Arbitrage Pricing Theory Assumptions Explained


Arbitrage pricing theory, often referred to as APT, was developed in the 1970s by Stephen Ross. It is considered to be an alternative to the Capital Asset Pricing Model as a method to explain the returns of portfolios or assets. When implemented correctly, it is the practice of being able to take a positive and expected return from securities that are either over- or undervalued within an inefficient market.

APT uses assumptions that are relatively simple, but it is a theory that can be rather difficult to apply because it requires complex statistical analysis from a tremendous amount of data. It will not work unless there is a trade that consists of at least two assets and one of them must assumed to be mispriced.

In APT, Stephens created three underlying assumptions that do not rely on the idea that an investor holds an efficient portfolio.

1. Asset returns can be explained by factors that are systematic.
To determine these factors, we must look at the history of the investment product, what the growth rate happens to be, and what the anticipated changes over a specific period of time happen to be. This creates risk percentage based on the diversification of the portfolio and what returns could be anticipated.

2. Investors can build a portfolio where specific risk is eliminated.
By using diversification, identified risks can be eliminated within a portfolio because it has been identified.

3. Portfolios that are properly diversified have no arbitrage opportunity.
If any opportunities for arbitrage were to exist, then the investors would exploit it away so that it didn’t exist.

By following these assumptions, the investor can sell securities that are relatively expensive and overpriced and then use the proceeds from that sale to purchase securities that are relatively underpriced.

How Can Sensitivities and Premiums Be Estimated?

In APT, there is a set of common factors that helps to influence the returns that an investor can achieve. This is because the market is not viewed as a monolithic entity. These common factors work together simultaneously so that the returns which can be achieved are affected.

In order for sensitivities and premiums to be estimated to create diversification within these common factors, that are additional assumptions that are necessary to make in order for a final outcome to be calculated.

  • All securities have expected variances and values that are finite.
  • It is possible for a percentage of agents to perform well within a portfolio that has been adequately diversified.
  • There are no taxes being levied on the portfolio.
  • There are no transaction costs required to make diversification changes within the portfolio.

When these assumptions are made, then we can focus on the central idea of the Arbitrage Pricing Theory: that some assets can be priced relative to that of other assets within the portfolio. In order for this to happen, one more assumption must be made: that the investor knows which states of nature may occur and what will happen within each of those states.

Each portfolio must be examined within a specific period of time using the data that the general market has created. Based on the performance of the security to the relative performance of the market, then incorporating the assumptions of APT, it can be determined what pricing should be assigned to the security and how sensitive it happens to be.

Why Do These Assumptions Need to Be Made?

When using APT, we can determine which states of nature are possible, but we do not know which will actually occur. This means all that we have to work with are the probabilities of each state and what happens within them should they occur.

Picture this idea as if it were a tree. There are multiple branches that shoot out from the main trunk. You know that you’ve planted a tree and that it will grow upright, but in what direction will the branches spring forth? We can plan and anticipate for a specific direction for those branches, but we won’t have factual knowledge about them until they begin to grow.

By making these assumptions and using the data that the market and each individual security is able to provide, investors can compare the pricing of each to the expected price that the APT model is able to predict. If the price is too low or too high, then the investor has options to begin reducing their risk back to zero.

The Arbitrage Pricing Theory Assumptions may not always be correct, but they do help investors see the bigger picture within their portfolio. This is why the structures of APT are used as the foundation of most commercial risk systems today.