Simple is common for approximations; Geometric is mathematically precise for compounding.
Daily Rate (Percentage):
Decimal Value (Raw):
Annualized Effective Rate:
Understanding the Daily Risk-Free Rate Calculation
The Daily Risk-Free Rate is a crucial metric in quantitative finance, particularly when calculating the Sharpe Ratio, Sortino Ratio, or performing daily volatility analysis for investment portfolios. It represents the theoretical return of an investment with zero risk over a single day.
Most interest rates, such as the 10-year US Treasury yield or the 3-month T-Bill rate, are quoted on an annualized basis. To evaluate the performance of trading strategies that operate on a daily timeframe, this annual rate must be de-annualized correctly.
Why Convert to a Daily Rate?
Financial analysts generally calculate portfolio returns and standard deviations using daily data points. To compare these daily returns against a benchmark (the risk-free asset), the benchmark itself must be expressed in the same daily timeframe. Using an annual rate against daily returns would lead to massive calculation errors in risk-adjusted performance metrics.
Calculation Methods
There are two primary ways to convert an annual rate to a daily rate:
1. Simple Arithmetic (Linear)
This is the most common method used in backtesting and by many financial data providers for simplicity.
Formula: Daily Rate = Annual Rate / Days in Year
For example, if the annual rate is 5% and we assume 252 trading days:
0.05 / 252 = 0.0001984 (or 0.0198%)
2. Geometric Compounding
This method assumes that the daily rate compounds to equal the annual rate at the end of the year. This is mathematically more rigorous for compounding assets.
Formula: Daily Rate = (1 + Annual Rate)^(1 / Days in Year) – 1
Choosing the Time Basis
The denominator in your calculation depends on the asset class and convention:
252 Days: The standard for equity markets (stocks), representing the approximate number of trading days in a year excluding weekends and holidays.
360 Days: Often used in banking and money markets (Day Count Convention).
365 Days: Used for cryptocurrencies or global macro models that account for every calendar day.
How to Use This Calculator
Enter Annual Rate: Input the current annual percentage yield (e.g., for a 4.5% T-Bill, enter 4.5).
Select Time Basis: Choose 252 for stock market analysis or 365 for crypto/calendar analysis.
Select Method: Choose Simple for standard Sharpe Ratio estimates or Compound for precise valuation models.
function calculateDailyRate() {
// 1. Get input values
var annualRateInput = document.getElementById("annualRfRate").value;
var timeBasis = document.getElementById("timeBasis").value;
var method = document.getElementById("calcMethod").value;
var resultBox = document.getElementById("rfResult");
// 2. Validate inputs
if (annualRateInput === "" || isNaN(annualRateInput)) {
alert("Please enter a valid Annual Risk-Free Rate.");
return;
}
var annualRatePercent = parseFloat(annualRateInput);
var basisDays = parseInt(timeBasis);
// Convert percentage to decimal for calculation (e.g., 5% -> 0.05)
var annualRateDecimal = annualRatePercent / 100;
var dailyRateDecimal = 0;
// 3. Calculation Logic
if (method === "simple") {
// Simple division: r_daily = r_annual / days
dailyRateDecimal = annualRateDecimal / basisDays;
} else {
// Geometric compounding: r_daily = (1 + r_annual)^(1/days) – 1
dailyRateDecimal = Math.pow((1 + annualRateDecimal), (1 / basisDays)) – 1;
}
// 4. Formatting Results
// Percentage string (e.g., 0.0198%)
var dailyRatePercentDisplay = (dailyRateDecimal * 100).toFixed(6) + "%";
// Raw decimal string (e.g., 0.000198)
var dailyRateDecimalDisplay = dailyRateDecimal.toFixed(9);
// Annualized check (to show the math works)
var checkAnnual = 0;
if (method === "simple") {
checkAnnual = dailyRateDecimal * basisDays * 100;
} else {
checkAnnual = (Math.pow((1 + dailyRateDecimal), basisDays) – 1) * 100;
}
// 5. Display Results
document.getElementById("resPercentage").innerHTML = dailyRatePercentDisplay;
document.getElementById("resDecimal").innerHTML = dailyRateDecimalDisplay;
document.getElementById("resEffective").innerHTML = checkAnnual.toFixed(2) + "%";
resultBox.style.display = "block";
}