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=α_i+β_i1F_1+β_i2F_2++β_i2F_n+ε_ir\_{i}=\alpha\_{i} +\beta\_{i1} F\_{1}+\beta\_{i2} F\_{2}+\cdot\cdot\cdot+\beta\_{i2} F\_{n}+\varepsilon \_{i}


  • Ri = Asset returns
  • αi = The asset specific factor
  • βin = Sensitivity of the ith asset to the factor n.
  • Fn = Systematic (Macroeconomic) factor

Some Observations

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