On Equation Finance Calculator Capital Asset Pricing Model formula for calculating the Capital Asset Pricing Model

What is the Capital Asset Pricing Model?

If you’re an investor and want to know the required rate of return on an asset within a portfolio you manage, the Capital Asset Pricing Model, or CAPM, is the model you need. The CAPM produces a required rate of return for an asset by taking into account the assets sensitivity to non-diversifiable risk, or systematic risk, and measuring it against market risks and the risk-free rate of the market the asset is in. The CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital. Though the CAPM has failed numerous empirical tests, it still remains popular because of its simplicity of application in most valuation situations. In short; if it works, it works. Research has shown the CAPM stands up well to criticism, although attacks against it have been increasing in recent years. Until something better presents itself, though, the CAPM remains a very useful item in the financial management toolkit.

The Capital Asset Pricing Model starts with the idea that individual investment contains two types of risk; Systematic Risk and Unsystematic Risk.

Systematic Risk

These are market risks - that is, general perils of investing - that cannot be diversified away. Interest rates, recessions, and wars are examples of systematic risks. These market risks are also considered non-diversifiable risks as they can’t be diversified away in a portfolio.

Unsystematic Risk

Also known as specific risk, this risk relates to individual assets. In more technical terms, it represents the component of an asset's return that is not correlated with general market moves. These risks are non-market risks that pertain to specific companies. As stated above, you can’t diversify away the risk of political instability, but you CAN diversify away the risk of bankruptcy of an individual firm or business’s investable assets.

CAPM Formula Variables

The Capital Asset Pricing Model evolved as a way to measure systematic risk. Sharpe, the legend behind CAPM, found that the return on an individual investment asset, or a portfolio of assets, should equal its cost of capital. The standard formula remains the CAPM, which describes the relationship between risk and expected return.

Risk Free Rate (Rf)

The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. In theory, the risk-free rate is the minimum return an investor expects for any investment because he will not accept additional risk unless the potential rate of return is greater than the risk-free rate.

Beta (β)

The beta of a potential investment is a measure of how much risk the investment will add to a portfolio. If an asset is riskier than the market, it will have a beta greater than one. Conversely, if an asset has a beta of less than one, the formula assumes it will reduce the risk of a portfolio.

Market Rate of Return (ERm)

The expected rate of return of the market when considering the aggregated return of all companies within a particular market. Simply put, the Market Rate of Return is the aggregated rate of return for a market and demonstrates the performance of that market in the form of a rate of return.

Market Risk Premium (ERm - Rf)

The Market Risk Premium is the Market Rate of Return minus the Risk-Free rate. This value gives the investor an indication of the return on the market after considering unsystematic risk and rates of return of individual firms within the market.

Rate of Return on an Individual Share or Portfolio (ERi)

The expected rate of return on a share or portfolio after calculating the CAPM and considering all variables such as Market Risk Premium, Risk Free Rate, and Beta. Generally, the expected rate of return is compared to an investor’s internal rate of return. For example, if an investor holds a required rate of return of 10% and the Capital Asset Pricing Model calculation yields a rate of return of 9% for a share or portfolio, the investor may consider the investment to be too risky in comparison to the potential profit yield.

How to Calculate the Capital Asset Pricing Model

The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return. Assume you’re an investor and wishing to add a particular security to your investment portfolio. You want to know the expected return on the security after considering systematic and unsystematic risk associated with that security within the market. The risk-free rate (Rf) of the security’s market is 2.5%, the expected return from the market (ERm) is 10%, and the listed beta (β) for the security is 1.3. The market risk premium (ERm - Rf) is 7.5%, calculated by subtracting the risk-free rate from the expected return on the market. With the values defined, you can now calculate the expected return on the security (ERi) with the CAPM formula as follows:

ERi = Rf - β * (ERm - Rf)

ERi = 0.025 – 1.3 * (0.1 – 0.025)

ERi = 0.1225 = 12.25%

Using the capital asset pricing model (CAPM), you would calculate the expected return on the security as 12.25%. If your required rate of return for an investment was 10% then you may consider investing in this security, due to the expected return being greater than your required rate of return.

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Advantages of the CAPM

With its insight into the financial markets’ pricing of securities and the determination of expected returns, CAPM has clear applications in investment management. Its use in this field has advanced to a level of sophistication far beyond the scope of this introductory exposition.

The CAPM has several advantages over other methods of calculating required return, explaining why it has been popular for more than 40 years:

1. It considers only systematic risk, reflecting a reality in which most investors have diversified portfolios from which unsystematic risk has been essentially eliminated.

2. It is a theoretically-derived relationship between required return and systematic risk which has been subject to frequent empirical research and testing.

3. It is generally seen as a much better method of calculating the cost of equity than the dividend growth model (DGM) in that it explicitly considers a company’s level of systematic risk relative to the stock market as a whole.

4. It is clearly superior to the WACC in providing discount rates for use in investment appraisal.

Summary of Capital Asset Pricing Model

CAPM has an important application in corporate finance. The finance literature defines the cost of equity as the expected return on a company’s stock. The stock’s expected return is the shareholders’ opportunity cost of the equity funds employed by the company.

In theory, the company must earn this cost on the equity-financed portion of its investments or its stock price will fall. If the company does not expect to earn at least the cost of equity, it should return the funds to the shareholders, who can earn this expected return on other securities at the same risk level in the financial marketplace. Since the cost of equity involves market expectations, it is very difficult to measure; few techniques are available.

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