Arbitrage Pricing Theory 101

The arbitrage pricing theory (APT) attempts to measure the price an asset should have on the market through a number of macro-economic factors. Developed by Stephen Ross in 1976, the model is used to identify what many call "mis-priced assets." These assets should be valued higher than they are, and they therefore present an opportunity for capital appreciation. The stocks are often called value stocks, and they are thought to outperform the market as a whole in any given period of time.

Arbitrage Pricing Theory

In the financial sense, arbitrage literally means to take advantage of one or more market imbalances to reduce the risk of a financial purchase. The APT is complicated and itt is made up of a number of variables, starting with two simple variables:

  • Erj - The assets expected return
  • Bj - The sensitivity of the asset to factor loading
  • F - a systemic factor of the analyst's choice
  • Ej - the assets random shock

Essentially, an analyst builds an equation where the expected return is added to a series of calculations of Bj(F). Each of these calculations is measuring the security's value based on a single economic factor. All of the factors are added together, the random shock is added, and the result is said to be the relative price of the asset.

Capital Asset Pricing Model

The APT is offered as one way to estimate value and risk on the market, but it is not the only way. Perhaps the most well-known model is the Capital Asset Pricing Model (CAPM). This model uses the risk free rate, beta and expected market return of a security to measure its likely return in comparison to the risk it presents. The CAPM relies on relatively few market factors, but it has been used by analysts looking to key into securities to determine whether the risk is, or is not, worth the expected return.

Farma-French Model

The Farma-French Model uses the CAPM, but it adds other factors in order to better accommodate for market trends. Namely, the Farma-French model anticipates the affect of value stocks and small cap stocks on the market. If a security being analyzed is either a value stock, i.e. undervalued, or a small cap stock, i.e. having a market capitalization under $2 billion, it will be weighted as more likely to profit under the Farma-French model.

Using Pricing Models to Invest

Any of the above pricing models is highly speculative. The arbitrage pricing model, in particular, depends on the number of variables used and the types of variables used to estimate relative value on the market. On the whole, a day-to-day investor will not spend the time to evaluate a security's price and value based on any of these models. However, an analyst will. For this reason, it is valuable to follow the advice and purchases of sophisticated analysts. If you do not have direct access to one, try following the movements of a sophisticated hedge fund or private equity group. These organizations constantly model risk and potential reward when guiding their investment decisions.

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