What is arbitrage pricing theory

Arbitrage pricing theory (APT) is a multifactor asset pricing model based on the idea that the returns of an asset can be predicted using the linear relationship between the expected return of the asset and a series of macroeconomic variables that capture systematic risk. Arbitrage pricing theory was developed by economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (Capm). Let's see what arbitrage pricing theory is and how to apply it using its formula. 

What is arbitrage pricing theory

Arbitrage pricing theory (APT) is a multifactor asset pricing model based on the idea that the returns of an asset can be predicted using the linear relationship between the expected return of the asset and a series of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily undervalued.

How Arbitrage Pricing Theory Works

Arbitrage pricing theory was developed by economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (Capm). Unlike the CAPM, which assumes that markets are perfectly efficient, the APT assumes that markets sometimes misvalue securities, before the market eventually corrects itself and the securities return to their fair value. With APT, arbitrageurs hope to take advantage of any deviation from fair market value. However, this is not a risk-free trade in the classic arbitrage sense, because investors assume the model is correct and make directional trades, rather than making risk-free profits.

Arbitrage Pricing Theory Calculation Formula

The beta coefficients of the APT model are estimated using linear regression. Generally, historical securities returns are regressed on the factor to estimate its beta. The calculation formula for the theory of arbitrage prices would be as follows:

Example of using arbitrage pricing theory

Let's give an example to understand it better in practice. The following four factors that explain the profitability of a stock have been identified and their sensitivity to each factor and the risk premium associated with each of them have been calculated:

• Gross domestic product (GDP) growth: ß = 0,6, PR = 4%
• Inflation rate: ß = 0,8, RP = 2%
• Gold price: ß = -0,7, RP = 5%
• Return of the Standard and Poor's 500 index ß = 1,3, RP = 9%
• The risk-free rate is 3%.

Using the APT formula, the expected profitability is calculated as: Expected return = 3% + (0,6 x 4%) + (0,8 x 2%) + (-0,7 x 5%) + (1,3 x 9%) = 15,2%.