How to Calculate the Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a financial model used to determine the expected rate of return for an asset or investment. It helps investors understand the potential return they might receive, considering its associated risk, aiding in asset valuation and portfolio management.

Understanding the CAPM Formula

The core of the Capital Asset Pricing Model is its formula: Expected Return = Risk-Free Rate + Beta (Market Return – Risk-Free Rate), or E(Ri) = Rf + β (E(Rm) – Rf).

E(Ri) is the Expected Return on the investment. Rf is the Risk-Free Rate, the theoretical return on an investment with no financial risk. Beta (β) measures the asset’s systematic risk, its sensitivity to overall market changes. E(Rm) is the Expected Market Return. The term (E(Rm) – Rf) represents the Market Risk Premium, the additional return investors expect for bearing market risk.

Determining the Risk-Free Rate

The risk-free rate represents the theoretical return on an investment with no default risk. U.S. Treasury securities are commonly used as proxies due to their extremely low default risk. These include Treasury bills (T-bills) for short maturities, Treasury notes (T-notes) for intermediate maturities, and Treasury bonds (T-bonds) for longer maturities.

The U.S. Department of the Treasury provides daily Treasury yield curve rates. Financial data providers and investment platforms also publish these rates. When selecting a risk-free rate, match its maturity to the investment horizon of the asset being analyzed. For instance, a 10-year Treasury note yield is often used as a standard proxy for longer-term investments due to its liquidity and frequent quotation.

While theoretically, the risk-free rate should align with the investment duration, professional practice often defaults to the 10-year U.S. Treasury yield. This is because the 10-year Treasury bond is heavily traded and liquid, making its yield a widely accepted benchmark. Some argue that shorter-term Treasury bills might be better proxies for the risk-free rate due to their lower inflation risk.

Calculating Beta

Beta (β) measures an asset’s systematic risk, illustrating its volatility relative to the overall market. A Beta of 1 indicates the asset’s price moves with the market. A Beta greater than 1 suggests higher volatility, while a Beta less than 1 implies lower volatility. For example, a stock with a Beta of 1.3 is expected to move 1.3% for every 1% market movement.

Beta is derived through statistical regression analysis, comparing an asset’s historical returns to a broad market index, such as the S&P 500. Most financial websites, investment platforms, and data terminals provide pre-calculated Beta values for publicly traded companies.

For private companies, where stock price data is unavailable, estimating Beta requires an indirect approach. One method involves identifying publicly traded comparable companies within the same industry. The average Beta of these comparable companies is then calculated, and adjustments are made for differences in financial leverage between the public and private entities, often involving unlevering and relevering Betas.

Estimating the Market Risk Premium

The Market Risk Premium (MRP) represents the additional return investors expect for investing in the overall market, or a broad market index, compared to a risk-free asset. This premium is a forward-looking estimate and its value can vary.

Common approaches to estimating the MRP include using historical average returns of a broad market index (like the S&P 500) minus the risk-free rate over a long period. For example, if the S&P 500 historically generated a 9% return and the 10-year U.S. Treasury bond yielded 5%, the historical MRP would be 4%. However, historical data may not always predict future expectations accurately.

Another method involves forward-looking estimates, which consider current market conditions and investor expectations. This can include implied equity risk premiums derived from current market prices and expected future cash flows, often using models like the Dividend Discount Model. Reputable financial institutions, academic researchers, and financial data providers often publish their estimates of the MRP, which can vary.

Applying the CAPM Formula

Once the numerical values for the Risk-Free Rate, Beta, and Market Return (or Market Risk Premium) have been determined, apply these figures to the CAPM formula. This straightforward calculation yields the expected return for a specific asset.

The formula is: Expected Return = Risk-Free Rate + Beta (Market Return – Risk-Free Rate). Let’s consider a hypothetical example. Assume the current risk-free rate (Rf) is 3%, the asset’s Beta (β) is 1.2, and the expected market return (E(Rm)) is 8%.

First, calculate the Market Risk Premium: (8% – 3%) = 5%. Next, multiply this premium by the asset’s Beta: 1.2 5% = 6%. Finally, add the risk-free rate to this product: 3% + 6% = 9%. This calculated expected return can then be used by investors to assess the attractiveness of the investment relative to its risk.