Risk Free Rate of Return Calculator

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Risk-Free Rate of Return Calculator

Calculation Result

The Annualized Risk-Free Rate is:

Note: This calculation uses the bond equivalent yield formula based on a 360-day year convention.

function calculateRiskFreeRate() { var faceValue = parseFloat(document.getElementById('faceValue').value); var purchasePrice = parseFloat(document.getElementById('purchasePrice').value); var daysToMaturity = parseFloat(document.getElementById('daysToMaturity').value); var resultWrapper = document.getElementById('rfResultWrapper'); var resultDisplay = document.getElementById('rfYieldResult'); if (isNaN(faceValue) || isNaN(purchasePrice) || isNaN(daysToMaturity) || purchasePrice <= 0 || daysToMaturity = faceValue) { alert("Purchase price must be less than face value for a standard discount security."); } // Calculation: ((Face Value – Price) / Price) * (360 / Days to Maturity) * 100 var yieldValue = ((faceValue – purchasePrice) / purchasePrice) * (360 / daysToMaturity) * 100; resultDisplay.innerText = yieldValue.toFixed(4) + "%"; resultWrapper.style.display = "block"; }

Understanding the Risk-Free Rate of Return

The Risk-Free Rate of Return is a fundamental concept in finance, representing the theoretical interest an investor would expect from an investment with zero risk over a specified period. In practice, while no investment is truly 100% risk-free, government-backed securities like U.S. Treasury Bills (T-Bills) are used as the standard proxy because the probability of default is considered negligible.

Why is the Risk-Free Rate Important?

This rate serves as the baseline for all other investment calculations. It is a critical component in:

  • Capital Asset Pricing Model (CAPM): Used to calculate the expected return of an asset based on its beta and the risk-free rate.
  • Sharpe Ratio: Used to calculate risk-adjusted returns by subtracting the risk-free rate from the portfolio return.
  • Cost of Equity: Corporations use it to determine their hurdle rates for new projects.

How to Calculate Using This Tool

Our calculator determines the annualized yield of a discount security (like a T-Bill) based on its current market price and maturity date. The formula used is:

Yield = [(Face Value – Price) / Price] × (360 / Days to Maturity) × 100

Practical Example

Imagine you purchase a 91-day Treasury Bill with a Face Value of 1,000. Because these are sold at a discount, you pay a Purchase Price of 988.50.

  1. Calculate the gain: 1,000 – 988.50 = 11.50
  2. Calculate the period return: 11.50 / 988.50 = 0.01163
  3. Annualize the return (using a 360-day year): 0.01163 * (360 / 91) = 0.0460
  4. Annualized Risk-Free Rate: 4.60%

Nominal vs. Real Risk-Free Rate

The value calculated above is the Nominal Rate. To find the Real Risk-Free Rate, you must account for inflation. If the nominal rate is 4.6% and inflation is 2%, your actual purchasing power only increases by approximately 2.6%. For high-precision financial modeling, the Fisher Equation is used to adjust for these inflationary pressures.

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