CAPM Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: August 20, 2026What Return Does a Stock's Risk Actually Justify?
The Capital Asset Pricing Model answers a specific question: given how much systematic risk a stock carries relative to the market, what return should an investor demand to hold it? It's the theoretical backbone behind beta as a risk measure, connecting the risk-free rate, the stock's beta, and the broader market's expected return into a single expected-return figure that analysts use as a benchmark for whether an investment is fairly priced.
The Formula
The term (Market Return − Risk-Free Rate) is the equity risk premium — the extra return the market as a whole is expected to deliver over a risk-free asset. Multiplying it by beta scales that premium up or down based on the individual stock's sensitivity to market moves.
Where This Matters
- Setting a discount rate — CAPM's output is a standard input to the cost of equity used in discounted cash flow valuation and WACC calculations.
- Judging whether a stock is fairly valued — comparing a stock's actual historical return to its CAPM-predicted return is one basic way analysts flag potential mispricing (this is, in fact, the same comparison that produces alpha).
- Portfolio construction — CAPM gives a theoretical basis for expecting higher-beta stocks to command higher average returns over time, informing how much risk to take on for a given return target.
Worked Example
| Step | Value |
|---|---|
| Equity risk premium (Market − Risk-Free) | 6.0% |
| Beta × Equity risk premium | 7.2% |
| Expected return | 10.2% |
3% + 1.2 × 6% = 10.2%. A beta of 1.2 means the stock is expected to earn 1.2 times the market's risk premium above the risk-free rate.
How to Use This Calculator
- Enter the risk-free rate (commonly a Treasury yield matching your time horizon).
- Enter the stock or portfolio's beta.
- Enter the expected market return.
- Select Calculate to get the CAPM expected return and the underlying equity risk premium.
Related Calculations
Feed this expected return into the WACC Calculator for a full cost-of-capital figure, or compare it against actual performance with the Portfolio Alpha Calculator.
Principles of Modern Portfolio Theory and the Capital Asset Pricing Model (CAPM)
A CAPM calculator computes the theoretical expected return on an equity investment based on its systematic market risk (β), the risk-free rate of return, and the broader equity market risk premium. Developed by Nobel laureate William Sharpe (1964), the Capital Asset Pricing Model establishes the foundational relationship between systematic risk and expected financial return.
The Fundamental CAPM and Security Market Line (SML) Formulas
Where Rf = Risk-Free Benchmark Yield (e.g., 10-Year US Treasury Bond Yield)
βi = Systematic Risk Beta Coefficient = Cov(Ri, Rm) / Var(Rm)
E(Rm) = Expected Benchmark Market Return (e.g., S&P 500 Historical Return)
[ E(Rm) - Rf ] = Equity Market Risk Premium (ERP)
Jensen's Alpha (α): α = Actual Return - Expected CAPM Return
Interpreting Systematic Risk Beta (β) Values
| Beta (β) Range | Market Sensitivity Behavior | Representative Industry Sectors |
|---|---|---|
| β = 0.0 | Zero correlation with stock market movements | Cash equivalents, short-term US Treasury Bills |
| β = 0.50 to 0.80 | Defensive / Low Volatility: Moves less than broader market | Regulated electric utilities, healthcare, consumer packaged goods |
| β = 1.00 | Market Neutral: Moves perfectly in tandem with market | S&P 500 Index Fund (SPY / VOO) |
| β = 1.20 to 1.80+ | Aggressive / High Volatility: Amplifies market swings | Semiconductors, biotechnology, high-growth technology SaaS |
| β < 0.0 | Negative correlation (moves opposite to market) | Gold mining equities, inverse volatility ETFs |
Step-by-Step Worked Calculation Example
Example: Calculating Required Expected Return for a High-Beta Tech Stock
Problem: A financial analyst evaluates a cloud software stock with a beta β = 1.40. The current 10-Year US Treasury yield (Risk-Free Rate Rf) is 4.25%. The expected long-term return of the S&P 500 E(Rm) is 9.75% (Equity Risk Premium = 9.75% - 4.25% = 5.50%). Calculate: (1) Expected required rate of return; and (2) Jensen's Alpha if the stock achieves an actual 13.0% return.
Step 1: Calculate Expected CAPM Return:
E(Ri) = 4.25% + 1.40 × ( 9.75% - 4.25% ) = 4.25% + 1.40 × ( 5.50% )
E(Ri) = 4.25% + 7.70% = 11.95% Required Expected Return
Step 2: Calculate Jensen's Alpha (α):
α = Actual Return (13.00%) - CAPM Expected Return (11.95%) = +1.05% Positive Alpha!
Conclusion: Because the stock generated 13.0% vs. its 11.95% hurdle rate, the manager delivered 1.05% in excess risk-adjusted alpha.
Multi-Factor Extensions: The Fama-French Three-Factor Model
While standard CAPM relies exclusively on single market beta (β), financial economists Eugene Fama and Kenneth French (1993) demonstrated that stock returns are driven by three distinct risk factors:
Where SMB = Small Minus Big (Small-Cap Premium) | HML = High Minus Low (Value Stock Premium)
Adding size and value factor exposures explains over 90% of diversified portfolio return variance compared to only 70% for standard single-factor CAPM.
Rolling Beta Calculations and Beta Instability
In empirical quantitative equity modeling, a company's historical equity beta is not static over time.
Quantitative portfolio managers compute 36-Month Rolling Betas, observing that cyclical companies exhibit elevated beta volatility (β > 1.5) during macroeconomic recessions and compressed betas (β < 0.8) during late-stage economic expansions, requiring periodic portfolio re-weighting.
Arbitrage Pricing Theory (APT) vs. Standard CAPM
Developed by economist Stephen Ross, Arbitrage Pricing Theory (APT) offers an alternative multi-factor framework:
Rather than assuming a single market portfolio proxy, APT models asset returns as a linear function of macroeconomic risk factors (unexpected changes in GDP growth, inflation shocks, yield curve term structure spreads, and corporate default risk premiums).
Downside Beta and Sortino Risk Modeling
Because standard CAPM beta penalizes both upward and downward price volatility equally, quantitative risk managers calculate Downside Beta (βdown):
Downside beta measures asset covariance exclusively during negative market trading sessions, providing a superior gauge of true capital loss risk during severe market corrections.
Unlevered vs. Levered Beta (Hamada's Equation)
In corporate mergers and acquisitions, financial analysts strip out capital structure debt effects to compute Unlevered Asset Beta (βu):
Adjusted Beta (Bloomberg / Merrill Lynch Technique)
In professional equity analysis, historical raw betas are smoothed using Marshall Blume's mean-reversion technique:
Beta Selection in Capital Budgeting
Corporate finance teams apply divisional pure-play betas when evaluating standalone projects, reflecting business unit risk rather than firm-wide average risk.
CAPM in Regulated Utility Ratemaking
Public utility regulatory commissions utilize the Capital Asset Pricing Model to determine the statutory allowed return on equity (ROE) for electric and water distribution utilities.
Systematic Risk Awareness
Understanding market beta empowers portfolio managers to build resilient asset allocations tailored to investor risk tolerance.