfolio fell to about 40 percent of the original principal during one of the 25-year holding periods. APPLICATION Let us complete this analysis by applying the framework we described in the previous chapter. A wealthy investor's goal is: Subject to funding my consumption needs, maximize the risk-adjusted real value of wealth that will be received, net of income and estate taxes, by my intended heirs and charitable beneficiaries. We will estimate the after-tax wealth that might have been accumulated under a range of asset allocation plans and spending requirements over 20-year holding periods. We will consider five asset allocation plans ranging from conservative to aggressive (see Table 30.6). We will define a conservative investor as having 40 percent in stock, 40 percent in bonds, and 20 percent in cash. We will define an aggressive investor as having 80 percent in stock, 15 percent in bonds, and 5 percent tables 30.5 through 30.11 show average, maximum, and minimum results for various rolling holding periods. The first such period begins January 1926. The next begins February 1926 and so forth. Calculating an average result by merely averaging the results of these various holding periods would overweight the data in the middle of the data set. The first month and last month of the data set will each be used in just one holding period. The second and next to last months would each be used in two holding periods. Months in the middle of the data set would be used in many different holding periods. In order to avoid any distortion, we calculated the average results by compounding the average returns in the underlying data set. The maximum and minimum results are based on the results of the rolling holding periods.