The Arbitrage Pricing Theory (APT) is a multi-factor model for determining the expected return of an asset based on its sensitivity to macroeconomic factors. It was developed by Stephen Ross in 1976 as a more flexible alternative to the Capital Asset Pricing Model. The APT assumes asset prices may temporarily deviate from their fair value, allowing arbitrageurs to profit by trading on price discrepancies until the market corrects. The model uses factor loadings to estimate an asset's expected return based on its exposure to macroeconomic factors like inflation, industrial production, and interest rates.

1. Arbitrage Pricing Model

2. • The Arbitrage Pricing Theory (APT) is a theory of asset pricing that holds
that an asset’s returns can be forecasted with the linear relationship of an
asset’s expected returns and the macroeconomic factors that affect the asset’s
risk
• The theory was created in 1976 by American economist, Stephen Ross. The
APT offers analysts and investors a multi-factor pricing model for securities,
based on the relationship between a financial asset’s expected return and its
risks.

3. • The APT aims to pinpoint the fair market price of a security that may be temporarily
incorrectly priced. It assumes that market action is less than always perfectly efficient, and
therefore occasionally results in assets being mispriced – either overvalued or undervalued –
for a brief period of time.
• However, market action should eventually correct the situation, moving price back to its fair
market value. To an arbitrageur, temporarily mispriced securities represent a short-term
opportunity to profit virtually risk-free
• The APT is a more flexible and complex alternative to the Capital Asset Pricing Model
(CAPM). The theory provides investors and analysts with the opportunity to customize their
research. However, it is more difficult to apply, as it takes a considerable amount of time to
determine all the various factors that may influence the price of an asset.

4. • . Assumptions
• The CAPM theory assumes single period investment horizon but the arbitrage pricing
theory believes in multi- period investment.
• The CAPM assumes that there are no taxes to be considered whereas the arbitrage pricing
theory does not believe in it.
• The CAPM also has the unrealistic assumption that investors can borrow and lend at risk
free rate of interest but arbitrage pricing theory does not assume the borrowing and lending
at the risk free rate of interest.
• The selection of portfolio is based on the mean and variance analysis according to CAPM
but not arbitrage pricing.

5. • Arbitrage in the APT
• The APT suggests that the returns on assets follow a linear pattern. An investor can leverage
deviations in returns from the linear pattern using the arbitrage strategy. Arbitrage is the
practice of the simultaneous purchase and sale of an asset on different exchanges, taking
advantage of slight pricing discrepancies to lock in a risk-free profit for the trade.
• However, the APT’s concept of arbitrage is different from the classic meaning of the term.
In the APT, arbitrage is not a risk-free operation – but it does offer a high probability of
success. What the arbitrage pricing theory offers traders is a model for determining the
theoretical fair market value of an asset. Having determined that value, traders then look for
slight deviations from the fair market price, and trade accordingly

6. • For example, if the fair market value of stock A is determined, using the
APT pricing model, to be $13, but the market price briefly drops to $11, then
a trader would buy the stock, based on the belief that further market price
action will quickly “correct” the market price back to the $13 a share level.

7. Mathematical Model of the APT
• Where:
• ER(x) – Expected return on asset
• Rf – Riskless rate of return
• βn (Beta) – The asset’s price sensitivity to factor
• RPn – The risk premium associated with factor
•

8. • Macro-Economic Factors
• Change in inflation
• Change in the level of industrial production
• Shifts in risk premiums
• Change in the shape of the term structure of interest rates
• The drawback of arbitrage pricing theory is that it does not specify the systematic
factors, but analysts can find these by regressing historical portfolio returns against
factors such as real GDP growth rates, inflation changes, term structure changes,
risk premium changes and so on.