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Capital Asset Pricing Model (CAPM) Calculator

Calculate the expected return of an asset based on its systematic risk (Beta) and the expected market return using CAPM.

Market Variables

Risk-Free Rate (%)

Typically the 10-Year Treasury yield.

Expected Market Return (%)

Average historical return (e.g., S&P 500 ~10%).

Asset Beta (β)

Volatility compared to the broader market (Market = 1.0).

Expected Return

11.1%

CAPM Required Return Rate

Market Risk Premium5.5%

The extra return expected from holding the market instead of a risk-free bond.

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What is Capital Asset Pricing Model (CAPM)?

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets. It is widely used throughout finance to price risky securities and generate expected returns for assets given the risk of those assets and cost of capital.

Mathematical Foundation

ER_i = R_f + \beta_i (ER_m - R_f)

ER_i

= Expected Return of the investment

R_f

= Risk-Free Rate (usually the yield on a 10-year US Treasury bond)

\beta_i

= Beta of the investment (measure of its volatility compared to the market)

(ER_m - R_f)

= Market Risk Premium (the extra return expected from holding risky market assets over risk-free assets)

Laws & Principles

Beta > 1: A Beta greater than 1.0 indicates that the security's price will be more volatile than the overall market. Accordingly, CAPM will dictate a higher Expected Return to compensate the investor for taking on that extra risk.
Beta < 1: A Beta less than 1.0 means the security is theoretically less volatile than the market (e.g., utility stocks). Thus, the Expected Return will be lower.

Step-by-Step Example Walkthrough

" You are analyzing a tech stock with a Beta of 1.2. The current 10-year Treasury yield (Risk-Free Rate) is 4.5% and you expect the S&P 500 (the market) to return 10% this year. "

Calculate Market Risk Premium: 10% - 4.5% = 5.5%
Multiply Premium by Beta: 5.5% × 1.2 = 6.6%
Add back Risk-Free Rate: 6.6% + 4.5% = 11.1%

Final Result: According to CAPM, you should demand an 11.1% Expected Return from this stock to compensate for its risk.

Quick Answer: What is the CAPM formula?

E(R) = R_f + β × (R_m − R_f) — Expected Return = Risk-Free Rate + Beta × Equity Risk Premium. Example: Risk-free rate = 4.5% (10-yr Treasury), Beta = 1.3, Market return = 10% → ERP = 5.5% → Expected return = 4.5% + 1.3 × 5.5% = 11.65%. If a stock with β = 1.3 is only expected to return 9%, it plots below the Security Market Line — it is overpriced for its risk. CAPM is the foundation of the Security Market Line, portfolio construction, cost of equity calculations, and discounted cash flow (DCF) valuation.

Beta (β) Interpretation Quick Reference

Beta measures an asset's sensitivity to market movements relative to a benchmark (typically the S&P 500). A beta of 1.0 means the asset moves exactly with the market. Beta is estimated from historical regression of asset returns against market returns (typically 3–5 years of monthly data).

Beta (β)	Risk Profile	Typical Examples	CAPM Impact
β = 0	No market risk	Treasury bills, cash	Expected return = risk-free rate only
0 < β < 1	Defensive	Utilities, consumer staples, REITs	Less volatile than market; lower required return
β = 1.0	Market-neutral	S&P 500 index fund	Expected return equals market return by definition
β > 1	Aggressive	Growth tech, semiconductors, biotech	Amplifies market moves; demands higher expected return
β < 0	Inverse	Gold, inverse ETFs, some puts	Negative ERP contribution; acts as hedge
Beta is backward-looking and unstable over time — a stock's 5-year beta can differ significantly from its 1-year beta. Levered beta (equity beta) reflects both business risk and financial risk from debt. Unlevered (asset) beta strips out leverage: β_asset = β_equity / (1 + (1−t) × D/E). For valuation, use forward-looking beta estimates or industry peer group betas re-levered to the subject company's capital structure.

Pro Tips & Common CAPM Mistakes

Do This

✓Use the current 10-year Treasury yield as your risk-free rate — it is the standard proxy used by investment banks, DCF models, and the CFA Institute. As of early 2025, the 10-year Treasury yield is approximately 4.2–4.6%. Using a 10-year maturity matches the long-term investment horizon implicit in equity valuation. Avoid using short-term T-bill rates (3-month) for long-duration assets — the term mismatch creates a downward bias in the estimated required return. For international markets: use the local sovereign bond yield in the relevant currency, adjusted for country risk premium (Damodaran's country risk premium database is the standard reference).
✓Use the historical equity risk premium of 5.0–6.0% for U.S. equities — the long-run market return above T-bills since 1926 is approximately 6.8%, implying an ERP of 6.4% vs T-bills or ~5.5% vs 10-year bonds. The Equity Risk Premium (ERP = R_m − R_f) is the single most debated input in finance. Damodaran's implied ERP (based on S&P 500 forward earnings vs current price) runs 4.5–5.5% in recent years. Kroll/Duff & Phelps recommends 5.5% ERP for U.S. appraisal work. For a DCF model: use 5.0% as a neutral base case and test 4.0–6.0% as sensitivity range.

Avoid This

✗Don’t confuse CAPM expected return with alpha — CAPM gives you what the asset should return for its risk; the actual return above that is alpha. If a stock with β = 1.2 returns 14% in a year when the CAPM expected return was 11%, it generated 3% alpha — excess return beyond what its systematic risk warranted. Alpha = Actual Return − CAPM Expected Return. Alpha is what active managers claim to generate. Most do not deliver positive alpha after fees over time — which is the empirical basis for index investing. CAPM itself assumes alpha = 0 in equilibrium (all assets are fairly priced on the SML). When you see a stock above the SML: the market expects it to revert downward (or the inputs are wrong).
✗Don’t apply a single-factor CAPM to small-cap stocks or distressed companies without adding size and distress premia — CAPM systematically underestimates required returns for these assets. The Fama-French 3-factor model adds a Small-Minus-Big (SMB) factor and a High-Minus-Low (HML) book-to-market factor to CAPM. For small-cap equities: add a size premium of 2–4% to the CAPM cost of equity (per Duff & Phelps). For privately held companies: add a company-specific risk premium (CSRP) of 2–6% to reflect lack of diversification, key-person risk, and limited liquidity. These premia are standard in business valuation under ASC 820, USPAP, and IRS Revenue Ruling 59-60.

Frequently Asked Questions

What does CAPM tell me and when should I use it?

CAPM answers the question: “What return should I demand for taking on this level of systematic risk?” It is used in three primary contexts: (1) Cost of equity in WACC calculations for DCF valuation (the most common corporate finance use). (2) Portfolio construction — identifying overvalued assets (above expected return = below SML = sell) and undervalued assets (below expected return = above SML = buy). (3) Capital budgeting — using the asset’s CAPM required return as the hurdle rate for project evaluation. CAPM assumes investors are fully diversified (only systematic/market risk is priced; idiosyncratic risk is diversified away), markets are efficient, and all investors have identical expectations. These assumptions hold approximately but not perfectly — which is why CAPM is a model, not a law.

Where do I find beta for a stock?

Published beta estimates are available from: Bloomberg (5-year monthly, most common for institutional use); Yahoo Finance / Google Finance (free, typically 5-year monthly); Damodaran’s website (aswathdamodaran.com — free industry-level unlevered betas updated annually, the standard for valuation work). Be aware that beta estimates vary significantly by time period, frequency (daily vs monthly), and benchmark index used. For valuation purposes, use industry peer group betas (re-levered to the subject company’s capital structure) rather than a single regression beta — this averages out the noise from individual beta estimation. The Hamada equation re-levers: β_L = β_U × (1 + (1 − t) × D/E), where t = tax rate and D/E = debt-to-equity ratio.

What is the Security Market Line (SML) and how does it relate to CAPM?

The Security Market Line (SML) is the graphical representation of CAPM — a straight line plotting expected return (y-axis) against beta (x-axis). The SML has: Y-intercept = risk-free rate (R_f); slope = equity risk premium (R_m − R_f). Every fairly-priced asset lies exactly on the SML. Above the SML: asset offers more return than CAPM requires for its risk → undervalued → buy signal. Below the SML: asset offers less return than warranted → overvalued → sell signal. The SML differs from the Capital Market Line (CML): the SML uses beta (systematic risk) while the CML uses standard deviation (total risk). The SML applies to all assets; the CML applies only to efficient portfolios on the efficient frontier.

What are the limitations of CAPM?

CAPM’s key limitations: (1) Single-factor model — empirical research (Fama & French, 1992) showed that size (small-cap) and value (high book-to-market) explain stock returns beyond beta alone, leading to multi-factor models. (2) Beta instability — a stock’s beta changes over time as business mix, leverage, and macro conditions shift; historical beta may not predict future beta. (3) Market proxy problem — the “market portfolio” in theory includes ALL risky assets globally (stocks, bonds, real estate, human capital). In practice, the S&P 500 is used as a proxy, which is imperfect (Roll’s critique). (4) Mean-variance assumptions — CAPM assumes normally distributed returns and no fat tails; real markets have skewness, kurtosis, and tail dependence. Despite limitations, CAPM remains the dominant model in corporate finance due to its simplicity and interpretability. Multi-factor models (Fama-French 3-factor, Carhart 4-factor, APT) provide better empirical fit but require more inputs.