CAPM Calculator

Compute expected return, alpha, and portfolio metrics using the Capital Asset Pricing Model. Essential for investment analysis.

CAPM Formula: E(Ri) = Rf + βi · (E(Rm) – Rf)

Where: Rf = risk-free rate, β = beta, (E(Rm)-Rf) = market risk premium

e.g., 10‑year Treasury yield
Systematic risk (typically 0.5–2.0)
S&P 500 historical ~8‑10%
Used to calculate Jensen‘s alpha
S&P 500 stock (β=1.2) Utility (β=0.65) Tech growth (β=1.8) Gold stock (β negative)

Understanding the Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) was developed in the 1960s by William Sharpe, John Lintner, and Jan Mossin, building on Harry Markowitz's modern portfolio theory. It describes the relationship between systematic risk and expected return for assets, and it is widely used for pricing risky securities, estimating cost of equity, and evaluating portfolio performance.

Core formula: E(Ri) = Rf + βi [E(Rm) – Rf]

where the term [E(Rm) – Rf] is the market risk premium.

Detailed Breakdown of Components

  • Risk‑free rate (Rf) — the return on an investment with zero risk, typically proxied by the yield on long-term government bonds (e.g., 10-year U.S. Treasury). It represents the time value of money.
  • Beta (β) — a measure of the asset's sensitivity to market movements. It is calculated as the covariance of the asset's return with the market return divided by the variance of the market return.
    • β = 1 : asset moves in line with the market.
    • β > 1 : asset is more volatile than the market (aggressive).
    • 0 < β < 1 : asset is less volatile (defensive).
    • β = 0 : no correlation with market (e.g., risk‑free asset).
    • β < 0 : asset moves opposite to the market (rare, e.g., gold, some inverse ETFs).
  • Market risk premium — the excess return investors expect for holding a risky market portfolio over a risk‑free asset. It reflects the overall risk aversion in the economy. Historical arithmetic average for U.S. stocks is around 6‑8%.

Assumptions Behind CAPM

The model rests on several key assumptions that simplify reality:

  1. Investors are risk-averse and seek to maximize the utility of terminal wealth.
  2. Markets are frictionless: no transaction costs, no taxes, and assets are perfectly divisible.
  3. All investors have the same one-period investment horizon.
  4. All investors have identical expectations about asset returns (homogeneous expectations).
  5. All assets are publicly traded and investors can borrow or lend any amount at the risk‑free rate.
  6. Investors are price‑takers (no single investor can influence prices).

While these assumptions are often violated in practice, CAPM remains a useful benchmark.

The Security Market Line (SML)

The SML is the graphical representation of CAPM. It plots expected return against beta. The slope of the SML is the market risk premium. All fairly priced assets lie exactly on the SML; assets above the line are undervalued (positive alpha), and assets below are overvalued (negative alpha).

Jensen‘s Alpha (α)

Alpha measures the abnormal return of an asset relative to its CAPM prediction:

α = Ractual – [Rf + β (Rm – Rf)]

A positive alpha indicates the asset outperformed the model's expectation (manager skill or mispricing), while a negative alpha suggests underperformance.

Portfolio CAPM

For a portfolio, both the expected return and beta are weighted averages of the individual assets:

  • βp = Σ wi βi
  • E(Rp) = Σ wi E(Ri) = Rf + βp (Rm – Rf)

This additive property makes CAPM convenient for portfolio analysis.

Empirical Evidence and Limitations

Early tests (1960s-70s) generally supported CAPM, but later research (e.g., Fama & French) revealed anomalies: size effect, value effect, momentum. CAPM cannot explain these cross‑sectional variations. As a result, multi‑factor models (like the Fama‑French three‑factor model) have been developed. Nevertheless, CAPM remains a foundational tool due to its simplicity and intuitive appeal.

How to Obtain Input Parameters in Practice

  • Risk‑free rate: Use current yield on 10‑year government bonds (e.g., from Treasury.gov).
  • Beta: Usually estimated by regressing historical stock returns against a market index (e.g., S&P 500) over 3‑5 years. Many financial websites provide beta estimates.
  • Market return: Based on long‑term historical average of the market index (e.g., 8‑10% for U.S. equities) or forward‑looking estimates.

CAPM vs. Other Models

Compared to the Arbitrage Pricing Theory (APT) or multi‑factor models, CAPM uses a single factor (market risk). APT allows multiple macroeconomic factors, while the Fama‑French model adds size and value factors. CAPM is easier to implement but may miss important sources of risk.

Calculator features:

  • Instant CAPM expected return and alpha.
  • Portfolio mode: combine up to 5 assets.
  • Security Market Line chart with your asset plotted.
  • Preset examples for common scenarios.
  • Real‑time updates as you type.

Frequently Asked Questions

Beta near 1 means the stock moves with the market. High beta (>1) offers higher expected return but more risk. Defensive stocks have beta <1. Negative beta is rare (e.g., gold, inverse ETFs).

Often based on historical excess return of a broad index (e.g., S&P 500) over risk‑free rate. Typical values range from 4% to 8% . Some practitioners use forward‑looking estimates from dividend discount models.

Investors are rational, markets are frictionless, no taxes, all investors have same expectations, and they can borrow/lend at risk‑free rate . In practice, CAPM is a useful approximation.

Yes, by using the beta of comparable public firms (industry average) and then adjusting for leverage (Hamada equation). This is common in private company valuation.

CAPM gives the cost of equity. WACC (Weighted Average Cost of Capital) combines cost of equity and after‑tax cost of debt to represent the overall cost of capital for a firm. CAPM is often used to estimate the cost of equity within WACC.