# Arbitrage Pricing Theory (APT)

We had seen earlier that CAPM, which is essentially a Single Index Model, considers that the returns of a stock are affected only by a single factor, which is the excess market returns.

The Arbitrage Pricing Theory takes a more complex approach and allows the returns of a stock to be influenced by multiple factors. These factors could be interest rates, inflation, exchange rates, etc.

The sensitivity of the returns to each factor is represented by the factor-specific beta coefficient.

This will help in pricing the asset more accurately, and if the actual price differs from the theoretical price, the arbitrage opportunities will exist which will eventually bring the price to its correct level.

Using APT, the returns of the risky asset can be represented as follows:

$r_{i}=\alpha_{i} +\beta_{i1} F_{1}+\beta_{i2} F_{2}+\cdot\cdot\cdot+\beta_{i2} F_{n}+\varepsilon _{i}$

Where:

- R
_{i}= Asset returns - α
_{i}= The asset specific factor - β
_{in}= Sensitivity of the ith asset to the factor n. - F
_{n}= Systematic (Macroeconomic) factor

### Some Observations

- The factors are macroeconomic aggregates rather than firm-specific characteristics.
- It’s a regression equation. The model is based on multivariate regression analysis.
- It assumes that the returns are generated by a factor model

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