Understanding the Arbitrage Pricing Theory for Financial Asset Valuation

The Model of Valuation of Financial Assets by the Arbitrage Pricing Theory

Stephen Ross developed this theory in 1976. It is an equilibrium model for asset valuation. Its central idea is the expected return on an asset must be a linear function of its systematic risk. The APT considers that the only risk that the market is willing to remunerate is the systematic one, since the rest of the risk can be eliminated via diversification. According to this model, the systematic risk is the fundamental explanatory factor of the performance of the profitability of financial assets, although that is not measured only by the beta coefficient of the profitability of an individual asset with respect to the profitability of the market portfolio, but by a series of 'beta' coefficients associated with other explanatory factors not specified a priori that operate together (common risk factors). According to this model, the profitability of an asset depends on several macroeconomic, market, and specific title factors. The APT assumes that the returns on assets are generated by a stochastic process of the type:

Fjt - risk premium associated with a given factor

bij - sensitivity of the profitability of the asset to a certain factor. The interpretation of the formula is direct: in an equilibrium market, the profitability that an investor expects to obtain from an asset is equal to that which he would obtain from a risk-free investment plus compensation for the systematic risk he has to bear. This compensation, in turn, is given by the different risk premiums with respect to the common explanatory factors of profitability, multiplied by the corresponding beta coefficients with respect to each of the factors contemplated. Unlike CAMP, the APT is not based on the efficiency hypothesis of the market portfolio. It is part of the assumption that in an equilibrium market there should be no untapped investment opportunities, that is, no investor who changes the composition of the portfolio will be able to obtain a higher return through arbitration than they would have obtained.