Financial Economics by Thorsten Hens

Author:Thorsten Hens
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg

Hence, the likelihood ratio process is equal to the marginal rates of substitution and we can compute for :

In principle it would thus suffice to know any utility function u i and any consumption process c i to determine the likelihood ratio process. But one may argue that individual decisions are subject to mistakes so that determining the likelihood ratio process from an arbitrarily chosen agent may be quite misleading. That is the reason why for empirical purposes the likelihood ratio process is determined from aggregate consumption assuming some simple parametric form of the utility function, like CRRA (see Sect. 2.​2.​3). How this aggregation will be justified is shown in Sect. 4.6. In any case we see that ℓ should be a decreasing function of aggregate consumption because u is typically concave. More specifically, for u′(c s ) = a − bc s ℓ is linear in c s and for u′(c s ) = c s −α ℓ is convex in c s etc.

Later, in Sect. 4.4, we give four examples for this identification. First we confirm that the CAPM is still a special case of our model, then we derive the APT by introducing background risk, we derive the C-CAPM by identifying the likelihood ratio process with the marginal rates of substitution of the investors and finally we derive a behavioral CAPM based on Prospect Theory.

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