Instead, our methodology values these options from a risk-averse investor's perspective using utility certainty equivalents.
Prior to T - 1, the computation is similar to Equation (12) but involves next period certainty equivalents
The investor exercises the option when the investor's own valuation of a share of ownership in the fund, expressed as a certainty equivalent, falls below the NAV.
Investors exercise when the current NAV exceeds the certainty equivalent of holding the hedge fund.
Prior to the terminal set of nodes, the value of the investment conditional on survival is given by its certainty equivalent, which we define as the current value of a risk-free security that matures at time T and provides a guaranteed level of utility equal to the expected utility of holding the hedge fund.
T-1,j] to express the certainty equivalent of the hedge fund investment at node (T - 1, j), so that the investor is indifferent between staying in the fund at node (T - 1, j) and exchanging for cash equal to [H.
Under CRRA utility, the indirect utility is also of the power form, which permits using the certainty equivalent in Equation (12) in the computation of Equation (13).
Table 1 shows these certainty equivalents for persons with two levels of risk tolerance--one is risk neutral and cares only about the expected value of the wealth distribution, the other is "moderately" risk averse.
We find that for the "moderately" risk-averse retiree, the certainty equivalent of the 100 percent stock allocation is substantially greater than the certainty equivalent of the life cycle allocation--$584,000 compared to $403,000.
TABLE 1 CERTAINTY EQUIVALENT WEALTH AT AGE 65, BY PORTFOLIO ALLOCATION RULES (in 1,000's of year 2000 dollars) Portfolio Allocation HS or Less College or More Risk Neutral 100% Riskless Index Bonds 199 265 50% Bonds, 50% Stocks 401 509 100% Stocks 852 1042 "Moderate" Risk Aversion 100% Riskless Index Bonds 199 265 50% Bonds, 50% Stocks 969 469 100% Stocks 523 686 Note: Assuming median value of SSW + DB Wealth Source: Poterba, Rauh, Venti and Wise (2005).