Arbitrage Pricing Theory

Arbitrage Pricing Theory is the most fundamental principle of the capital markets. The pricing theory states that two identical assets cannot be traded at different prices and afford you the opportunity of an instantaneous risk free profit. However, while the securities are identical, the markets and market makers are not; especially if you take into account the different clearing exchange houses and currencies.

What is Arbitrage Pricing Theory or APT?

Arbitrage Pricing Theory is a model created by Stephen Ross in 1976 based on the Capital Asset Pricing Model CAPM; with the idea of predicting assets returns using the relationship between the risk-free rate and the common risk factors (risk-premium).

Arbitrage Pricing Theory Formula

Risk-free rate (Rf) the yield of ten years government bond.
Beta (Bn): the sensitivity or “correlation” to the volatility of a particular risk factor (Rfn).

In terms this equation, calculates the portfolio’s expected returns (Er) in relationship with the particular grouping of independent economic indicators.

The most important type of economic indicators are the leading ones; which will change before the business cycle changes.The best leading economic indicator is the stock market, S&P 500.

How to Use the APT

The best way to apply the Arbitrage Pricing Theory is by trying to price the value of a single security focusing only in the risk premium. For example, let’s say there are only 5 factors that can affect the price of crude oil:

1. Supply: Rf1
2. Demand: Rf2
3. Weather: Rf3
4. Dollar Strength: Rf4
5. Geopolitical Tension: Rf5

Now the real complexity of this problem is knowing the coefficient of sensitivity and this is how arbitrageurs make their money by predicting what factors are influencing the commodity to be mispriced and how soon and in what direction will they converge.

Case Study

Develop a spreadsheet that can automatically solve the Arbitrage Pricing Theory Equation.