Optimal Asset Allocation Over The Life Cycle For Heterogeneous Investors

Markowitz’s Portfolio Selection theory of1952has been seminal to agreat amount of research about not only optimal portfolio choices, but alsooptimal asset allocation for an individul investor who seeks to maximizehis or her utility through consumption. This field of research has obviousapplications in the everyday life since every single person or householdconstantly has to make allocation decision to reach optimal happiness.Very early the theory has been expanded to a multi-period optimizationproblem, attempting to capture the dynamism of the allocation mechanicbut only in the late20th century and in the last decade, the fast-growingpower of computers made possible the realization of models too complexto be solved analytically and required numerical approximation.In line with recent research about optimal asset allocation, this paperbuilds a model about an individual investor subject to labor incomebackground risk–that is to say his or her labor income possess a stochasticcomponent–who can at each period of his or her life-cycle chose betweenconsumption, investment and savings. However, where other authorsconsider only one investment option–usually a proxy for the marketportfolio–this paper proposes to divide the market into two types ofstocks: stocks correlated with labor income and stocks uncorrelated withlabor income. Stocks correlated with labor income can be viewed as stocksfrom the same industry as the one the investor works in and are referred toas industry stocks. The logic behind this choice is not only to analyze therelationship between labor income risk and asset allocation choices, butalso to present the investor with a way of dealing with his or her own laborincome risk through more liberty in the risky assets choices. It alsodifferentiates investors’ situations according to their labor income situation. This paper builds its own model of life-cycle optimal asset allocationby extending standard models with one more control variable and onemore random variable. These additions lead to a methodical algorithmoptimization in order to make the problem solvable by a standard computerin a reasonable amount of time. The paper describes theoretical andpractical issues encountered and solved during the research. In everymodel, the choice of parameters is crucial. This paper has decided to focuson Chinese data and makes use of both existing literature and databases togather realistic parameters. It then studies results of the algorithm througha parameters sensitivity analysis.The results show that the expected optimal asset allocation over thelife-cycle is in effect driven by several forces. First, the relative risk andreturn profiles of the two risky assets make them more or less attractive tothe investor. Then a positive correlation between the labor income and theindustry stocks make them less desirable whereas a negative correlationallows them to be used for hedging the labor income risk. Depending onthe borrowing constraints and the starting wealth, results may vary, but ingeneral this study shows that the expected optimal investment in industrystocks–relative to expected labor income–is “hump”-shaped centered onthe middle of the life-cycle. On the other hand, expected optimalconsumption follows a steady slowly growing trend with age and savingsare found to be following the wealth available at the beginning of eachperiod, minus a constant...