The Arbitrage Pricing Theory (APT): What Is It?
An asset’s returns may be anticipated using the linear connection between the asset’s expected return and various macroeconomic factors that represent a systematic risk, according to the arbitrage pricing theory (APT), a multi-factor asset pricing model. It is a helpful tool for value investors to employ when examining portfolios to find assets that could be momentarily mispriced.
In the APT model, linear regression estimates the beta coefficients. To estimate the factor’s beta, past security returns are typically regressed on it.
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
Risk-free rate of returnβn=Sensitivity of the asset price to macroeconomic factor n
Ei=Risk premium associated with factor i
How the Theory of Arbitrage Pricing Operates
Stephen Ross, an economist, created the arbitrage pricing hypothesis in 1976 as an alternative to the capital asset pricing model (CAPM). Unlike the CAPM, APT posits that markets occasionally overprice assets before the market finally corrects itself and the securities move back to fair value. Arbitrageurs intend to profit on any differences from fair market value using APT.
However, since investors are betting on the model’s accuracy and making directional trades rather than locking in risk-free gains, this is not an arbitrage operation in the traditional sense.
An APT Mathematical Model
APT is more sophisticated than the CAPM, yet it is more versatile. Market risk is the sole component that the CAPM considers, but the APT method considers several parameters. Figuring out how susceptible a security is to various macroeconomic threats requires a lot of investigation.
Investors will experience a range of outcomes based on their selection of the criteria and how many of them are employed. However, most of a security’s return is often explained by four or five factors. (Read more about how the CAPM and arbitrage pricing theory vary to learn more about the distinctions between the two.)
APT factors are the types of systematic risk that a diversified investment portfolio cannot eliminate. Unexpected increases in inflation, changes in the gross national product (GNP), changes in corporate bond spreads, and shifts in the yield curve are among the macroeconomic variables that have shown to be the most accurate price forecasters. Other frequently utilized variables are the gross domestic product (GDP), commodity prices, market indexes, and currency rates.
Example of Application of Arbitrage Pricing Theory
As an illustration, the following four components may explain the return on a stock, and their sensitivity and related risk premiums have been determined.
- Growth of the gross domestic product: ß = 0.6, RP = 4%
- Rate of inflation: ß = 0.8, RP = 2%
- Prices for gold: ß = -0.7, RP = 5%
- Return for the Standard & Poor’s 500 Index: ß = 1.3, RP = 9%
- 3% is the risk-free rate.
- The anticipated return is determined as follows using the APT formula:
The expected return is equal to 3% plus (0.6 x 4%) plus (0.8 x 2%) plus (-0.7 x 5%) plus (1.3 x 9%) is 15.2%.
Conclusion
- An asset’s returns may be anticipated using the linear connection between the asset’s expected return and various macroeconomic factors that represent a systematic risk, according to the arbitrage pricing theory (APT), a multi-factor asset pricing model.
- APT, unlike the CAPM, posits that markets occasionally overprice assets before the market finally corrects itself and the securities move back to fair value.
- Arbitrageurs intend to profit on any differences from fair market value using APT.
