## Presentation of the APT

Created by **Stephen Ross**, the model **APT (Arbitrage pricing theory)** is one of the most famous models of valuation of financial assets. It is in a way the main competitor of the CAPM model.

The APT is founded on the basic idea **that there are no arbitrage opportunities that last over time**. Indeed, an asset A as risky as an asset B, but more profitable, would see its demand increase rapidly, until its profitability again becomes equal to that of asset B, thus canceling any arbitrage opportunity.

The other basic assumption of the APT rests in the fact that the**we can model the expected profitability of an action by a linear function of various macroeconomic factors or specific to the security sector, weighted according to their impact on the action by a specific beta coefficient**.

These factors are many and varied and can range from oil prices to US GDP to European policy rates or the exchange rate of a currency pair. These are all factors likely to influence the price of the asset studied.

Thus, for an asset j we will have:

with:

E (rj) = the expected return on asset i

rf = the return on the risk-free asset

RPn = the value of the risk premium associated with the nth systematic factor influencing the price of the asset (these premiums are assumed to have a zero average)

bjn = the Beta which represents the sensitivity of the asset to the factor RPn

## APT in practice

According to the model, the expected return on the asset is obtained by adding the return on the risk-free asset (government bonds) to a series of systematic factors weighted according to the sensitivity of the asset to them.

**To do this, we need to proceed in three steps:**

**1. Identify the factors that influence the return on assets2. Measure the impact of these factors on the asset (Beta)3. Estimate the value of the risk premium associated with these factors**

**1. The factors** are not specified in Ross theory, they are determined empirically on a case-by-case basis and **must obey certain specific rules** :

– their impact on asset prices manifests itself in unexpected movements of the latter.

– the influence of these factors should be non-diversifiable, ie more global than specific to a single company.

– precise and dated information must be available on these factors

– the relationship between these factors and the asset should be able to be proven on an economic basis. This avoids all the wacky factors such as the position of the stars in the sky.

Here is

**certain macroeconomic factors that have a recurring influence on the price of financial assets** :

– variations in the growth of the GDP of a State

– variations in inflation

– variations in the prices of raw materials (oil, metals, etc.)

– variations in the yield curve for government bonds

– variations in the credit spread of bonds *corporate*, i.e. the variation in credit risk associated with companies

– …

These factors can be represented by indices (GDP, inflation) or prices on the markets of *futures* (raw materials)…

**2.** **We can quantify the impact of these factors (Beta) on the asset** by a linear regression of the past returns of the asset compared to the evolution of the chosen factors.

**3.** **The risk premium associated with each factor** is equal to the difference between the return provided by the factor to the asset in the model and the return on the risk-free asset.

**Once all these steps have been completed, we can finally calculate the expected return on the asset.**

Of course,

**the APT is not a perfect model and we can oppose it a number of criticisms**, in particular the fact that the factors are not mentioned in the model and that they have to be determined empirically, which imposes heavy calculations. Likewise, estimating a Beta for each factor makes the task even more difficult, and it is not said that the factors and their influence on the asset remain fixed over time.

However, **the APT is perhaps a more realistic model than that of the CAPM** because it considers an unlimited number of systematic factors influencing the return on the asset, against a single factor (the market) and a single beta for the CAPM.

It is for this same reason that **the APT is used much less than its competitor in the world of finance, because it is much more complex to implement than the CAPM**.

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