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Concept
Intertemporal portfolio choice
Summary
Intertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion. The set of asset proportions at any time defines a portfolio. Since the returns on almost all assets are not fully predictable, the criterion has to take financial risk into account. Typically the criterion is the expected value of some concave function of the value of the portfolio after a certain number of time periods—that is, the expected utility of final wealth. Alternatively, it may be a function of the various levels of goods and services consumption that are attained by withdrawing some funds from the portfolio after each time period.
Stochastic programming#Multistage portfolio optimization
In a general context the optimal portfolio allocation in any time period after the first will depend on the amount of wealth that results from the previous period's portfolio, which depends on the asset returns that occurred in the previous period as well as that period's portfolio size and allocation, the latter having depended in turn on the amount of wealth resulting from the portfolio of the period before that, etc. However, under certain circumstances the optimal portfolio decisions can be arrived at in a way that is separated in time, so that the shares of wealth placed in particular assets depend only on the stochastic asset return distributions of that particular period.
If the investor's utility function is the risk averse log utility function of final wealth
then decisions are intertemporally separate. Let initial wealth (the amount that is investable in the initial period) be and let the stochastic portfolio return in any period (the imperfectly predictable amount that the average dollar in the portfolio grows or shrinks to in a given period t) be depends on the portfolio allocation—the fractions of current wealth inherited from the previous period that are allocated at the start of period t to assets i (i=1, ...
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