APT - Arbitration Pricing Theory

Arbitration pricing theory is based on a much lesser number of assumptions about the stock market character as compared to CAPM. The "arbitration" concept suggests earning guaranteed no-risk profit from market speculation. As arbitration example can serve a situation when a stock is traded in different markets, while the current market price of this stock in those markets is different. In that case the following sequence of actions is apparent: sell the stock short (sale of borrowed securities) in the market where the stock price is higher and buy the same amount of stock in another market where it costs less. Imagine now that such an opportunity really exists. Since there are many participants in the stock market, it is hardly worth hoping that nobody else would notice such an opportunity - notice they will, and start capitalizing on it. But "unexpected" demand increase in one market with lower stock prices, and offer increase in another market with higher stock prices, will inevitably result in the leveling of prices: higher demand stimulates price increase, while higher offer brings it down. The situation described is an example the simplest arbitration. However, there might be other, more complex types (multi-stage, distributed in time).

Arbitration pricing theory is based on one assumption: arbitration (of any kind) is impossible in balanced market conditions. If such an opportunity exists, market will quickly "liquidate" it.

Further reasoning on impossibility of arbitration portfolio creation leads to basic equation of asset pricing, which can be considered as a practical result of this theory. It is interesting to note the fact that APT equation is a generalization of CAPM equation, although the arbitration theory has been created as its alternative.

According to this equation, asset value fluctuation is influenced not only by the market factor (market portfolio value), but by other factors as well, including non-market risk factors - national currency exchange rate, energy prices, inflation and unemployment rates, etc. If only one factor is considered as risk factor - market portfolio value - the equation will coincide with that of CAPM.

Taking several factors into account allows creating a stricter model. It results in:

• More precise asset price change forecasting;
• Reduction of non-systematic risk, even without portfolio creation.

Classic CAPM model takes into account only one factor, and asset is characterized by two parameters: "beta" sensitivity coefficient, describing risk associated with this coefficient, and average residual yield E responsible for specific risk, i. e. risk not explainable with the selected factor influence. APT model provides for a possibility of taking into account several factors. Now asset is characterized with a number of "beta" parameters, each of them representing asset sensitivity to a particular factor and characterizing systematic risk associated with this factor, and, as before, residual yield E. However, now the amount of specific (not factor explained) risk has become lesser.

Transition from single-factor CAPM model to multifactor APT model provides not only advantages, but raises new problems as well.

1. How many and what factors should be selected for a multifactor model?

   This is a really big problem not only for APT model, but for any multifactor model describing the stock market as well. It is absolutely clear that not all parameters available for analysis influence asset price behavior. However, it is not so easy to understand, which and how many of them do. It is not constructive to build a model of all factors available at once - insignificant factors will play a role of noise and may considerably distort any results received with the model.
    

2. Are risk factors identical for all assets alike?

   The second question is more delicate than the first one. And more complicated. While intuitive decision could be offered for solving the first problem – select some basic macroeconomic or industry parameters influencing, according to intuitive perception, the stock prices - that could not be done for solving the second problem. Because behavior of each asset is, generally speaking, individual. Therefore, each asset has his own composition and number of risk factors. What reasons should decide, which set of factors match one asset, and which set of factors match another one?
    

3. Is composition and number of risk factors changing with time?

   Assume that somehow one could manage to find composition and number of factors influencing a concrete asset. Can that factor composition change over a certain period of time? Our research results demonstrate an unsteady character of interrelations in the stock market. It means that the model is applicable only during a limited period, after which it becomes necessary to rebuild it. The risk factors may be different, too.
    

4. Can factors influence the price not immediately, but after a certain period of time?

   The question bears the answer in itself - they certainly can. Thus, increase in oil prices may have an effect on transportation stock prices not at once, but some time later. If there are several factors, each factor may have its individual timing. How do we determine it?
    

5. How to rank companies by several parameters at once?

   Having constructed a CAPM model for several assets, you could sort them out by sensitivity, systematic or non-systematic risk, with the aim of selecting the most attractive assets. In a multifactor case, asset is characterized by a number of systematic risks associated with each factor. How to analyze them all?
    

We will solve all these uneasy problems for you. Our methods and technologies are specially developed to solve such problems. Service complex offered within the framework of a multifactor model contains integrated mechanisms to solve most of the problems listed above.

Services offered within APT model framework:

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