Example of equilibrium model as Capital Asset Pricing Model

Question

Explain the example of equilibrium model as Capital Asset Pricing Model.

Answer 1

Capital Asset Pricing Model is an illustration of an equilibrium model, as opposed to a no-arbitrage model like Black-Scholes. The mathematics of Capital Asset Pricing Model is very easy. We relate the random return upon the ith investment, Ri, to the random return upon the market as an entire (or several representative index), RM by

R_i=α_i+β_iR_M+ ?_i

There i is random with zero mean and standard deviation ei, and uncorrelated along with the market return RM and another ?_j. There are three parameters related with all assets as: αi, βi and ei. In this representation we can notice that the return upon an asset can be decomposed in three parts: a constant drift; that random part common along with the index; and a random part not correlated with the index, ?_i. The random part
i is unique to the ith asset. See how all the assets are associated to the index but are otherwise totally uncorrelated.