Measure of the stock's volatility relative to the market (Market = 1.0).
Historical average return of the market (e.g., S&P 500).
Required Rate of Return
0.00%
function calculateRRR() {
// 1. Get input values
var rfInput = document.getElementById("riskFreeRate").value;
var betaInput = document.getElementById("stockBeta").value;
var rmInput = document.getElementById("marketReturn").value;
// 2. Parse values to floats
var rf = parseFloat(rfInput);
var beta = parseFloat(betaInput);
var rm = parseFloat(rmInput);
// 3. Validation
if (isNaN(rf) || isNaN(beta) || isNaN(rm)) {
alert("Please enter valid numeric values for all fields.");
return;
}
// 4. Calculate Market Risk Premium
var marketRiskPremium = rm – rf;
// 5. Calculate Required Rate of Return using CAPM Formula: RRR = Rf + Beta * (Rm – Rf)
var rrr = rf + (beta * marketRiskPremium);
// 6. Display Results
var resultContainer = document.getElementById("rrr-result-container");
var resultValue = document.getElementById("rrr-final-value");
var breakdown = document.getElementById("rrr-formula-breakdown");
resultContainer.style.display = "block";
resultValue.innerHTML = rrr.toFixed(2) + "%";
// Provide a text explanation of the math
breakdown.innerHTML = "Calculation Logic:" +
rf + "% (Risk-Free) + [" + beta + " (Beta) × (" + rm + "% – " + rf + "%)]" +
"= " + rf + "% + [" + beta + " × " + marketRiskPremium.toFixed(2) + "% (Risk Premium)]" +
"= " + rf + "% + " + (beta * marketRiskPremium).toFixed(2) + "%" +
"= " + rrr.toFixed(2) + "%";
}
Understanding the Formula to Calculate Required Rate of Return
The Required Rate of Return (RRR) is a critical concept in finance and investing. It represents the minimum return an investor expects to achieve on an investment to compensate for the risk they are taking. If an investment cannot provide this return, it is generally considered unwise to proceed.
While there are several methods to estimate RRR, the most widely accepted method for equity assets is the Capital Asset Pricing Model (CAPM).
The CAPM Formula
The standard formula used in our calculator above is:
RRR = Rf + β(Rm – Rf)
Here is a detailed breakdown of the components:
Rf (Risk-Free Rate): This is the theoretical return of an investment with zero risk. In practice, the yield on current 10-year U.S. Treasury bills is often used as the proxy for the risk-free rate.
β (Beta): This measures the volatility (systematic risk) of a specific stock or asset compared to the overall market. A beta of 1.0 means the stock moves exactly with the market. A beta greater than 1.0 implies higher volatility (and higher risk), while a beta less than 1.0 implies stability.
Rm (Expected Market Return): This is the average return expected from the broader market (such as the S&P 500) over a similar time horizon.
(Rm – Rf): This term is known as the Market Risk Premium. It represents the extra return the market offers over the risk-free rate to compensate investors for taking on equity risk.
Example Calculation
Let's say you are analyzing a technology stock. You want to know what return you should demand to justify purchasing it.
Risk-Free Rate: 3.5% (Current Treasury Yield)
Beta: 1.5 (The stock is 50% more volatile than the market)
Expected Market Return: 10% (Historical average)
Using the formula:
RRR = 3.5% + 1.5 × (10% – 3.5%)
RRR = 3.5% + 1.5 × (6.5%)
RRR = 3.5% + 9.75%
RRR = 13.25%
In this scenario, if the stock is not projected to return at least 13.25%, it is not meeting your required rate of return based on its risk profile.
Why is RRR Important?
The Required Rate of Return is used primarily for valuation. In Discounted Cash Flow (DCF) analysis, the RRR is often used as the discount rate to determine the present value of future cash flows. A higher RRR results in a lower present value (lower current stock price justification), reflecting the higher risk associated with the investment.
Limitations
While the CAPM formula is the industry standard, it relies on assumptions. Beta is based on historical data which may not predict future volatility. Additionally, estimating the "Expected Market Return" is subjective and can vary between analysts.