Arbitrage Theory

24/11/2020 0 By indiafreenotes

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset’s returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced.

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 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. The linear factor model structure of the APT is used as the basis for many of the commercial risk systems employed by asset managers.

Assumptions in the Arbitrage Pricing Theory

The Arbitrage Pricing Theory operates with a pricing model that factors in many sources of risk and uncertainty. Unlike the Capital Asset Pricing Model (CAPM), which only takes into account the single factor of the risk level of the overall market, the APT model looks at several macroeconomic factors that, according to the theory, determine the risk and return of the specific asset.

These factors provide risk premiums for investors to consider because the factors carry systematic risk that cannot be eliminated by diversifying.

The APT suggests that investors will diversify their portfolios, but that they will also choose their own individual profile of risk and returns based on the premiums and sensitivity of the macroeconomic risk factors. Risk-taking investors will exploit the differences in expected and real returns on the asset by using arbitrage.

The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (CAPM). Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.

However, this is not a risk-free operation in the classic sense of arbitrage, because investors are assuming that the model is correct and making directional trades rather than locking in risk-free profits.

Arbitrage in the APT

The APT suggests that the returns on assets follow a linear pattern. An investor can leverage deviations in returns from the linear pattern using the arbitrage strategy. Arbitrage is the practice of the simultaneous purchase and sale of an asset on different exchanges, taking advantage of slight pricing discrepancies to lock in a risk-free profit for the trade.

However, the APT’s concept of arbitrage is different from the classic meaning of the term. In the APT, arbitrage is not a risk-free operation – but it does offer a high probability of success. What the arbitrage pricing theory offers traders is a model for determining the theoretical fair market value of an asset. Having determined that value, traders then look for slight deviations from the fair market price, and trade accordingly.

Arbitrage Pricing Theory

The Formula for the Arbitrage Pricing Theory Model Is       

E(R)I =E(R)z+(E(I)−E(R)z) ×βn     

where:

E(R)I =Expected return on the asset

Rz=Risk-free rate of return

βn=Sensitivity of the asset price to macroeconomic

factor n

Ei=Risk premium associated with factor i