A measure of volatility relative to the market (1.0 = Market Avg).
Historical average return of the stock market (e.g. S&P 500).
Market Risk Premium:0.00%
Risk-Adjusted Premium:0.00%
Expected Rate of Return:0.00%
function calculateReturn() {
// 1. Get input values by ID matching the HTML
var rfInput = document.getElementById("rfInput").value;
var betaInput = document.getElementById("betaInput").value;
var rmInput = document.getElementById("rmInput").value;
// 2. Parse values to floats
var rf = parseFloat(rfInput);
var beta = parseFloat(betaInput);
var rm = parseFloat(rmInput);
// 3. Validation: Check if inputs are numbers
if (isNaN(rf) || isNaN(beta) || isNaN(rm)) {
alert("Please enter valid numerical values for all fields.");
return;
}
// 4. Calculate Market Risk Premium (Rm – Rf)
var marketPremium = rm – rf;
// 5. Calculate Beta Adjusted Premium (Beta * (Rm – Rf))
var riskAdjustedPremium = beta * marketPremium;
// 6. Calculate Final Expected Return (Rf + Beta * (Rm – Rf))
var expectedReturn = rf + riskAdjustedPremium;
// 7. Update the HTML results
document.getElementById("displayPremium").innerText = marketPremium.toFixed(2) + "%";
document.getElementById("displayRiskAdjusted").innerText = riskAdjustedPremium.toFixed(2) + "%";
document.getElementById("displayResult").innerText = expectedReturn.toFixed(2) + "%";
// 8. Make result box visible
document.getElementById("result-box").style.display = "block";
}
Understanding the Expected Rate of Return with Beta
Investors often face the challenge of determining whether a stock or asset is worth the risk. The Capital Asset Pricing Model (CAPM) is the standard financial tool used to calculate the expected rate of return for an asset, taking into account its sensitivity to non-diversifiable risk (systematic risk).
This calculator uses the CAPM formula to estimate what return an investor should demand as compensation for the risk they are taking by holding a specific asset.
The Formula
The mathematical foundation for this calculation is:
E(Ri) = Rf + βi (E(Rm) – Rf)
Where:
E(Ri): Expected Rate of Return on the asset.
Rf: Risk-Free Rate (usually government bonds).
βi (Beta): The sensitivity of the asset's returns to the market.
E(Rm): Expected Return of the Market.
(E(Rm) – Rf): The Market Risk Premium.
Input Definitions
1. Risk-Free Rate (%)
The Risk-Free Rate represents the return on an investment with zero risk of financial loss. In practice, analysts typically use the yield on 10-year U.S. Treasury Bonds as the proxy for the risk-free rate. A common historical baseline is between 2% and 5%.
2. Beta Value (β)
Beta measures the volatility of a stock in relation to the overall market. It determines how much compensation (premium) you need for the risk taken.
Beta = 1.0: The stock moves exactly in sync with the market.
Beta > 1.0: The stock is more volatile than the market (Aggressive). Example: Tech startups.
Beta < 1.0: The stock is less volatile than the market (Defensive). Example: Utilities or Consumer Staples.
Beta < 0: The stock moves inversely to the market (Rare). Example: Gold (sometimes) or inverse ETFs.
3. Expected Market Return (%)
This is the average return expected from the broader market portfolio, such as the S&P 500. Historically, the stock market has returned approximately 8% to 10% annually over long periods.
Example Calculation
Scenario: You are analyzing a technology stock with high volatility.
Risk-Free Rate: 4.0%
Beta: 1.5 (50% more volatile than the market)
Market Return: 10.0%
Step 1: Calculate Market Premium: 10% – 4% = 6%
Step 2: Adjust for Beta: 1.5 × 6% = 9%
Step 3: Add Risk-Free Rate: 4% + 9% = 13%
Conclusion: To justify the risk of this tech stock, you should expect a return of at least 13%.
Why is this important?
Using Beta to calculate the expected return allows investors to make "apples-to-apples" comparisons between different assets. A stock offering a 12% return might look attractive, but if its Beta is 2.5, the CAPM formula might indicate you should actually demand a 15% return to justify that level of risk. In that case, the stock would be considered overvalued.