Have you ever heard of the term Arbitrage Pricing Theory? It is one of the most common mechanisms which is used by the investors to help them with their identification of any particular asset in question.

For those who want to know a bit more about the topic, this is the perfect place to be. Here we are going to discuss the Arbitrage Pricing Theory as well as the other aspects which might come along the concept so that you can have a better idea of how APT helps in estimating the price of any assets.

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**What is Arbitrage Pricing Theory?**

The name in itself is an implication of the theory and what it does. It is a mechanism which the investors use to identify a particular asset.

Imagine, a joint-stock share has an incorrect price. The investors will be able to bring the cost of the stock share down and by knowing the value that it has. So, it can be said without any doubt that APT is one of the most important mechanisms to use for sure.

**Introduction to The Arbitrage Price Theory**

The Arbitrage Pricing Theory is something that can be used for asset pricing.

APT involves a process which holds that the asset in question and the returns which are related to it can be pre-determined pretty easily when the relationship that the assents returns have with all the different macroeconomic factors affecting the risk of the asset.

The Arbitrage Theory was created for the people in the year 1976, and since then, it has been one of the most commonly used mechanisms by the people.

The economist Stephen Ross is responsible for the creation of this amazing theory, and it is certainly worth knowing.

**Why is Arbitrage Price Theory Important?**

This is the theory which is helping the investors and analysts in finding out a proper multi-pricing structure and model for the asset security based on a relationship that the expected returns of the asset have with the risk.

The theory, in particular, does the job of pointing out that the fair market price of the asset security might be priced incorrectly. The main assumption which is made by the theory is that the action in the market is always less than efficient and perfect.

Therefore, it can be said that the resulted pricing on the assets is not correctly done. Either the assets end up being over-valued or under-valued, which for sure can be a problem during that period.

But then again, the market action should be able to eventually correct the entire situation or the problem where the prices of the asset return to the fair state in the market.

For an arbitrageur, the mispriced securities of the assets represent the short-term opportunities for virtually making a profit and that too, without any particular risks.

When we talk about the flexibility of the APT or the Arbitrage Price Theory, it can be said that the flexibility of APT is a bit more than the Capital Asset Pricing Model or the CAPM. Not just that but APT proves to be a very complex alternative to the CAPM option as well.

This is a theory that will provide the investors as well as the analysts a chance to customize all the research that they have made on the market and the assets too.

However, the application of the theory is a bit more difficult than one can imagine and that too takes a lot of time. It can take a little bit of time to deduce the factors of risk, which will be able to influence the price of the asset in question.

**The formula of Arbitrage Price Theory**

Return on a stock is based upon a below-given relationship of APT-

Expected Return = rf + b1 x (factor 1) + b2 x (factor 2)… + bn x (factor n)

Let us have a look at what is the meaning of different symbols used in this formula-

- rf- Risk-free Interest that investor would prefer to receive from their risk-free investments
- b- Sensitivity of the stock or security to different factors
- Factor- Risk premium related to each entity

The risk premium is further based upon two other factors-

- Risk premium related to the aforementioned factors
- The sensitivity of stock to each of the factors

Risk Premium = r – rf = b(1) x (r factor(1) – rf) + b(2) x (r factor(2) – rf)… + b(n) x (r factor(n) – rf)

This formula can also be represented in another way-

?E(R) I? = E(R)z ?+ (E(I) ? E(R)z?) × ?n

Meaning of these symbols are-

- ?E(R)I ?= Expected return on the asset
- Rz?=Risk-free rate of return
- ?n=Sensitivity of the asset price to macroeconomic factor n
- Ei=Risk premium associated with factor i?

**How to use Arbitrage Price Theory Formula?**

In case calculated risk premium is greater than the expected risk premium via the above-mentioned formula then investors should sell the stock.

If the expected risk premium is greater than the calculated risk premium, investors should buy the stock till LHS and RHS of the formula are not balanced.

Actually, the arbitrage in Arbitrage Price Theory is actually implemented for depicting how investors would use the formula for making the LHS and RHS in balance.

Let us dive deep and understand more about the arbitrage-

**Arbitrage in the Arbitrage Pricing Theory **

This particular makes a statement that the returns which are provided on the assets have a pattern which is liner in nature. The investors will be able to leverage all the deviation in return from this particular liner pattern, and all they have to do is use this particular theory in question.

The Arbitrage is basically a certain form of practice which is done with the simultaneous purchasing and then selling of an asset. This way, the investors will be able to take the benefit of the different discrepancies that happen and then lock in the profit, which is free of any risk for their trading.

But then the meaning of arbitrage in theory is a bit different from the classic meaning that this particular term has. To be completely honest, in theory, arbitrage doesn’t necessarily mean an operation which is free of any particular risks, but then there is a very high chance of achieving success.

The arbitrage theory offers the traders with a particular model which can be used in order to find out the value of an asset in the fair market and that too theoretically.

After the determination of the value is completed, the traders will then be able to focus on some other aspects such as the deviations that happen in the price from the fair market asset price.

This way, they will be able to make their trade in the best way.

So, there is no doubt that this arbitrage, in theory, is something that can be a great benefit to the investors as well as the traders too.

Don’t you quite get what we are talking about?

**Example of Arbitrage Price Theory**

Let us give you an example here so that you can understand in the best way.

Say that the value in the fair market for a stock A is already determined with the help of the Arbitrage Pricing Model. However, there is a drop in the price.

In such a case, the trader will easily be able to buy that particular stock on the basis of the belief that the price action that happens in the market will be able to correct the asset price and make it equal to the fair price.

**Three Assumptions of APT**

There is a certain point of difference when it comes to the assumptions made by the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory.

While the Capital Asset Pricing Model assumes that the investors will be holding the efficient and effective portfolios, the Arbitrage Pricing Theory doesn’t really do that. However, the latter does have some important underlying assumptions, and we are going to talk about them a little bit.

So, here we are going to present the underlying assumptions which have been found in APT-

- The systematic factors are enough to explain the asset returns in the best way.
- Investors who are investing in the asset will be able to build the respective portfolios of their assets where there is an elimination of the risk with the help of diversification.
- There are some portfolios which are pretty well-diversified. There will be no opportunity for arbitrage on these portfolios. In case there are some opportunities for the arbitrage, then these opportunities will definitely be exploited right away by the investors.

**Benefits of Arbitrage Price Theory**

Now that you know a bit more about the theory let us move on to some of the other important parts which you might be interested in.

Why do you think that the model is so popular amongst the investors?

Here we are going to discuss why this model matters so much. So, you need to read it till the end to know what we are talking about right here. Arbitrage Price Theory is the theory of asset pricing that measures the estimated return from the asset as a linear function of different factors.

The reason why APT is considered to be such a revolutionary idea is that it will allow the users to easily adapt this model in order to analyze the security in the best way.

There are some other pricing models which are available in the market which help the investors in deciding the value of the security; there is nothing that is able to work as well as this theory and the pricing model.

Apart from that, APT is also pretty useful when it comes to the building of the portfolios because with the help of these managers will be able to test the exposing factors of the portfolio easily.

**Wrapping it up!**

So, what is APT going to be for you? Are you going to choose the amazing APT model or the other ones that are provided to you in the market?

Share your experience with APT with us in the comments.