CAPM Calculator

The Capital Asset Pricing Model (CAPM) answers the question of what rate of return an asset should provide when its risk is known. Since it was developed by William Sharpe and others in the 1960s, it has been the basis for most estimates of cost of equity in corporate finance.

This calculator allows you to solve the formula both ways. If you input the risk-free rate, beta, and expected market return, then you can find the expected return. Alternatively, if you leave one of the four fields blank, this calculator will calculate the missing value.

What does the CAPM measure?

The CAPM assumes that investors should expect two types of returns. The first is compensation for the capital investment itself, typically represented by the risk-free rate, often tied to government bond yields. The second is compensation for taking on risks that cannot be reduced through diversification. This risk is called systematic risk or market risk. The amount of this second return depends on how strongly an asset moves with the market, and it's precisely this that beta measures.

Only systematic risk is relevant to pricing. Firm-specific shocks such as lawsuits or product failures are non-systematic risks that can be diversified away by holding many assets. The model assumes that there is no additional compensation from the market for taking on these kinds of risks. All remaining risks, i.e., those that cannot be avoided even with complete diversification, are what beta and risk premium compensate for.

The formula for the CAPM is:

The expected return on an asset is the sum of the risk-free rate and beta multiplied by the market risk premium.

$E(R_i)$ represents the expected return of an asset, $R_f$ is the risk-free rate, $\beta_i$ is the beta of the asset and $E(R_m)$ is the expected market return. $E(R_m) - R_f$ is the market risk premium, which is the extra return that's expected from a broad market above the risk-free rate. When you multiply the beta by this premium, you get the risk premium for that particular asset. Add to it the risk-free rate and you get the expected return.

Example calculation:

Assume the risk-free rate is 4 percent, beta is 1.2 and expected market return is 10 percent. We want to find the market risk premium, which is the compensation for owning the market instead of something like U.S. Treasury bonds.

Since this asset has a beta of 1.2, the premium earned is equal to the above value multiplied by 1.2.

If you add the risk-free rate of interest, then the expected return is 11.2 percent.

The 11.2% represents the return that this model expects for an asset with a market risk of that magnitude. Of that, 4 percentage points is the risk-free base rate that would be earned anyway, while the remaining 7.2 percentage points is pure compensation for the risk. This explains why assets with higher betas must promise higher returns to make them worth investing in.

Interpretations of beta

As beta is a central component of the model, it is important to understand how it should be interpreted. Beta is the slope obtained by regressing an asset's return on the market return and therefore by definition is a backward-looking measure. Here are some guidelines:

A beta of 1.5 generally means that the asset's price will fluctuate with 50% more volatility than the market. A beta of 0.5 indicates that the security's price will move about half as much as the market. If a company has recently changed its debt structure, historical beta may not reflect current riskiness and analysts often calculate comparable companies' betas based on the firm's capital structure and use this value.

The cost of equity according to the CAPM

In the area of corporate finance, the expected return derived from the CAPM is also referred to as cost of equity. Because shareholders do not bill invoices, a company cannot directly derive the cost of equity from a financial statement like it would for interest payments on debt. The CAPM fills this gap and converts the required return into a calculable value.

This value is then included in the weighted average cost of capital (WACC). The company's free cash flow is discounted using WACC, while the free cash flow to equity holders is only discounted by the cost of equity. The cost of equity itself is also an input into WACC. Thus, CAPM is usually the first step in a valuation. It estimates the cost of equity and then uses it along with the after-tax cost of debt to determine the discount rate for discounted cash flow models or minimum required return on new projects.

Select input values:

The risk-free rate must be adjusted for the currency and time period being valued. For long-term valuations in U.S. dollars, the yield on a 10-year U.S. Treasury bond is a common benchmark. For other currencies, yields on government bonds with similar maturities are used. You can get an idea of this range by looking at current yields on 10-year bonds.

You can usually find the beta on a single page at Bloomberg, Yahoo Finance or research sites of securities firms. The beta is generally calculated using returns over two to five years and refers to a broad index of assets. For market return, long-term data with a nominal value of about 10 percent is a standard in textbooks for S&P 500. This leads to an equity risk premium of between 4 and 6 percent, which corresponds to historical levels. For a more comprehensive evaluation, the currently published implicit premiums by Aswath Damodaran are more reliable than a single historical average value.

The Security Market Line:

When expected return is plotted on the vertical axis and beta is plotted on the horizontal axis, application of the CAPM results in a straight line called the Security Market Line. It begins at the risk-free rate with a beta of zero, runs through the market return with a beta of one, and rises with a slope equal to the market risk premium. All assets whose price is correct will lie exactly on this line. Assets above the line have returns that exceed what is justified by their risk and could be undervalued. Assets below the line are possibly overvalued. The graph in this calculator shows this line and indicates where an asset lies.

The limitations of the CAPM.

While the CAPM is simple and therefore widely used, it makes strong assumptions. It assumes that the market is efficient, investors are rational and diversify broadly, and only systematic risk matters. In reality, there are factors such as taxes, fees, transaction costs, and liquidity effects that the model ignores. Also, beta itself has often been criticized because its estimation relies on historical data, and past performance is no guarantee of future results. Additionally, a company's capital structure changes over time, which can affect its risk profile. Eugene Fama and Kenneth French have argued for decades that the CAPM cannot explain certain patterns in returns, such as those associated with size and value. This has led to the development of three-factor and five-factor models. So, while the results from the CAPM are a good starting point, they should not be taken as gospel truth. You should also compare your results to other companies in similar industries.