Now, when we've covered the basics of Factor Analysis, let’s dive into the first and likely the most famous factor model - The Capital Asset Pricing Model, or simply - CAPM.

Before we move forward, however, we need to define an important component that will be essential for this model.

Excess Return

An important component to discuss is Excess Return.

Although we haven't directly defined it yet, we’ve actually used this concept earlier.

Practically, excess return can be computed using the following formula:

As we mentioned earlier, we in fact used excess return to compute the Sharpe Ratio.

Defining Model

Now, when we’ve discovered what excess return is, let’s define The Capital Asset Pricing Model itself.

To do this, we will use the following formula:

Here, we also consider market's excess return in addition to portfolio's one.

The expected return of the market is practically measured using a broad market index, such as the S&P 500.

Alternatively, we can rewrite the following formula in the next way, with the same notation:

Here, we can see, that this expression looks like a special case of linear regression, where the bias is constant and equal to risk-free rate, while market's excessive return is an independent variable, used for predicting portfolio's expected return.

We'll use this fact later.

So, practically, The Capital Asset Pricing Model is utilized to compute the expected return of an asset or portfolio, where the market's return is taken into account as a factor.

Another key concept to introduce is Beta, which we will explore in a more detailed way in the following video, along with additional explanations and code examples:

Here is a corresponding Google Colab.

In conclusion, it's important to emphasize that another use of beta is estimating risk.

If portfolio has a high beta, whether positive or negative, it indicates that the portfolio is very risky. Therefore, we should generally avoid using this portfolio.