Capital Asset Pricing Model (CAPM) - Beta, Alpha, and the Price of Risk

By EC Assets Research Team, Portfolio Research · Published 20 May 2026 · Updated 28 May 2026

Capital Asset Pricing Model — The CAPM holds that investors are rewarded only for systematic (undiversifiable) risk, pricing an asset's expected return as E[R] = R_f + β·(E[R_m] − R_f). It defines beta as market sensitivity and alpha as return beyond what beta predicts - the foundation of performance attribution, despite well-documented empirical failures.

What the CAPM Says

The Capital Asset Pricing Model (CAPM), developed by William Sharpe and others in the 1960s on the foundations of Markowitz's portfolio theory, makes one bold claim: in equilibrium, the only risk an investor is rewarded for bearing is systematic risk - the risk that cannot be diversified away. Everything else, the idiosyncratic risk specific to a single company, can be eliminated by holding a broad portfolio, so the market does not pay you to hold it.

The model expresses an asset's expected return as the risk-free rate plus a premium proportional to its sensitivity to the market:

E[Rᵢ] = R_f + βᵢ · (E[R_m] − R_f)

where R_f is the risk-free rate, E[R_m] − R_f is the equity (market) risk premium, and βᵢ is the asset's beta - its sensitivity to market moves, βᵢ = Cov(Rᵢ, R_m) / Var(R_m). A beta of 1 moves with the market; a beta of 1.5 amplifies it; a beta of 0.5 dampens it. The whole expected return of an asset, in this model, is determined by that single number.

The Logic Behind It

Start from Markowitz: every investor holds the same optimal risky portfolio (the market) and blends it with cash. If that is true, the only risk that matters for any individual asset is how much it contributes to the market portfolio's risk - its covariance with the market, summarised by beta. Idiosyncratic risk washes out in the diversified whole, so it commands no premium. Plotting expected return against beta gives a straight line, the Security Market Line: every fairly-priced asset sits on it.

Alpha - Deviation from the Line

CAPM also defines the benchmark against which active managers are judged. Alpha is the return an asset or manager earns beyond what its beta predicts:

Alpha = realised return − [R_f + β · (R_m − R_f)]

Positive alpha is return that cannot be explained by market exposure - the holy grail of active management, and the thing most managers fail to deliver net of fees. CAPM thus splits any track record into two parts: beta (cheap, replicable market exposure) and alpha (scarce, valuable skill).

Worked Example

Suppose the risk-free rate is 4%, the expected market return is 9% (so the equity risk premium is 5%), and a stock has a beta of 1.2.

E[R] = 4% + 1.2 × 5% = 10%

CAPM says this stock should be expected to return 10%, compensating for its 20%-greater-than-market sensitivity. If it actually delivers 12%, the extra 2% is alpha - outperformance beyond what its market risk warranted. If it delivers 8%, it earned negative alpha: it underperformed the return its risk justified.

[!key] CAPM's enduring contribution is the separation of beta from alpha. Beta is market exposure you can buy cheaply through an index fund; alpha is genuine skill, scarce and worth paying for. Most of what is sold as alpha turns out, on inspection, to be beta in disguise.

Where CAPM Fails Empirically

CAPM is elegant and almost certainly wrong in detail. Decades of evidence show that beta alone does not explain returns:

• Low-beta anomaly. Low-beta stocks have historically delivered higher risk-adjusted returns than CAPM predicts, and high-beta stocks lower - the opposite of the model.
• Missing factors. Size, value, momentum, quality, and profitability all explain return variation that beta does not. This evidence drove the multi-factor models of Fama-French and Carhart, which generalise CAPM by adding more systematic risk factors.
• Unobservable inputs. The "true" market portfolio (all assets, including human capital and private wealth) is unobservable, and expected returns and betas must be estimated with error.

Why It Matters for Institutional Investors

• The beta/alpha decomposition. Performance attribution, fee justification, and manager evaluation all rest on separating market beta from genuine alpha. An allocator's first question of any return stream is: how much of this is just beta I could have bought for a few basis points?
• Cost of capital. Corporate finance uses CAPM to estimate the cost of equity that feeds discount rates and the WACC - so it shapes valuation far beyond portfolio management.
• The gateway to factor investing. CAPM's empirical failures are the reason factor investing exists. Understanding CAPM - and precisely where it breaks - is the prerequisite for understanding the multi-factor models that now dominate quantitative equity.

[!warning] Treat reported alpha with suspicion. Much of it disappears once you control for exposure to factors beyond the market - size, value, momentum, carry. A manager's "alpha" is often just uncompensated factor beta repackaged at active-management fees. Always ask what the return looks like after adjusting for all the cheap, systematic exposures.

References

1. Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3).
2. Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments. Review of Economics and Statistics, 47(1).
3. Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. The Journal of Finance, 47(2).
4. Black, F., Jensen, M., & Scholes, M. (1972). The Capital Asset Pricing Model: Some Empirical Tests.