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Financial Accounting: Help and Review18 chapters | 251 lessons

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Lesson Transcript

Instructor:
*Jay Wagner*

Learn about the Capital Asset Pricing Model (CAPM), one of the foundational models in finance. We'll look at the underlying assumptions, how the model is calculated, and what it can do for you.

In finance, one of the most important things to remember is that return is a function of risk. This means that the more risk you take, the higher your potential return should be to offset your increased chance for loss.

One tool that finance professionals use to calculate the return that an investment should bring is the **Capital Asset Pricing Model** which we will refer to as **CAPM** for this lesson. CAPM calculates a required return based on a risk measurement. To do this, the model relies on a risk multiplier called the beta coefficient, which we will discuss later in this lesson.

Like all financial models, the CAPM depends on certain assumptions. Originally there were nine assumptions, although more recent work in financial theory has relaxed these rules somewhat. The original assumptions were:

- Investors are wealth maximizers who select investments based on expected return and standard deviation.
- Investors can borrow or lend unlimited amounts at a risk-free (or zero risk) rate.
- There are no restrictions on short sales (selling securities that you don't yet own) of any financial asset.
- All investors have the same expectations related to the market.
- All financial assets are fully divisible (you can buy and sell as much or as little as you like) and can be sold at any time at the market price.
- There are no transaction costs.
- There are no taxes.
- No investor's activities can influence market prices.
- The quantities of all financial assets are given and fixed.

Obviously, some of these assumptions are not valid in the real world (most notably no transaction costs or taxes), but CAPM still works well, and results can be adjusted to overcome some of these assumptions.

Before we can use the CAPM formula, we need to understand its risk measurement factor known as the **beta coefficient**. By definition, the securities market as a whole has a beta coefficient of 1.0. The beta coefficients of individual companies are calculated relative to the market's beta. A beta *above* 1.0 implies a *higher* risk than the market average, and a beta *below* 1.0 implies *less* risk than the market average. Most companies' betas fall between 0.75 and 1.50, but any number is possible, including negative numbers; a negative beta would be highly unlikely, however, since it would imply less risk than a 'risk free' investment.

For actual use, the beta coefficients of most companies can be found on financial websites as well as in electronic publications. You can do a quick search to find companies' beta coefficients.

The CAPM formula is sometimes called the Security Market Line formula and consists of the following equation:

*r** = *kRF* + *b*(*kM* - *kRF*)

It is basically the equation of a line, where:

*r** = required return

*kRF* = the risk-free rate

*kM* = the average market return

*b* = the beta coefficient of the security

You will sometimes see the *kM* - *kRF* term replaced by *kMRP*. *kMRP* (the market risk premium) = *kM* - *kRF*, so this is just a shortcut when the market risk premium has already been calculated. Remember again that the beta of the market is 1.0, so *kMRP* is just the additional return required from the market as a whole.

We should also take a moment to talk about the **risk-free rate**, *kRF*. Investments are subject to many risks that may come from the economy, the nature of the market, the industry in which a company operates, or the company itself. Of these risk factors, the only one that is universal is the risk that inflation will decrease an investor's purchasing power. In theory, the risk-free rate is the return that an investment with *no* risks should earn, but in practice it includes the ever-present risk of inflation.

Let's calculate a couple of required returns using fictional companies X and Z to see how this works. For our calculations, we will use the return on Company X as the risk-free rate and the 1-year return on Company Z as the market return. Let's hypothetically use beta coefficients for Company X and Company Z as 0.10% and 20.63%, respectively. Hypothetically, let's also provide Company R, S, and T with these current beta coefficients:

Company R = 0.25

Company S = 1.82

Company T = 0.68

Based on these figures, Company R, with a beta of 0.25, should have a required return of 5.2325 or 5.23%.

Company S, on the other hand, would have a required return of 37.4646 or about 37.46%.

That's quite a gap, but it reflects the additional risk an investor accepts when investing in Company S rather than Company R.

So how would you *use* the CAPM in real life? When considering an investment, you need to know if the return you expect to receive makes up for the risk you're undertaking. Using the same inputs as before, let's say that you're considering making an investment in Company T, which has a beta coefficient of 0.68. You find your inputs and calculate the required return: 14.0604 or about 14.06%.

So, if you are to invest in Company T, you can expect a return of at least 14.06%. If your return meets or goes beyond that expectation, you invest. If not, you look for another investment.

When using CAPM to make investment decisions, remember that it is an approximation and that it is based entirely on quantitative (mathematical) methods. That makes it a good guide, but it is not exact - very little in finance is - and it ignores non-numerical reasons why you may want to make a specific investment.

One more caveat to the use of the CAPM: both the returns you use and the company's beta coefficient are subject to change, so when you use the CAPM, make sure you have the most recent numbers to input.

Remember that the CAPM is an approximation based on certain assumptions, some of which may not be valid to your analysis. So why use the CAPM? There are several reasons.

First of all, the CAPM is a simple formula. You don't have to know or use statistical methods to find the risk inherent in a stock; you can simply look up its beta. Second, in spite of its simplicity and sometimes flawed assumptions, the CAPM has proven to be reasonably accurate over time. Finally, even though the CAPM is a theoretical calculation, it can be used in real-world measurements.

Let's review. One tool that finance professionals use to calculate the return that an investment should bring is the **Capital Asset Pricing Model**. **CAPM** calculates a required return based on a risk measurement. To do this, the model relies on a risk multiplier called the **beta coefficient**. A beta above 1.0 implies a *higher* risk than the market average, and a beta below 1.0 implies *less* risk than the market average.

The formula for calculating CAPM is:

*r** = *kRF* + *b*(*kM* - *kRF*)

The advantages to using the CAPM are that it is a simple formula; it has proven to be reasonably accurate over time; and it can be used in real-world measurements.

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