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Category Investments & Stocks

Risk-Free Rate (%) 10-year government bond yield

Expected Market Return (%) S&P 500 avg ≈ 10.5%

Beta Coefficient (β) 1.0 = market, >1 = aggressive, <1 = defensive

Actual Return (%) optional For Jensen's Alpha calculation

Investment Amount ($) optional To see dollar return projection

Enter values and click Calculate

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About

The Capital Asset Pricing Model quantifies the relationship between systematic risk and expected return for an asset. It relies on three inputs: the risk-free rate R_f, the expected market return E(R_m), and the asset's beta coefficient β. A miscalculated beta or an outdated risk-free rate leads to mispriced assets and flawed portfolio allocation decisions. Institutional investors use CAPM as a baseline hurdle rate; retail investors who skip this step often overpay for risk they don't understand.

This calculator applies the standard CAPM equation and computes Jensen's Alpha when an actual return is provided, flagging whether an asset has historically outperformed or underperformed its risk-adjusted expectation. Note: CAPM assumes normally distributed returns and a single-period horizon. It does not account for liquidity risk, skewness, or multi-factor exposures captured by models like Fama-French. Pro tip: use the 10-year government bond yield of the relevant currency as R_f, not short-term T-bill rates, unless your horizon is under one year.

Formulas

The Capital Asset Pricing Model expresses expected return as a linear function of systematic risk:

E(R_i) = R_f + β_i × (E(R_m) − R_f)

Where E(R_i) is the expected return of asset i, R_f is the risk-free rate, β_i is the beta coefficient measuring the asset's sensitivity to market movements, and E(R_m) is the expected return of the market portfolio.

The Market Risk Premium is defined as:

MRP = E(R_m) − R_f

Jensen's Alpha measures excess return above the CAPM prediction:

α = R_actual − E(R_i)

Where R_actual is the realized historical return. A positive α indicates the asset outperformed its risk-adjusted expectation. A negative α indicates underperformance.

The Security Market Line (SML) plots expected return against β. Every fairly priced asset should lie on this line. Assets above the SML are considered undervalued (positive alpha); assets below are overvalued.

Reference Data

Asset Class / Index	Typical β	Historical Annualized Return	Risk Profile
U.S. 10-Year Treasury	0.00	4.2%	Risk-Free Proxy
S&P 500 Index	1.00	10.5%	Market Benchmark
Utilities Sector (XLU)	0.45	7.8%	Defensive / Low Vol
Consumer Staples (XLP)	0.60	8.5%	Defensive
Healthcare (XLV)	0.75	9.2%	Moderate
Industrials (XLI)	1.05	10.8%	Cyclical
Financials (XLF)	1.15	11.0%	Cyclical / Leveraged
Technology (XLK)	1.20	13.5%	Growth / High Vol
Consumer Discretionary (XLY)	1.10	11.8%	Cyclical
Energy Sector (XLE)	1.30	9.0%	High Vol / Commodity
Small-Cap Growth (IWO)	1.35	11.2%	High Risk / Growth
Emerging Markets (EEM)	1.25	8.0%	High Risk / Geopolitical
Real Estate (VNQ)	0.80	9.5%	Interest Rate Sensitive
Gold (GLD)	0.05	5.5%	Safe Haven / Low Corr
Aggregate Bonds (AGG)	-0.05	4.0%	Negative Correlation
Bitcoin (BTC)	1.80	55.0%	Speculative / Extreme Vol
Leveraged ETF (TQQQ 3×)	3.00	32.0%	Extreme / Decay Risk
Inverse ETF (SH −1×)	-1.00	-8.5%	Hedging / Decay Risk

Frequently Asked Questions

Use the yield on a government bond matching your investment horizon. For long-term equity analysis, the 10-year Treasury yield is standard. For short-term analysis under one year, the 3-month T-bill rate is appropriate. Always match the currency: use U.S. Treasuries for USD-denominated assets, Bunds for EUR assets.

Beta (β) is computed as the covariance of the asset's returns with the market returns divided by the variance of the market returns: β = Cov(R_i, R_m)Var(R_m). Most financial data providers (Yahoo Finance, Bloomberg, Morningstar) publish trailing betas calculated over 60 months of monthly returns against the S&P 500. Be aware that beta is backward-looking and unstable across different time windows.

A negative β indicates the asset moves inversely to the market. Inverse ETFs and certain gold positions can exhibit β < 0. Under CAPM, a negative-beta asset would have an expected return below the risk-free rate, which seems counterintuitive but reflects its hedging value. The model treats such assets as portfolio insurance, not standalone investments.

Jensen's Alpha (α) quantifies whether a manager or asset has generated returns above what CAPM predicts for its level of systematic risk. A consistently positive α suggests genuine skill or mispricing. However, a single-period alpha is noisy. Statistical significance requires testing over multiple periods. A positive alpha may also reflect exposure to factors not captured by CAPM (size, value, momentum).

CAPM assumes: (1) investors can borrow and lend at R_f without limit, (2) markets are frictionless with no taxes or transaction costs, (3) returns are normally distributed, and (4) all investors hold the same expectations. Empirically, the low-beta anomaly shows that low-β stocks often outperform CAPM predictions while high-β stocks underperform. The Fama-French three-factor model adds size and value factors to address these gaps.

The SML plots expected return against β (systematic risk only) and applies to all assets individually. The Capital Market Line (CML) plots expected return against total standard deviation (σ) and applies only to efficient portfolios combining the market portfolio with the risk-free asset. An asset can lie below the CML (inefficient) yet still sit on the SML if it is fairly priced for its systematic risk.