# Arbitrage pricing theory (APT)

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186 Arbitrage pricing theory (APT) assumes that expected return of a financial asset can be predicted using macro-economic factors. APT proposes an idea of a linear regression model between expected return of an asset and various macro-economic factors.

Expected return of the financial asset should be sensitive to the changes in each macro-economic factor in the proposed linear regression model; where sensitivity factors represent the beta co-efficients in the regression model.

Arbitrage pricing theory (APT) does not predict completely risk free return which we generally understand from the term Arbitrage.

APT Equation:

E(rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 + bj4RP4 + …

where:
E(rj) = the asset’s expected rate of return
rf = the risk-free rate
bj = the sensitivity of the asset’s return to the particular factor
RP = the risk premium associated with the particular factor

APT Theory: Arbitrage pricing theory was proposed by economist Stephen Ross in 1976, as an alternative to Capital Asset pricing model (CAPM). CAPM tries to estimate the incremented expected return based on additional risk while investing in a risky portfolio rather than investing  in risk free portfolio; whereas APT assumes market sometimes misprice the financial asset and a trader or arbitrager tries to take advantage of this miss-pricing before market corrects itself.

Arbitrage pricing model; tries to predict the fair value of an asset based on linear regression model and whenever a financial asset seems to be under\over valued at a given market price as per predicted value of linear regression model; the arbitrager tries to take the opposite position and take advantage of the mispricing before market corrects itself.

Breaking APT: APT theory proposed by Stephen; assumes whenever current market price of an asset diverges from the predicted price of an asset; arbitrage should bring the market value back to the fair value of the asset. Arbitrage assumes that:

1. Based on one price law: Two items with exactly same features cannot be sold at different prices.
2. If they sell at a different price, arbitrage will take place in which arbitrageurs buy the good which is cheap and sell the one which is higher priced till all prices for the goods are equal.

The APT has number of advantages like APT is not restrictive like CAPM in its requirements about the individual portfolio. 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.

Assumptions of Arbitrage Pricing Theory:

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 return on the asset by using arbitrage.

APT has three major assumptions:

1. Capital markets are perfectly competitive.
2. Investors always prefer more to less wealth.
3. The stochastic process generating expected asset returns can be expressed as a linear function of a set of macro-economic variables.

Contrast to CAPM:

1. In APT, the assumption of investors utilizing a mean-variance framework is replaced by an assumption of the process of generating security returns.
2. APT requires that the returns on any stock be linearly related to a set of indices.
3. In APT, multiple factors have an impact on the returns of an asset in contrast with CAPM model that suggests that return is related to only one factor, i.e., systematic risk

1. Fewer restrictions: APT has fewer restrictions regarding the types of information allowed to perform predictions. Because there is more information available, with fewer overall restrictions, the results tend to be more reliable with the arbitrage pricing theory than with competitive models.
2. Allows for more source of Risk: The APT allows for multiple risk factors to be included within the data set being examined instead of excluding them. This makes it possible for individual investors to see more information about why certain stock returns are moving in specific ways.
3. APT does not specify risk factor: APT allows the arbitrager to decide upon the risk factor (Macro –Economic Variable) to be included into the model.
4. APT gives investor to decide upon the arbitrage opportunity: As APT model gives investor the flexibility to choose the macro-economic variable while deciding upon the linear regression model; so investor could decide the opportunity as per market understanding.

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