ICAPM
The Intertemporal Capital Asset Pricing Model, or ICAPM, was an alternative to the CAPM provided by Robert Merton. It is a linear factor model with wealth and state variable that forecast changes in the distribution of future returns or income.
In the ICAPM investors are solving lifetime consumption decisions when faced with more than one uncertainty. The main difference between ICAPM and standard CAPM is the additional state variables that acknowledge the fact that investors hedge against shortfalls in consumption or against changes in the future investment opportunity set.
Merton considers a continuous time market in equilibrium. The state variable (X) follows a brownian motion:
The investor maximizes his Von Neumann–Morgenstern utility:
whereT is the time horizon and B[W(T),T] the utility from wealth (W).
The investor has the following constraint on wealth (W). Let be the weight invested in the asset i. Then:
where is the return on asset i. The change in wealth is:
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