Nominal Risk-Free Rate (Adjusted for Default):0.00%
Real Risk-Free Rate (Approximation):0.00%
Real Risk-Free Rate (Fisher Exact):0.00%
function calculateRiskFree() {
// 1. Get Input Values
var nominalYieldInput = document.getElementById("nominalYield").value;
var inflationRateInput = document.getElementById("inflationRate").value;
var defaultSpreadInput = document.getElementById("defaultSpread").value;
// 2. Validate Inputs
if (nominalYieldInput === "" || inflationRateInput === "") {
alert("Please enter both the Government Bond Yield and the Expected Inflation Rate.");
return;
}
var nominal = parseFloat(nominalYieldInput);
var inflation = parseFloat(inflationRateInput);
var spread = parseFloat(defaultSpreadInput);
if (isNaN(nominal) || isNaN(inflation)) {
alert("Please enter valid numeric values.");
return;
}
if (isNaN(spread)) {
spread = 0;
}
// 3. Logic & Calculations
// A. Adjusted Nominal Risk-Free Rate (Removing Country Risk Premium)
// If analyzing a risky country, we subtract the default spread to find the "true" risk-free component.
var adjustedNominal = nominal – spread;
// B. Real Risk-Free Rate (Approximation)
// Formula: Nominal – Inflation
var realApprox = adjustedNominal – inflation;
// C. Real Risk-Free Rate (Fisher Equation Exact)
// Formula: (1 + Nominal) = (1 + Real) * (1 + Inflation)
// Real = [(1 + Nominal) / (1 + Inflation)] – 1
// Note: Inputs are percentages, convert to decimals first
var nominalDecimal = adjustedNominal / 100;
var inflationDecimal = inflation / 100;
var realExactDecimal = ((1 + nominalDecimal) / (1 + inflationDecimal)) – 1;
var realExact = realExactDecimal * 100;
// 4. Update UI
document.getElementById("resNominalAdjusted").innerHTML = adjustedNominal.toFixed(2) + "%";
document.getElementById("resRealApprox").innerHTML = realApprox.toFixed(2) + "%";
document.getElementById("resRealExact").innerHTML = realExact.toFixed(2) + "%";
document.getElementById("results").style.display = "block";
}
How to Calculate Risk-Free Rate for CAPM
The Capital Asset Pricing Model (CAPM) is a cornerstone of modern financial theory, used to determine the expected return on an asset based on its systematic risk. At the very foundation of this formula lies the Risk-Free Rate (Rf).
The Risk-Free Rate represents the theoretical return on an investment with zero risk of financial loss. While no investment is truly "risk-free" in the absolute sense, government bonds issued by stable, sovereign entities (like the U.S. Treasury) are used as the standard proxy.
CAPM Formula:
E(Ri) = Rf + βi * (E(Rm) – Rf)
Where:
Rf = Risk-Free Rate (The focus of this calculator)
βi = Beta of the asset
E(Rm) = Expected return of the market
Selecting the Right Proxy
To calculate the risk-free rate, you do not use a complex mathematical derivation but rather select a market proxy. However, adjustments are often required based on the economic environment:
For Short-Term Models: The 3-Month Treasury Bill yield is often used.
For Long-Term Valuation (Standard): The 10-Year Treasury Note yield is the industry standard for valuing stocks and corporate projects, as equity is a long-duration asset.
Calculation Method 1: The Inflation Adjustment (Fisher Equation)
If you are building a financial model in "real terms" (excluding inflation), you must convert the nominal government bond yield into a real risk-free rate. This calculator uses the Fisher Equation to perform this conversion.
The Approximation: Real Rf ≈ Nominal Yield – Expected Inflation
The Exact Formula: Real Rf = [(1 + Nominal Yield) / (1 + Expected Inflation)] – 1
Calculation Method 2: The Country Risk Adjustment
If you are valuing a company in a developing market where government bonds are not rated AAA, the government bond yield includes a default risk premium. To find the true "risk-free" rate for CAPM in this context, you must subtract the country's default spread.
Formula:Risk Free Rate = Local Govt Bond Yield – Country Default Spread
For example, if a developing nation's 10-year bond yields 8% and the default spread compared to US Treasuries is 2%, the adjusted Risk-Free Rate is 6%.
Why This Matters for Valuation
The Risk-Free Rate is the starting point (the y-intercept) of the Security Market Line. If you overestimate the risk-free rate by failing to adjust for default risk or inflation, you will artificially inflate the Cost of Equity. This leads to a lower valuation (Discounted Cash Flow) and potentially rejecting profitable investment opportunities.