# What is Capital Asset Pricing Model?

Authored by
Team Espresso
November 10 2022
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The Capital Asset Pricing Model is a mathematical relationship between the risk involved in investing in a financial asset and the expected returns from that asset. The ‘riskiness’ of the investment refers to the systematic risk associated with investing in the corresponding market. That is, in the case of using the CAPM model for stocks, riskiness refers to the dangers of investing in the stock market in general. Based on the expected return determined as per this model, investors and business managers make important investment decisions. While the Capital Asset Pricing Model is intuitive, it has certain shortcomings which make it a less than perfect tool for pricing assets.

## What is CAPM formula?

The relationship between the riskiness and expected return of an asset is given by the CAPM formula as follows:

ERᵢ = Rf + βᵢ * (ERₘ - Rf)

In the above formula,

ERᵢ refers to the expected return from the risky investment,

Rf refers to the risk-free rate of return,

βᵢ is the beta or sensitivity of the investment

(ERₘ - Rf) is the risk premium.

Let’s look at each of these components of the CAPM formula in greater detail below:

### Expected return from the risky investment (ERᵢ)

The expected return from an investment refers to the gain or loss that the investor can expect to receive from the investment. In the simplest of cases, the expected return can be calculated as the simple average of the return generated by the investment over the past few periods. Alternatively, this can also be computed as the weighted average of the returns from the asset in different time periods. In this case, the likelihood or probability of each of these scenarios unfolding act as the weights of the calculation.

### Risk-free rate of return (Rf)

This is the rate of return offered by an investment with zero risk associated with it. Since every investment in the world comes with some level of risk involved, investors tend to use the rate of return on government bonds as a proxy for this rate as these are perceived as the safest financial assets.

### Beta of the investment (βᵢ)

The beta of an investment is the correlation of returns from that investment, as compared to the market returns. Put simply, a value of beta higher than 1 shows that the returns of the investment under consideration are more volatile than the market returns. This means that whenever the market goes up by 1%, the investment goes up by more than 1% corresponding to its beta.

### Risk premium (ERₘ - Rf)

The risk premium refers to the incremental return that investors can expect to get from putting their money in risky assets, as compared to risk-free assets.

The CAPM formula provided above clearly shows that the expected return that investors can hope to earn from a risky asset is equal to the risk-free rate of return plus beta times the risk premium. Since the risk-free rate of return and risk premium is mostly fixed for the entire market, the CAPM formula shows that the expected return from a stock depends on the beta of the investment.

## Problems with the Capital Asset Pricing Model

• The risk-free rate of return is a theoretical concept because, in the practical world, no financial instrument is completely free from risks.
• The expected return of the market is backwards-looking and might not be representative of future movements.
• Estimating the beta value is not a straightforward task. This is because this value is subject to change over time and subject to market conditions.

## Practical value of the Capital Asset Pricing Model

Even though the model is not flawless, the CAPM calculation is used broadly in the financial domain to understand better the risks and rewards associated with investment decisions. Practically speaking, there are several uses of the CAPM model for multiple market stakeholders.

From the perspective of the investors, the expected returns determined from the CAPM calculation convey information about the returns that they can anticipate in the coming period from the investment. On the other hand, business managers interpret the CAPM meaning slightly differently. The expected return shows a business manager the benchmark of returns that the shareholders expect from purchasing stocks of their company. With this information, the business managers can then compute the cost of capital for their company and use this for corporate finance decisions. In general, businesses will only choose to invest in businesses where the cost of capital is lower than the returns from the project.

## Conclusion

The Capital Asset Pricing Model is a simple linear relationship between the expected returns from an asset and the market risk premium. While the model is intuitive and easy to understand, some of its assumptions - such as the absence of transaction costs and rationality of all market participants - are unrealistic, impacting its practicality. Even with its flaws, the model is used extensively by investors to evaluate investment opportunities and businesses to evaluate the financial feasibility of their projects.

## FAQ

Q. What is the Capital Asset Pricing model?

It is a tool that can be used to determine the expected return that an investor can expect from a risky asset.

Q. What is the CAPM formula?

The CAPM formula is given by the following equation:

ERᵢ = Rf + βᵢ * (ERₘ - Rf)

where

ERᵢ refers to the expected return from the risky investment,

Rf refers to the risk-free rate of return,

βᵢ refers to the beta of the investment,

(ERₘ - Rf) is the risk premium.

Q. What are some problems associated with CAPM?

The model, in its simple form, works only when some assumptions are satisfied. Some of these assumptions are unrealistic and are almost never observed in the real world. For example, the model assumes that there are no transaction costs and that all agents in the market are rational.

In terms of the calculation as well, one might run into several problems such as the backward-looking nature of expected market return and the value of beta varying over time.

Q. What are some practical uses of the CAPM?

The model is often used by investors to find the expected return from an asset. It is also used by businesses to determine the cost of equity, which then becomes an important input in calculating the cost of capital to the company.

Some stable and well-performing companies build a track record of paying high dividends to their shareholders. To spot such companies, you can look at the consistency of their financial records.