The theoretical return of an investment with zero risk (e.g., 10-year Treasury yield).
A measure of the security's volatility in relation to the market.
The average expected return of the market index (e.g., S&P 500).
Equilibrium Rate of Return (Ke)
0.00%
function calculateEquilibrium() {
var rfInput = document.getElementById("riskFreeRate").value;
var betaInput = document.getElementById("securityBeta").value;
var rmInput = document.getElementById("marketReturn").value;
var resultDiv = document.getElementById("resultOutput");
var finalRateDiv = document.getElementById("finalRate");
var breakdownDiv = document.getElementById("calculationBreakdown");
// Input Validation
if (rfInput === "" || betaInput === "" || rmInput === "") {
alert("Please fill in all fields (Risk-Free Rate, Beta, and Expected Market Return).");
return;
}
var rf = parseFloat(rfInput);
var beta = parseFloat(betaInput);
var rm = parseFloat(rmInput);
if (isNaN(rf) || isNaN(beta) || isNaN(rm)) {
alert("Please enter valid numbers.");
return;
}
// Logic: CAPM Formula = Rf + Beta * (Rm – Rf)
// Rm – Rf is the Market Risk Premium
var marketRiskPremium = rm – rf;
var riskPremium = beta * marketRiskPremium;
var equilibriumRate = rf + riskPremium;
// Display Results
resultDiv.style.display = "block";
finalRateDiv.innerHTML = equilibriumRate.toFixed(2) + "%";
// Detailed Breakdown
var breakdownHtml = "Calculation Breakdown:";
breakdownHtml += "Risk-Free Rate: " + rf + "%";
breakdownHtml += "Market Risk Premium (Rm – Rf): " + marketRiskPremium.toFixed(2) + "%";
breakdownHtml += "Security Risk Premium (Beta × Market Risk Premium): " + riskPremium.toFixed(2) + "%";
breakdownHtml += "Formula: " + rf + " + (" + beta + " × (" + rm + " – " + rf + ")) = " + equilibriumRate.toFixed(2) + "%";
breakdownDiv.innerHTML = breakdownHtml;
}
How to Calculate a Security's Equilibrium Rate of Return
Investors and financial analysts use the Equilibrium Rate of Return to determine the fair expected return on a security (such as a stock) given its level of systematic risk. This calculation is fundamentally based on the Capital Asset Pricing Model (CAPM).
The core concept is that an investor should be compensated for two things: time value of money and risk. If a security is riskier than the general market, it must offer a higher potential return to be considered "in equilibrium."
The CAPM Formula
The standard formula used in the calculator above is:
E(Ri) = Rf + βi * (E(Rm) – Rf)
E(Ri): The Equilibrium (Expected) Rate of Return.
Rf (Risk-Free Rate): The return of a theoretical risk-free investment, often represented by the yield on a 10-year government bond.
βi (Beta): A coefficient representing the sensitivity of the security's returns to market movements. A beta of 1.0 means the stock moves with the market. A beta > 1.0 implies higher volatility.
E(Rm) (Expected Market Return): The average return expected from the overall market (e.g., S&P 500).
(E(Rm) – Rf): This difference is known as the Market Risk Premium.
Real-World Example
Let's calculate the equilibrium rate for a technology stock with high volatility.
Adjust for the stock's risk (Beta): 1.5 × 5.5% = 8.25%
Add the Risk-Free Rate: 3.5% + 8.25% = 11.75%
In this scenario, the equilibrium rate of return is 11.75%. If the stock is currently priced such that it is expected to return only 10%, it is considered overvalued (it does not offer enough return for the risk). If it is expected to return 13%, it is undervalued (offering excess return).
Why is Beta Important?
Beta is the lever in this calculation. If you hold a defensive stock (like a utility company) with a Beta of 0.5, your equilibrium return will be lower because you are taking less risk. Conversely, aggressive growth stocks require higher equilibrium rates to justify their inclusion in a balanced portfolio.
Limitations of Equilibrium Calculation
While widely used, this model assumes markets are efficient and that Beta is a perfect measure of risk. It does not account for "unsystematic risk" (risk specific to the company, like management failure) because the model assumes you can diversify that risk away.