An Introduction to Arbitrage Pricing Theory
Arbitrage Pricing Theory is a theory of asset pricing starting with specific assumptions on the distribution of asset returns and relies on approximate arbitrage arguments.
The implementation of The Arbitrage Pricing Theory involves three steps:
- Identify the factors
- Estimate factor loadings of assets
- Estimate factor premia
Identify the Factors
Since the theory itself does not specify the factors, we have to construct the factors empirically:
- Using macroeconomic variables (changes in GDP growth, changes in T-bill yield, changes in yield spread between T-bonds and T-bills, changes in default premium on corporate bonds, changes in oil prices, etc.)
- Using statistical analysis – factor analysis (estimate covariance of asset returns, extract factors from the covariance matrix)
- Data mining (Explore different portfolios to find those whose returns can be used as factors)
SEE ALSO: What Is the Capital Asset Pricing Model (CAPM)?
Factor Loadings
Given the factors, we can regress past asset returns on the factors to estimate factor loadings.
Factor Premia
Given the factor loading of individual assets, we can construct factor portfolios.
Strength and Weaknesses of The Arbitrage Pricing Theory
- The model gives a reasonable description of return and risk.
- Factors seem plausible.
- No need to measure market portfolio correctly.
- Model itself does not say what the right factors are.
- Factors can change over time.
- Estimating multi-factor models requires more data.
The Bottom Line
Arbitrage Pricing Theory is based on the factor model of returns and the approximate arbitrage argument that predicts a return using the relationship between an expected return and macroeconomic factors.
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