Arbitrage pricing theory

Arbitrage pricing theory (APT) holds that the expected return of a financial asset can be modelled as a linear function of various macro-economic factors, where sensitivity to changes in each factor is represented by a factor specific Beta. 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.

Asset pricing

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Arbitrage

The APT predicts that asset prices must reflect the return implied by the model - as above the asset price should equal the expected end of period price discounted at the APT rate. If the price diverges, arbitrage by investors should bring it back into line. (See Rational pricing.)

(a) Where today's price is too low:

The implication is that at the end of the period the correctly priced asset would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate. The arbitrageur could therefore 1) short sell any correctly priced asset today 2) buy the mispriced-asset with the proceeds. At the end of the period he would 3) sell the mispriced asset 4) use the proceeds to buy back the correctly priced asset and 5) pocket the difference.

(b) Where today's price is too high:

The implication is that at the end of the period the correctly priced asset would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at less than this rate. The arbitrageur could therefore 1) short sell the mispriced-asset today 2) buy any correctly priced asset with the proceeds. At the end of the period he would 3) sell the correctly priced asset 4) use the proceeds to buy back the mispriced-asset and 5) pocket the difference.

Relationship with the Capital asset pricing model

The APT along with the Capital asset pricing model (CAPM) is one of two influential theories on asset pricing. The APT differs from the CAPM in that it is less restrictive in its assumptions. It allows for an explanatory (as opposed to statistical) model of asset returns. It assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". In some ways, the CAPM can be considered a "special case" of the APT in that the Securities market line represents a single-factor model of the asset price, where Beta is exposure to changes in value of the Market.

Using the APT

Chen, Roll and Ross identified the macro-economic factors that best explained security returns: surprises in inflation; surprises in GNP; surprises in investor confidence; surprise shifts in the yield curve. As with the CAPM, the Betas are found via a regression of historical security returns on the factor.

References

• Chen, N.F, and Ingersoll, E., Exact pricing in linear factor models with finitely many assets: A note, Journal of Finance June 1983
• Roll, Richard and Stephen Ross, An empirical investigation of the arbitrage pricing theory, Journal of Finance, Dec 1980,
• Ross, Stephen, The arbitrage theory of capital pricing, Journal of Economic Theory, v13, 1976