Capital Asset Pricing Model (CAPM)

How to Calculate CAPM (Step-by-Step)

The capital asset pricing model (CAPM) is a fundamental method in corporate finance used to determine the required rate of return on an investment given its risk profile.

The model attempts to establish a relationship between the risk and expected return by an investor using three key variables, which are the risk-free rate (rf), the beta (β) of the underlying asset (or investment), and the equity risk premium (ERP) – all of which we’ll discuss in further detail shortly.

But prior to delving into the core components of the capital asset pricing model (CAPM) theory, we’ll start with a review of the discount rate concept under the context of valuation.

Simply put, the discount rate represents the “hurdle rate” (i.e. the minimum rate of return) corresponding to the risk profile of an investment, which could refer to shares issued by a public company or a proposed project that a business is attempting to decide whether to pursue.

Specific to performing a cash flow oriented valuation on a company, the implied value equals the sum of its future cash flows discounted to their present value (PV) using an appropriate discount rate.

Under the specific context of equity investors, the discount rate that pertains to solely common shareholders is referred to as the “cost of equity” — which is the required rate of return to equity investors that the capital asset pricing model is used to calculate.

Unlevered free cash flows are discounted using the weighted average cost of capital (WACC), whereas levered free cash flows are discounted with the cost of equity.

But regardless of the type of cash flow being discounted, the cost of equity serves an integral role in either approach.

CAPM Equation in Finance: Model Assumptions

The cost of equity is most commonly estimated using the CAPM, which links the expected return on a security to its sensitivity to the overall market.

The CAPM formula comprises three components:

1. Risk-Free Rate (rf): The return received from risk-free investments — most often proxied by the 10-year treasury yield
2. Beta (β): The measurement of the volatility (i.e. systematic risk) of a security compared to the broader market (S&P 500)
3. Equity Risk Premium (rm – rf): The incremental return received from investing in the market (S&P500) above the risk-free rate (rf, as described above)

To explain the fundamental drivers, we’ll briefly discuss each concept in more detail.

1. Risk-Free Rate (rf)

Starting off, the risk-free rate should theoretically reflect the yield to maturity of default-free government bonds of equivalent maturity to the duration of each cash flow being discounted.

But due to the lack of liquidity in government bonds with the longest maturities (i.e. less trade volume and data sets), the current yield on 10-year US treasury notes has become the standard proxy for the risk-free rate assumption for companies based in the US.

2. Beta (β)

In corporate finance, beta (β) measures the systematic risk of a security compared to the broader market (i.e. non-diversifiable risk).

The beta of an asset is calculated as the covariance between expected returns on the asset and the market, divided by the variance of expected returns on the market.

The relationship between beta (β) and the expected market sensitivity is as follows:

• β = 0: No Market Sensitivity
• β < 1: Low Market Sensitivity
• β = 1: Same as Market (Neutral)
• β > 1: High Market Sensitivity
• β < 0: Negative Market Sensitivity

For instance, a company with a beta of 1.0 would expect to see returns consistent with the overall stock market returns. So if the market has gone up by 10%, the company should also see a return of 10%.

But if that company were to have a beta of 2.0, it would expect a return of 20% assuming the market had gone up by 10%.

• Systematic Risk: Often referred to as market risk, systematic risk is inherent to the entire equities market, as opposed to being specific to a particular company or industry. In short, systematic risk is unavoidable and cannot be mitigated through portfolio diversification (e.g. global recessions).
• Unsystematic Risk: Unsystematic risk refers to company-specific (or industry-specific) risk that can actually be reduced through portfolio diversification (e.g. supply chain shutdowns, lawsuits). The benefits of diversification become more profound if the portfolio contains investments in different asset classes, industries, and geographies.

The common source of criticism is most often related to beta, as many criticize it as a flawed measure of risk.

• Trailing-Basis: The standard procedure for estimating the beta of a company is through a regression model that compares the historical market index returns and company-specific returns, in which the slope of the regression line corresponds to the beta of the company’s shares (the calculation is thus “backward-looking”). However, the past performance (and correlation) of a company relative to the market may not be an accurate indicator of future share price performance.
• Capital Structure Mix: The capital structure (debt/equity ratio) of companies also progressively changes over time, which can alter their risk profiles and performance.

3. Equity Risk Premium (ERP)

Our third input, the equity risk premium, or “market risk premium”, measures the incremental risk (or excess return) of investing in equities over risk-free securities.

Since investing in risky assets such as equities comes with additional risk (i.e. potential for loss of capital), the equity risk premium serves as additional compensation for investors to have an incentive to take on the risk.

The equity risk premium has been around the 4% to 6% range, based on historical spreads between the S&P 500 returns over the yields on risk-free government bonds.