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Arbitrage Pricing Theory (APT)

Let's digress a bit on the underlying theory of factor models. Under some fairly general assumptions and using a no-arbitrage argument, we can show that the factor returns (betas) in factor models must be related across assets and that the asset's return is linear in the factors. The seminal work is Ross (1976).

Other references on APT and multifactor models can be found at www.kellogg.northwestern.edu/faculty/korajczy/htm/aptlist.htm.

Not only is the no-arbitrage argument less restrictive than the equilibrium requirement underlying CAPM, arbitrage pricing theory (APT) expands the number of factors beyond just the market return. This is a powerful result, as we see further on where we try to estimate parameters for large portfolios of assets; APT requires estimating several factor returns that can then be used to model the covariance matrix of returns across assets. This greatly reduces the data requirements necessary for estimation purposes. Recall that in the N asset case, we need to estimate covariances and N variances. For large portfolios, we will see that there are insufficient observations available to do so as N begins to overwhelm the number of time periods T. The S&P 500, for example, requires estimates for 500 variances and 124,750 covariances. ...