Arbitrage pricing theory

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Arbitrage pricing theory (APT), in finance, is a general theory of asset pricing, that has become influential in the pricing of shares.

APT 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 model. If the price diverges, arbitrage should bring it back into line.

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

Contents 1 The APT model 2 Arbitrage and the APT 2.1 Arbitrage in expectations 2.2 Arbitrage mechanics 3 Relationship with the capital asset pricing model 4 Using the APT 4.1 Identifying the factors 4.2 APT and asset management 5 See also 6 References 7 External links

[edit] The APT model

If APT holds, then a risky asset can be described as satisfying the following relation:

where

• E(r_j) is the risky asset's expected return,
• RP_k is the risk premium of the factor,
• r_f is the risk-free rate,
• F_k is the macroeconomic factor,
• b_jk is the sensitivity of the asset to factor k, also called factor loading,
• and ε_j is the risky asset's idiosyncratic random shock with mean zero.

That is, the uncertain return of an asset j is a linear relationship among n factors. Additionally, every factor is also considered to be a random variable with mean zero.

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),

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