The anticipated return of the individual stock or portfolio.
Usually the yield on a 10-year Treasury bond.
The anticipated return of the market index (e.g., S&P 500).
Calculated Beta Coefficient
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function calculateBeta() {
// Get input values
var raInput = document.getElementById('assetReturn').value;
var rfInput = document.getElementById('riskFreeRate').value;
var rmInput = document.getElementById('marketReturn').value;
// Validation
if (raInput === "" || rfInput === "" || rmInput === "") {
alert("Please fill in all fields to calculate Beta.");
return;
}
// Parse values to floats
var Ra = parseFloat(raInput); // Expected Return of Asset
var Rf = parseFloat(rfInput); // Risk-Free Rate
var Rm = parseFloat(rmInput); // Expected Return of Market
// Check for denominator zero (Market Risk Premium cannot be 0)
var marketPremium = Rm – Rf;
if (marketPremium === 0) {
alert("The Market Risk Premium (Market Return – Risk Free Rate) cannot be zero. This would result in undefined Beta.");
return;
}
// Calculation: Beta = (Asset Return – Risk Free Rate) / (Market Return – Risk Free Rate)
var assetPremium = Ra – Rf;
var beta = assetPremium / marketPremium;
// Display results
var resultBox = document.getElementById('resultBox');
var resultDisplay = document.getElementById('betaResult');
var interpretationDisplay = document.getElementById('betaInterpretation');
resultDisplay.innerHTML = beta.toFixed(3);
resultBox.style.display = "block";
// Generate Interpretation text based on Beta value
var interpText = "Analysis: ";
if (beta === 1) {
interpText += "The asset moves exactly in sync with the market.";
} else if (beta > 1) {
interpText += "High Volatility. The asset is theoretically " + ((beta – 1) * 100).toFixed(1) + "% more volatile than the market. It offers higher potential returns but comes with higher risk.";
} else if (beta > 0 && beta < 1) {
interpText += "Low Volatility. The asset is theoretically " + ((1 – beta) * 100).toFixed(1) + "% less volatile than the market. It is considered a defensive investment.";
} else if (beta === 0) {
interpText += "No correlation. The asset's return is uncorrelated with the market (e.g., cash or gold).";
} else if (beta < 0) {
interpText += "Negative Correlation. The asset theoretically moves in the opposite direction of the market (e.g., inverse ETFs or put options).";
}
interpretationDisplay.innerHTML = interpText;
}
How to Calculate Beta with Risk-Free Rate
Beta (β) is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole. It is a core component of the Capital Asset Pricing Model (CAPM). While Beta is often looked up on financial websites, understanding how to calculate it using the risk-free rate allows investors to reverse-engineer expectations or analyze private assets.
β = (E(Ra) – Rf) / (E(Rm) – Rf)
Where:
E(Ra): The Expected Return of the Asset.
Rf: The Risk-Free Rate (usually the 10-year Treasury yield).
E(Rm): The Expected Return of the Market.
(E(Rm) – Rf): This is known as the Market Risk Premium.
Understanding the Inputs
To use the calculator above effectively, you need three specific data points:
Expected Asset Return: This is the total return you anticipate from the stock or fund over a specific period. This can be based on historical averages or analyst projections.
Risk-Free Rate: This represents the theoretical return of an investment with zero risk. In practice, the yield on government bonds (like the US 10-Year Treasury Note) is the standard proxy.
Market Return: This is the expected return of the benchmark index, such as the S&P 500. Historically, this averages around 10% annually.
Calculation Example:
Imagine a tech stock is expected to return 15% next year.
The current 10-year Treasury yield (Risk-Free Rate) is 4%.
The expected return of the S&P 500 (Market) is 9%.
This Beta of 2.2 indicates the stock is more than twice as volatile as the market.
Interpreting Your Beta Result
Once you calculate Beta, the number tells you about the relationship between the asset and the market:
Beta > 1.0: Aggressive. The stock tends to move more than the market. If the market goes up 10%, a stock with a beta of 1.5 might go up 15%.
Beta = 1.0: Neutral. The stock carries the same systematic risk as the market index.
Beta < 1.0: Defensive. The stock is less volatile than the market. Utility companies often fall into this category.
Beta < 0: Inverse. The asset generally moves in the opposite direction of the market.
Why Use the Risk-Free Rate?
Using the risk-free rate isolates the "risk premium"—the extra return an investor demands for taking on risk. By subtracting the risk-free rate from both the asset and the market, the formula focuses purely on the compensation for volatility, providing a clearer picture of systematic risk than simple return comparisons.