How to Calculate Expected Rate of Return with Beta

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CAPM Expected Rate of Return Calculator

Usually the yield on government bonds (e.g., 10-year Treasury).
Volatility relative to the market (Market Beta = 1.0).
The average annual return expected from the stock market index (e.g., S&P 500).

Calculation Result

function calculateCAPM() { var rf = parseFloat(document.getElementById('riskFreeRate').value); var beta = parseFloat(document.getElementById('assetBeta').value); var rm = parseFloat(document.getElementById('marketReturn').value); var resultDiv = document.getElementById('capmResult'); var outputVal = document.getElementById('outputValue'); var outputForm = document.getElementById('outputFormula'); if (isNaN(rf) || isNaN(beta) || isNaN(rm)) { alert("Please enter valid numerical values for all fields."); return; } // CAPM Formula: Expected Return = Risk-Free Rate + Beta * (Market Return – Risk-Free Rate) var marketRiskPremium = rm – rf; var expectedReturn = rf + (beta * marketRiskPremium); outputVal.innerHTML = expectedReturn.toFixed(2) + "%"; outputForm.innerHTML = "Formula: " + rf + "% + " + beta + " × (" + rm + "% – " + rf + "%) = " + expectedReturn.toFixed(2) + "%"; resultDiv.style.display = "block"; }

How to Calculate Expected Rate of Return with Beta (CAPM)

The Capital Asset Pricing Model (CAPM) is a cornerstone of modern finance, used to determine the theoretically appropriate required rate of return of an asset. By using Beta, investors can understand how much premium they should receive for taking on the specific systematic risk of a stock or portfolio.

The CAPM Formula

To calculate the expected rate of return, we use the following equation:

Expected Return = Rf + [β × (Rm – Rf)]
  • Rf (Risk-Free Rate): The return on an investment with zero risk, typically represented by government bond yields.
  • β (Beta): A measure of a stock's volatility in relation to the overall market.
  • Rm (Expected Market Return): The return the market as a whole is expected to provide.
  • (Rm – Rf): This is known as the Market Risk Premium.

Step-by-Step Calculation Example

Imagine you are looking at a technology stock. You find the following data points:

  1. Risk-Free Rate: The 10-year Treasury Note is yielding 4.0%.
  2. Beta: The stock has a Beta of 1.5 (meaning it is 50% more volatile than the market).
  3. Market Return: You expect the S&P 500 to return 10.0% over the next year.

The Calculation:

1. Subtract the Risk-Free Rate from the Market Return: 10.0% – 4.0% = 6.0% (Market Risk Premium).
2. Multiply the result by Beta: 1.5 × 6.0% = 9.0%.
3. Add the Risk-Free Rate back: 4.0% + 9.0% = 13.0%.

In this scenario, the expected rate of return for the stock is 13.0%.

Understanding Beta Values

Beta is the variable that dictates the sensitivity of the asset's return to market movements:

Beta Value Meaning
β < 0 Negative Correlation: Asset moves opposite to the market (rare).
0 < β < 1 Less Volatile: Defensive stocks (e.g., Utilities) that move less than the market.
β = 1.0 Market Match: Moves exactly in sync with the benchmark index.
β > 1.0 More Volatile: Aggressive stocks (e.g., Tech/Growth) that swing more than the market.

Why Use Beta to Calculate Return?

The primary reason for using Beta in calculations is to adjust for risk. If you take on a stock that is twice as volatile as the market (Beta of 2.0), you should logically expect a higher potential return to compensate for that extra risk. Conversely, if an investment's expected return is lower than what the CAPM model suggests, it may be considered overvalued or a poor risk-adjusted choice.

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