Arbitrage pricing theory

In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly—the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line.

The theory was proposed by the economist Stephen Ross in 1976.

Risky asset returns are said to follow a factor intensity structure if they can be expressed as:

Idiosyncratic shocks are assumed to be uncorrelated across assets and uncorrelated with the factors.

The APT states that if asset returns follow a factor structure then the following relation exists between expected returns and the factor sensitivities:

That is, the expected return of an asset j is a linear function of the asset's sensitivities to the n factors.

Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market, and the total number of factors may never surpass the total number of assets (in order to avoid the problem of matrix singularity).

Arbitrage is the practice of taking positive expected return from overvalued or undervalued securities in the inefficient market without any incremental risk and zero additional investments.

In the APT context, arbitrage consists of trading in two assets – with at least one being mispriced. The arbitrageur sells the asset which is relatively too expensive and uses the proceeds to buy one which is relatively too cheap.

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