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How to Calculate Risk-Free Rate in CAPM
The Risk-Free Rate ($R_f$) is a foundational component of modern finance, serving as the baseline return an investor expects for taking zero risk. In the context of the Capital Asset Pricing Model (CAPM), it represents the y-intercept of the Security Market Line (SML).
Calculating the risk-free rate correctly is critical for valuing equities, estimating the cost of equity ($K_e$), and determining the Weighted Average Cost of Capital (WACC). While theoretically a "risk-free" asset does not exist, financial analysts use specific proxies to estimate this rate.
CAPM Formula:
E(Ri) = Rf + βi * (E(Rm) – Rf)
Where:
Rf = Risk-Free Rate (Calculated above)
βi = Beta of the asset
E(Rm) – Rf = Market Risk Premium
1. Choosing the Right Proxy
To calculate the risk-free rate, you must first select an appropriate government security. The choice depends on the investment horizon:
- 10-Year Treasury Note: This is the standard proxy used for equity valuation and corporate finance because stocks are long-duration assets. Using a long-term rate matches the duration of cash flows.
- 3-Month T-Bill: Sometimes used for short-term modeling, but generally considered too volatile and not reflective of long-term inflation expectations for CAPM purposes.
2. The Calculation Logic
For developed economies like the United States or Germany, the calculation is often as simple as looking up the current yield on the 10-year government bond.
However, for emerging markets or when adjusting for specific economic conditions, the formula expands:
Nominal Rf = Government Bond Yield – Sovereign Default Spread
If a country has a risk of defaulting on its debt, its bond yield includes a premium for that risk. To find the true risk-free rate, you must subtract this default spread (often derived from Credit Default Swaps or the spread between the local bond and a US Treasury bond).
3. Nominal vs. Real Risk-Free Rate
Most CAPM calculations utilize the Nominal Risk-Free Rate, which includes expected inflation. However, if your cash flow projections are in real terms (excluding inflation), you must use the Real Risk-Free Rate.
The Fisher Equation approximates this relationship:
Real Rf ≈ Nominal Rf – Expected Inflation Rate
Our calculator provides both the nominal rate (for standard CAPM) and the real rate (for inflation-adjusted analysis).
Why It Matters
A small change in the risk-free rate can significantly alter the valuation of a company. As $R_f$ rises, the required rate of return ($K_e$) increases, which lowers the present value of future cash flows, typically resulting in lower stock valuations.
function calculateRiskFreeRate() {
// 1. Get input values
var bondYieldInput = document.getElementById('govtBondYield');
var spreadInput = document.getElementById('defaultSpread');
var inflationInput = document.getElementById('inflationRate');
var bondYield = parseFloat(bondYieldInput.value);
var spread = parseFloat(spreadInput.value);
var inflation = parseFloat(inflationInput.value);
// 2. Validate inputs
if (isNaN(bondYield)) {
alert("Please enter a valid Government Bond Yield.");
return;
}
// Handle empty optional fields (treat as 0)
if (isNaN(spread)) {
spread = 0;
}
if (isNaN(inflation)) {
inflation = 0;
}
// 3. Calculate Nominal Risk-Free Rate
// Formula: Yield – Default Spread
var nominalRf = bondYield – spread;
// 4. Calculate Real Risk-Free Rate (Fisher Equation)
// Exact formula: (1 + Nominal) = (1 + Real) * (1 + Inflation)
// Real = ((1 + Nominal) / (1 + Inflation)) – 1
// We convert percentages to decimals for calculation, then back to %
var nominalDecimal = nominalRf / 100;
var inflationDecimal = inflation / 100;
var realRfDecimal = ((1 + nominalDecimal) / (1 + inflationDecimal)) – 1;
var realRf = realRfDecimal * 100;
// 5. Display Results
document.getElementById('nominalRfDisplay').innerHTML = nominalRf.toFixed(2) + "%";
document.getElementById('realRfDisplay').innerHTML = realRf.toFixed(2) + "%";
document.getElementById('baseYieldDisplay').innerHTML = bondYield.toFixed(2) + "%";
document.getElementById('adjustmentDisplay').innerHTML = "-" + spread.toFixed(2) + "%";
// Show the results box
document.getElementById('results').style.display = "block";
}