The Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT) are two of the most popular asset pricing models used by analysts and investors. In two previous posts we have looked at these two models individually (CAPM here and APT here). In this post we'll pit the two models against each other so you can identify which is more useful to you when you have an investment decision to make.

## Weigh In: A quick comparison

Both models have the same objective; identify the expected rate of return on an asset. In doing so, they allow the analyst to identify the price that the asset should have now and determine whether the asset is worth investing in.

Let's see how they measure up:

**APT**

- States that the return on an asset is dependent on its sensitivity to various factors
- Factors can be macroeconomic or company specific.
- Sensitivities are computed using a linear regression of historical returns of the asset on the relevant factor.

**CAPM**

- A particular example of the APT
- Only one relevant factor: the sensitivity of the asset to changes in the market.
- This sensitivity is called beta, and it is a key attribute of any asset.

This similarity between the two models is unsurprising as APT was developed as an extension of CAPM.

## Round 1: Ease of use and practicality

Based on the discussion above, we can say that the APT will always be more accurate than CAPM, if the additional factors have any explanatory power. The issue is whether the accuracy gain is enough to merit the time and effort involved in deciding what factors to use, and gathering the relevant data.

The primary advantage of CAPM is that it is simple to calculate. The only factor you need to consider is the market risk premium, which is reasonably easy to calculate. This means that you can usually compute a CAPM model fairly quickly. APT, by contrast, requires more time and expertise from the analyst, both in determining which factors to include for each asset and in calculating the sensitivities for each of those factors.

The right choice of factors to include is not necessarily constant across assets or over time. If you are pricing a portfolio, you may need to devise a different APT model for each asset if your objective is to maximize accuracy. Likewise if you return to an APT model after a few months, you need to consider whether the factors you have used still make sense.

The advantage of CAPM is that it does not have any of these problems. The model contains the same single factor every time.

## Round 2: Empirical accuracy

As mentioned previously, APT was developed as an extension to CAPM. The reason for this was that CAPM has long struggled to prove itself accurate in empirical tests. Intuitively, the notion of one single factor explaining the return on any asset sounds unlikely, and it has generally proven to be this way. In particular there are size effects and value effects which cause inaccuracies in CAPM for small stocks and value stocks.

Estimating the empirical performance of APT is a more difficult job, as the usefulness of the model is dependent on the choice of factors, however the APT does generally perform well empirically.

Both models, but particularly CAPM, have some issues translating theory into practice.

For instance, CAPM makes many assumptions, some of which are difficult to justify in the real world. To give one example, CAPM assumes all individuals can borrow and lend at the risk-free rate, which is in practice the rate the US government can borrow at. Clearly, this is not a realistic assumption. APT relaxes many of these assumptions, so can be seen as preferable on the basis of being more realistic.

Generally speaking APT performs better in empirical contexts, however you have to decide for yourself what relevance academic studies have to your investment decisions.

## Final verdict

The fact that both models have stood the test of time indicates that both have their merits. The main advantage of CAPM is its simplicity. As the asset price is only related to one other variable, it is comparatively easy to calculate the CAPM rate of return. By contrast APT requires you to determine which variables are relevant to a particular asset, and then calculate the sensitivities for all of them. However, if you can manage this successfully, then APT is likely to give a more accurate and reliable result.

Deciding which model to use is largely a decision of how much time and information you have available. If you have access to the relevant variables to construct an APT model, then it is probably preferable to do so. Otherwise, CAPM is a reasonable alternative.

Finally, you may want to consider whether you are pricing a single asset or a portfolio. For a single asset, accuracy is likely to be a priority, which could lead to you favouring APT. For a portfolio, the inaccuracy of CAPM on individual assets may be less of a problem than the multiple calculations and models required of APT.

Ultimately, you can consider which model best suits your needs. Given that CAPM is relatively easy to calculate, I suggest computing this initially, and then evaluating whether it is worthwhile to continue to evaluate the APT. Either method should give you a reasonable estimate of whether an asset merits your investment at the current time.