# Capital Asset Pricing Model (CAPM)

Guide to Understanding the 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 formula is comprised of 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)

Beta 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 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%.

 1.) 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 Systematic risk is unavoidable and cannot be mitigated through portfolio diversification (e.g. global recessions) 2.) 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.

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.

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.

## CAPM Graph: Expected Return vs. Risk Relationship

The following graph of the capital asset pricing model (CAPM) illustrates the relationship between expected returns (y-axis) with beta (x-axis).

The green dotted line represents the risk-free rate (rf), while the orange dotted line depicts the market return (i.e. the market beta is equal to 1.0).

Thus, the difference between the yield from the risk-free rate and the market return is the equity risk premium (ERP).

Learn More → The Capital Asset Pricing Model: Theory and Evidence (American Economic Association)

## CAPM Formula

Per the capital asset pricing model (CAPM), the cost of equity – i.e. the expected return by common shareholders – is equal to the risk-free rate plus the product of beta and the equity risk premium (ERP).

Expected Return (Ke) = rf + β (rm rf)

Where:

• Ke → Expected Return on Investment
• rf → Risk-Free Rate
• β → Beta
• (rm – rf) → Equity Risk Premium (ERP)

For a simple example calculation of the cost of equity using CAPM, use the assumptions listed below:

• Risk-Free Rate = 3.0%
• Beta: 0.8
• Expected Market Return: 10.0%

Next, by entering this into our formula, we get:

• Cost of Equity (Ke) = 3% + 0.8 (10% – 3%)
• Ke = 8.6%

## CAPM Calculator – Excel Model Template

We’ll now move to a modeling exercise, which you can access by filling out the form below.

Submitting ...

## Step 1. Equity Risk Premium Calculation (ERP)

Suppose we have three companies that each share the following assumptions:

• Risk-Free Rate = 2.5%
• Expected Market Return = 8.0%

Since we’re given the expected return on the market and risk-free rate, we can calculate the equity risk premium for each company using the formula below:

• Equity-Risk Premium (ERP) = 8.0% – 2.5% = 5.5%

## Step 2. Cost of Equity Calculation (ke)

The difference in expected returns among the three companies will be attributable to the beta (i.e. systematic risk).

• Company A = 0.5 Beta
• Company B = 1.0 Beta
• Company C = 1.5 Beta

To calculate the cost of equity (Ke), we’ll take the risk-free rate and add it to the product of beta and the equity risk premium, with the ERP calculated as the expected market return minus the risk-free rate.

For example, Company A’s cost of equity can be calculated using the following equation:

• Cost of Equity (Ke) = 2.5% + (0.5 × 5.5%) = 5.3%

Under the provided assumptions, the expected equity returns for the three companies come out to 5.3%, 8.0%, and 10.8%, respectively.

## Step 3. CAPM Expected Returns Analysis

The key takeaways from our practice exercise calculating the cost of equity using the capital asset pricing model (CAPM) are the following:

1. The lowest potential returns (and risk) come from the company with the lowest beta
2. The returns from the company with a beta of 1.0 are in line with that of the market
3. The company with the highest potential returns (and risk) has the highest beta

A company with a high beta implies increased risk and higher volatility relative to the overall market (i.e. greater sensitivity to market fluctuations).

Therefore, a higher cost of equity would be used by investors to discount the future cash flows generated by the company — which directly leads to a lower valuation, all else being equal.

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Inline Feedbacks
Analyst
November 28, 2022 2:18 am

The beta used here is the ‘levered’ beta, right?

calcuing
March 25, 2022 6:11 am

To calculate the CAPM,risk-free rate and add it to the product of beta and the equity risk premium, with the CAPM calculated as the expected market return minus the risk-free rate.

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