Security’s Equilibrium Rate of Return Calculator

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Equilibrium Rate of Return Calculator (CAPM)

The return on a zero-risk investment (e.g., T-Bills).
A measure of the security's volatility relative to the market.
The average expected return of the market index.

Equilibrium Rate of Return

0.00%

Understanding Security's Equilibrium Rate of Return

In financial theory, specifically within the Capital Asset Pricing Model (CAPM), the equilibrium rate of return represents the return required by investors to compensate them for the risk associated with holding a specific security. In an efficient market, this is the point where the supply of the security equals the demand.

This calculator helps investors determine if a stock or asset is fairly valued given its risk profile (Beta) compared to the broader market.

The Formula

The calculation is based on the Capital Asset Pricing Model (CAPM) formula:

E(Ri) = Rf + βi * (E(Rm) – Rf)

Where:

  • E(Ri): The Equilibrium (Expected) Rate of Return for the security.
  • Rf: The Risk-Free Rate (typically the yield on government treasury bills).
  • βi (Beta): The sensitivity of the security's returns to market returns.
  • E(Rm): The Expected Return of the Market.
  • (E(Rm) – Rf): The Market Risk Premium.

What Do The Inputs Mean?

Risk-Free Rate (Rf)

This is the theoretical rate of return of an investment with zero risk. In practice, the yield on 10-year U.S. Treasury bonds is often used as a proxy. If the current Treasury yield is 4%, you would enter 4.

Security Beta (β)

Beta measures systemic risk.

  • Beta = 1.0: The security moves exactly in line with the market.
  • Beta > 1.0: The security is more volatile than the market (higher risk, higher expected return).
  • Beta < 1.0: The security is less volatile than the market (lower risk, lower expected return).

Expected Market Return (Rm)

This is the average return expected from the market portfolio (e.g., the S&P 500). Historically, this often ranges between 8% and 10% over long periods, though it varies based on economic conditions.

Example Calculation

Imagine you are analyzing a tech stock with a high volatility. Here is how the equilibrium rate is calculated:

  • Risk-Free Rate: 3%
  • Security Beta: 1.5 (50% more volatile than the market)
  • Expected Market Return: 9%

Calculation:

Equilibrium Rate = 3% + 1.5 * (9% – 3%)

Equilibrium Rate = 3% + 1.5 * (6%)

Equilibrium Rate = 3% + 9% = 12%

This means that for the risk taken (Beta of 1.5), an investor requires a 12% return for the market to be in equilibrium.

Why is this important?

If an analyst estimates that the stock will actually return 15% (Fundamental Analysis), but the CAPM Equilibrium Rate is only 12%, the stock is considered undervalued (it offers more return than required for its risk level), representing a "Buy" signal.

Conversely, if the expected return is only 8%, but the equilibrium rate is 12%, the stock is overvalued given its risk profile.

function calculateEquilibrium() { // Get input values var rfInput = document.getElementById('riskFreeRate').value; var betaInput = document.getElementById('securityBeta').value; var rmInput = document.getElementById('marketReturn').value; // Convert to numbers var rf = parseFloat(rfInput); var beta = parseFloat(betaInput); var rm = parseFloat(rmInput); // Validation if (isNaN(rf) || isNaN(beta) || isNaN(rm)) { alert("Please enter valid numbers for all fields."); return; } // CAPM Logic: E(Ri) = Rf + Beta * (Rm – Rf) // Note: We keep numbers as percentages in the variable but treat the math logic carefully. // Formula using percentages directly: E% = Rf% + Beta * (Rm% – Rf%) var marketRiskPremium = rm – rf; var riskPremiumForSecurity = beta * marketRiskPremium; var equilibriumRate = rf + riskPremiumForSecurity; // Display results var resultDiv = document.getElementById('result'); var equilibriumDisplay = document.getElementById('equilibriumResult'); var detailDisplay = document.getElementById('riskPremiumDetail'); resultDiv.style.display = 'block'; equilibriumDisplay.innerText = equilibriumRate.toFixed(2) + "%"; detailDisplay.innerHTML = "Base Risk-Free Rate: " + rf.toFixed(2) + "%" + "Plus Security Risk Premium: " + riskPremiumForSecurity.toFixed(2) + "%"; }

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