Essays on endowment fund management

and people’s emotional disposition. Regret could be defined as the pain relative to not having taken a better action, whereas disappointment is the pain from comparing the actual outcome with a better one. In other words, regret captures the difference between the performance of the selected portfolio and the performance of any other foregone portfolio; whereas disappointment captures the discrepancy between actual and expected performance. Shefrin (2000) presents an example from financial markets that would help us differentiate these closely related concepts, both of which is based on the act of comparison: It was late July of 1998 when financial markets were jittery about economic problems in Asia and the market had just fallen by 20 percent. Imagine a conversation between you and two of your friends, George and Paul. George had a lot of his portfolio in stocks and was fretting about a severe market decline. In the end, he decided to sell his stocks and buy CDs instead. Paul, instead, had been holding CDs which had just matured. He thought that the market would rebound and considered buying mutual fund shares. However, he renewed his CDs. Thereafter, the market appreciated by over 25 per cent. Both investors held CD portfolios during this period. Both would have been better off by holding stocks. The question is; which one feels worse about the situation? Most people would say George is not only disappointed about the outcome but also experiences regret stemming from the action he took. So, he seems to be worse off emotionally. Interestingly, this example proves the point that behavioral 92 aspects are typically path-dependent, meaning where you start, what you think and when all lead to distinct emotions at the end. Regret and disappointment are important factors when it comes managing investment portfolios that are connected to a certain kind of benchmarking mechanism. We could say that comparis n is the psychological basis for benchmarking. I agree with Shefrin that people are hard-wired to engage in comparison, and measure themselves against some benchmark. I would further argue that the challenge becomes how to come up with the most relevant benchmark in any given situation so that whatever actions we might take would not result in regret and disappointment. Those who are fearful of experiencing regret may fear taking an action that will leave them vulnerable to regret. People are especially prone to feeling the regret of a decision that turned out badly when they feel responsible for that decision. Institutional investors such as pension plans and endowments transfer responsibility when they engage the services of money managers. In addition to tra sferring the responsibility of managing the funds at the institutions, board members hire consultants for advice on which money managers to choose for the institutional portfolio. It could be conjectured that trustees at various pension funds and endowments create a psychological option for themselves by taking these actions on behalf of the institution for which they serve as fiduciaries. When the portfolios perform well, they can take the credit, otherwise, they can shift the blame to the money managers and consultants. Very recently, Unilever (U.K.) even sued Merrill Lynch Asset Management for negligence and reportedly settled the case outside 93 the court system at the expense of the money management firm. So, we started witnessing legal actions against money managers that perform below par for not having adhered to the guidelines set forth by the client. There is also one more reason why institutions find the (partial) transfer of responsibility appealing: cognitive limitations. I would argue that some fiduciaries are unable to differentiate between payoff-irrelevant information (also called ‘noise’) and payoff-relevant information, mostly due to cognitive biases in processing information. Lastly, the fact that investors have the tendency to evaluate gains and losses frequently leads to second-guessing exercises and attempting to resolve the regret and disappointment issue. Here, I will concentrate on the disappointment aversion framework, introduced by Gul (1991)27, and investigate the optimal hedging behavior for a disappointment-averse hedger. Unlike the notion of risk aversion, feelings of disappointment violate the separability axioms that impose that preferences are independent across states; that is, outcomes in events that did not occur affect attitudes towards outcomes that did. Regret, on the other hand, involves comparing outcomes in a given event with those that would have occurred in the same event had the agent chosen a different act or lottery or portfolio for that matter. Disappointment involves comparing outcomes from different events in the same act or lottery. In principle, one could be disappointed without ever having choices to make. The preferences will be a one parameter extension of standard 27 Grant and Kajii (1998) and Skiadas (1997) provided two other notions of disappointment aversion. Grant et al. (2001) demonstrate how different formalizations lead to different notions of disappointment aversion by comparing the models of Gul, Grant & Kajii, and Skiadas. 94 iso-elastic preferences in the usual expected utility framework. They have the characteristic that good outcomes that are above the certainty equivalent are downweighted relative to bad outcomes. The use of disappointment averse preferences is particularly beneficial in the case of currency hedging due to the complexity of the issue and resulting behavioral concerns of fiduciaries. It is shown that disappointment aversion utility displays first order risk aversion, where the risk premium is proportional to standard deviation, as opposed to variance in the case of expected utility. This feature helps one to account for the phenomenon that individuals are risk averse with respect to gambles which yield a large loss with small probability (as in the stock market) but risk loving with respect to gambles that involve winning a large prize with small probability (as in lottery gambles). Both disappointment aversion and loss aversion, according to the prospect theory of Kahneman and Tversly (1979), define the utility function asymmetrically over gains and losses relative to a reference point. For a loss- aversion utility function, the reference point is arbitrarily exogenously chosen, whereas disappointment-averse utility function determines the reference point endogenously that could be updated over time. The second appealing aspect of this kind of framework is that it is fully axiomatic and provides a normative theory, eliminating the need for ad hoc techniques witnessed in the descriptive theoretical frameworks. Lastly, the fact that standard preferences are a spe ial case of disappointment averse preferences with the loss aversion parameter put 95 equal to one. Thus, one could capture many of the asymmetric affects of loss aversion without resorting to behavioral theory28. The preferences of a disappointment averse agent could be summarized by [ ]( ),U R b , where U is a conventional utility function describing the utility of earning the rate of return R f om a given investment, and 0b ³ is a parameter that measures the degree of disappointment aversion. In the absence of disappointment aversion, the agent’s utility level is simply [ ]( )U R . Now, I will define the expected utility of a disappointment-averse agent as ( )V b with b representing the degree of disappointment aversion. Suppose that the agent faces uncertain rates of return, R, i n states of nature. Let m denote the certain return that yields the same utility level as the uncertain return: ( ) ( )V Ub m= . This means, the investor is indifferent between the prospect of a safe return and risky return in states of nature. The agent reveals disappointment aversion if she attaches extra disutility to circumstances wher the realized return is below m . The disappointment-averse utility function could be defined as: [ ] [ ]( ) ( ) ( ) ( ) |V E U R E U U R Rb b m m= - - < [ ]( ) ( ) |E U U R Rm m- < is the expected value of ( ) ( )U U Rm - , conditional on the realized return being below the certainty equivalent return. In other words, the term [ ]( ) ( ) |E U U R Rm m- < measures the average disappointment. It is the expected discrepancy between the certainty equivalence utility and the actual 28 A different treatment of an investor’s asymmetric response to gains and losses is given by Roy (1952), Browne (1999), Stutzer (2000), and Maenhout (2001), who model agents with the objective of minimizing the possibility of undesirable outcomes. 96 utility in states of nature where the realized return is below the certainty- equivalent return. Basically, the disappointment-averse expected utility equals the conventional expected utility, adjusted downwards by a measure of disappointment aversion, b , times the “conditional expected disappointment.” I will now define two states of nature, whereby the agent earns the return R in state 1 or 2, and 1 2R R> with probabilities ( ),1a a- , respectively. Now, we are in a position to redefine ( )V b : [ ]1 2 2( ) ( ) (1 ) ( ) (1 ) ( ) ( )V U R U R V U Rb a a b a b= + - - - - Further rearranging of the terms helps separate the utilities of earning 1R and 2R : ( ) ( ) ( )1 2( ) 1 1 ( ) 1 1 ( )V U R U Rb a a d a ad= - - + - +é ùë û where ( )1 1 b d a b = + - If the agent is disappointment-av rse, that is 0b > , he attaches extra weight ( )1 a ad- to bad states; i.e., in the case of 2R , when is disappointed (relative to the probability weight used in the conventional utility), and attaches a lesser weight ( )1a a d- - to good states. Note that when 0b = , V(.) simplifies to the conventional expected utility. I will define 1R and 2R as follows: ( )1 1 1f c f c LR W cm m m m= - - + + ( )2 2 2f c f c LR W cm m m m= - - + + 97 where 111 0 lnc S S m æ ö = ç ÷ è ø and 122 0 lnc S S m æ ö = ç ÷ è ø and 11 12S S< . Stated differently, in the case of an iternational portfolio, the good state refers to the spot currency rate being smaller than the one in the bad state. This refers to the fact that a smaller spot rate indicates appreciation of the foreign currency against the U.S. dollar, providing higher rturn on invested capital due to currency movements. All the remaining variables are as defined before. The objective is to find an optimal hedging behavior by maximizing the disappointment-averse utility function, V(b). On taking partial derivative with respect to W, we have ( ) ( ) ( ) ( ) ( )1 1 2 2( ) 1 1 ( ) 1 1 ( )f c f f c fV U R c U R cW b a a d m m a ad m m ¶ ¢ ¢= - - - - + - + - -é ùë û¶ The optimal value of W, *W , must satisfy the following condition: ( ) 0 V W b¶ = ¶ . The optimal forward position should equate the following two terms in the above equation: ( ) ( ) ( )( ) ( )1 1 2 21 1 ( ) 1 1 ( )f c f f c fU R c U R ca a d m m a ad m m¢ ¢- - - - = - - + - -é ùë û If we assign the same probability to states 1 and 2, this relationship could be simplified further. Given the fact that ( )1a a= - ; ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 ( ) 1 1 ( ) 1 ( ) 1 ( ) ( ) ( ) f c f f c f f c f f c f f c f c f f U R c U R c U R c U R c U R c U R c a a d m m a ad m m a ad m m a ad m m a a d m m a a d m m ¢ ¢- - - - = - - + - -é ùë û ¢ ¢- - - = - + - - ¢ ¢- - - = + - - 98 When a increases, the RHS increases more than the LHS. As a result, 1( )U R¢ must increase to restore the equality. That is, 1R must decrease, or equivalently, *W must decrease. In other words, an increase in th probability of the good state occurring reduces the optimal forward position, which is an intuitive conclusion based on the definition of the good state. That is, the higher the probability of the foreign currency appreciating , the less likely it is to hedge these currency positions. In other words, the endowment benefit more by not hedging any significant portion of the foreign exchange exposure. It could also be shown that * 0 W b ¶ < ¶ . As the hedger becomes more disappointment-averse, a smaller forward position will be held. This result is in line with the conclusion derived in the previous section, which introduced behavioral arguments into the traditional expected utility framework by defining different risk aversion parameters for asset and currency volatilities. 4. 4. Conclusion The purpose of this chapter was to incorporate behavioral issues as it relates to the active management of currency hedging of international portfolios in the context of traditional expected utility maximization as well as the axiomatic disappointment aversion frameworks. I have introduced separate risk aversion parameters for asset and currency markets, and due to the asymmetric nature of the compensation structure of currency managers, concluded that lower hedge ratios would arise, ceteris paribus. Alternatively, I evaluated the same problem in the disappointment averse utility function setting, and concluded that the more the 99 endowment fund manager gets disappointment averse, the less likely it is to have higher hedge ratios. Whatever the style of problem solving might be, the right approach for designing currency overlay program including the choice of the appropriate benchmark, the combination of an effectively diversified group of managers as well as performance monitoring should entail the analysis of the effects of various outcomes on the fund’s asset liability structure given financial objectives and governance constraints. As a further research inquiry I would a priori argue that the level of surplus, as defined by assets minus liabilities or excess return distribution, could be a significant determinant for the modeling of the active currency hedging issue. 100 References Abel, Andrew B. 1990. “Asset Prices under Habit Formation and Catching Up with the Joneses.” American Economic Review Papers and Proceedings 80, 38- 42. Admati, A. R., and O. Pfleiderer. 1997. “Does it all ad up? Benchmarks and the compensation f active portfolio managers.” Journal of Business 70, 323- 50. 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Weil, P. 1989. “The equity premium puzzle and the riskfree rate puzzle,” Journal of Monetary Economics. 109 Appendix Sensitivity Analysis Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5%, g=0.97, r=5%, n=-1 110 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % m=8%, s=20%, a=2%, p=2%, r=5%, g=0.42, r=5%, n=-1 111 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % 1 4 % 1 6 % 1 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % m=10%, s=20%, a=2%, p=2%, r=5%, g=0.7, r=5%, n=-1 112 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % m=14%, s=20%, a=2%, p=2%, r=5%, g=1.25, r=5%, n=-1 113 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=16%, s=20%, a=2%, p=2%, r=5%, g=1.53, r=5%, n=-1 114 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5%, g=0.97, r=1%, n=-1 115 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5%, g=0.97, r=3%, n=-1 116 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=7%, n=-1 117 Spending rate 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=9%, n=-1 118 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % m=12%, s=16%, a=2%, p=2%, r=5%,g=1.52, r=5%, n=-1 119 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=18%, a=2%, p=2%, r=5%,g=1.2, r=5%, n=-1 120 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=22%, a=2%, p=2%, r=5%,g=0.8, r=5%, n=-1 121 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % 1 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % m=12%, s=24%, a=2%, p=2%, r=5%,g=0.67, r=5%, n=-1 122 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=5%, n=-2 123 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % 4 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=8%, s=20%, a=2%, p=2%, r=5%,g=0.42, r=5%, n=-2 124 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=10%, s=20%, a=2%, p=2%, r=5%,g=0.7, r=5%, n=-2 125 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % 9 0 % m=14%, s=20%, a=2%, p=2%, r=5%,g=1.25, r=5%, n=-2 126 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % 1 4 % 1 6 % 1 8 % 2 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % m=16%, s=20%, a=2%, p=2%, r=5%,g=1.53, r=5%, n=-2 127 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=1%, n=-2 128 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=3%, n=-2 129 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=7%, n=-2 130 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % 4 0 % 4 5 % 5 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=9%, n=-2 131 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % 9 0 % m=12%, s=16%, a=2%, p=2%, r=5%,g=1.52, r=5%, n=-2 132 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=18%, a=2%, p=2%, r=5%,g=1.2, r=5%, n=-2 133 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=22%, a=2%, p=2%, r=5%,g=0.8, r=5%, n=-2 134 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=24%, a=2%, p=2%, r=5%,g=0.67, r=5%, n=-2 135 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=5%, n=0 136 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % m=8%, s=20%, a=2%, p=2%, r=5%,g=0.42, r=5%, n=0 137 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % m=10%, s=20%, a=2%, p=2%, r=5%,g=0.7, r=5%, n=0 138 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=14%, s=20%, a=2%, p=2%, r=5%,g=1.25, r=5%, n=0 139 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % 1 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=16%, s=20%, a=2%, p=2%, r=5%,g=1.53, r=5%, n=0 140 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=1%, n=0 141 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=3%, n=0 142 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=7%, n=0 143 Spending rate 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=9%, n=0 144 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=16%, a=2%, p=2%, r=5%,g=1.52, r=5%, n=0 145 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=18%, a=2%, p=2%, r=5%,g=1.2, r=5%, n=0 146 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % 4 % 5 % 5 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=22%, a=2%, p=2%, r=5%,g=0.8, r=5%, n=0 147 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=24%, a=2%, p=2%, r=5%,g=0.67, r=5%, n=0 148 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=5%, n=+1 149 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=8%, s=20%, a=2%, p=2%, r=5%,g=0.42, r=5%, n=+1 150 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=10%, s=20%, a=2%, p=2%, r=5%,g=0.7, r=5%, n=+1 151 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=14%, s=20%, a=2%, p=2%, r=5%,g=1.25, r=5%, n=+1 152 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=16%, s=20%, a=2%, p=2%, r=5%,g=1.53, r=5%, n=+1 153 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=1%, n=+1 154 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=3%, n=+1 155 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=7%, n=+1 156 Spending rate 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=9%, n=+1 157 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=16%, a=2%, p=2%, r=5%,g=1.52, r=5%, n=+1 158 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=18%, a=2%, p=2%, r=5%,g=1.2, r=5%, n=+1 159 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=22%, a=2%, p=2%, r=5%,g=0.8, r=5%, n=+1 160 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=24%, a=2%, p=2%, r=5%,g=0.67, r=5%, n=+1 161 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=5%, n=+2 162 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=8%, s=20%, a=2%, p=2%, r=5%,g=0.42, r=5%, n=+2 163 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=10%, s=20%, a=2%, p=2%, r=5%,g=0.7, r=5%, n=+2 164 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=14%, s=20%, a=2%, p=2%, r=5%,g=1.25, r=5%, n=+2 165 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=16%, s=20%, a=2%, p=2%, r=5%,g=1.53, r=5%, n=+2 166 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=1%, n=+2 167 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=3%, n=+2 168 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=7%, n=+2 169 Spending rate 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=20%, a=2%, p=2%, r=5%,g=0.97, r=9%, n=+2 170 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=16%, a=2%, p=2%, r=5%,g=1.52, r=5%, n=+2 171 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=18%, a=2%, p=2%, r=5%,g=1.2, r=5%, n=+2 172 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % 4 % 4 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=22%, a=2%, p=2%, r=5%,g=0.8, r=5%, n=+2 173 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % 3 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % 1 8 0 % 2 0 0 % m=12%, s=24%, a=2%, p=2%, r=5%,g=0.67, r=5%, n=+2 174 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=4.5%,g=0.63, r=6%, n=-2 175 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % 4 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % m=12%, s=20%, a=2%, p=2%, r=5.5%,g=1.16, r=6%, n=-2 176 Spending rate 0 % 5 % 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 % 4 0 % Stock allocation 0 % 1 0 % 2 0 % 3 0 % 4 0 % 5 0 % 6 0 % 7 0 % 8 0 % m=12%, s=20%, a=2%, p=2%, r=6%,g=1.25, r=6%, n=-2 177 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 5 0 % 1 0 0 % 1 5 0 % 2 0 0 % 2 5 0 % m=12%, s=20%, a=2%, p=2%, r=4.5%,g=0.63, r=6%, n=-1 178 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % 1 4 % 1 6 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % m=12%, s=20%, a=2%, p=2%, r=5.5%,g=1.16, r=6%, n=-1 179 Spending rate 0 % 2 % 4 % 6 % 8 % 1 0 % 1 2 % 1 4 % 1 6 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % m=12%, s=20%, a=2%, p=2%, r=6%,g=1.25, r=6%, n=-1 180 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % Stock allocation 0 % 5 0 % 1 0 0 % 1 5 0 % 2 0 0 % 2 5 0 % 3 0 0 % 3 5 0 % m=12%, s=20%, a=2%, p=2%, r=4.5%,g=0.63, r=6%, n=0 181 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % 1 0 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5.5%,g=1.16, r=6%, n=0 182 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % m=12%, s=20%, a=2%, p=2%, r=6%,g=1.25, r=6%, n=0 183 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % Stock allocation 0 % 5 0 % 1 0 0 % 1 5 0 % 2 0 0 % 2 5 0 % 3 0 0 % 3 5 0 % m=12%, s=20%, a=2%, p=2%, r=4.5%,g=0.63, r=6%, n=+1 184 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5.5%,g=1.16, r=6%, n=+1 185 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % m=12%, s=20%, a=2%, p=2%, r=6%,g=1.25, r=6%, n=+1 186 Spending rate 0 % 1 % 1 % 2 % 2 % 3 % Stock allocation 0 % 5 0 % 1 0 0 % 1 5 0 % 2 0 0 % 2 5 0 % 3 0 0 % 3 5 0 % m=12%, s=20%, a=2%, p=2%, r=4.5%,g=0.63, r=6%, n=+2 187 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % 9 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % 1 6 0 % m=12%, s=20%, a=2%, p=2%, r=5.5%,g=1.16, r=6%, n=+2 188 Spending rate 0 % 1 % 2 % 3 % 4 % 5 % 6 % 7 % 8 % Stock allocation 0 % 2 0 % 4 0 % 6 0 % 8 0 % 1 0 0 % 1 2 0 % 1 4 0 % m=12%, s=20%, a=2%, p=2%, r=6%,g=1.25, r=6%, n=+2 189 Vita Kurtay N. Ogunc was born in Istanbul, Turkey to Aysel and Kurtul Ogunc. After graduating from the Saint George Austrian College with a High School Diploma, he went on to receive a Bachelorof Business Administration degree from Marmara University in 1990, majoring in finance and quantitative methods. He then married her college sweetheart, Asli K. Ogunc, and together, they moved to the U.S. to pursue graduate studies. Kurtay obtained the Master of Business Administration degree from Western Michigan University in 1992, majoring in finance, and Master of Applied Statistics from Louisiana State University in 1997. He taught various courses in the Department of Information Systems & Decision Scien e and the Department of Finance at the E. J. Ourso College of Business Administration of LSU for 3 ½ years. Since January of 1994, the semester Kurtay joined LSU, he has worked in the investment operations of the Associate Vice Chancellor for Finance for six years in different roles, the last one being the Investment Manager in charge of the funds managed by the LSU Foundation. In May of 2000, Kurtay moved to Washington, DC to become the research coordinator of the investment consulting division and a specialist consultant in charge of currency overlay managers at Watson Wyatt & Company, a global human capital consulting firm. He will complete the degree of Doctor of Philosophy in May 2002.