Capital Asset Pricing Model

Where E(Ri) is the expected return of the asset, Rf is the risk-free rate, βi is the asset's beta — its measure of systematic risk — and E(Rm) − Rf is the market risk premium — the excess return of the market portfolio above the risk-free rate that compensates investors for bearing systematic market risk.

Sharpe received the Nobel Memorial Prize in Economic Sciences in 1990 — shared with Harry Markowitz and Merton Miller — in recognition of his development of the CAPM and related contributions to financial economics. 

The CAPM is tested directly on the Series 65 examination in the context of beta, systematic risk, the security market line, the market risk premium, and the evaluation of investment performance through Jensen's alpha.

The Foundational Assumptions of CAPM

The CAPM rests on a set of simplifying assumptions about investors and markets that produce its clean mathematical result — and understanding these assumptions is essential for understanding both the model's power and its limitations.

All investors are rational and risk averse — they make portfolio decisions by evaluating only the expected return and standard deviation of portfolio outcomes, as in Markowitz's mean-variance framework. 

All investors have the same expectations — they agree on the expected returns, standard deviations, and correlations of all available assets, producing identical efficient frontiers and the same tangency portfolio for every investor. 

All investors can borrow and lend unlimited amounts at the same risk-free rate — represented by the treasury bill rate. 

Markets are frictionless — there are no transaction costs, no taxes, and no restrictions on short selling. All assets are perfectly divisible and perfectly liquid. The investment horizon is a single period — all investors evaluate portfolios over the same time horizon.

These assumptions are clearly simplifications of reality — markets have transaction costs, investors disagree about expected returns, and borrowing rates differ from lending rates. 

The CAPM's lasting importance despite these simplifying assumptions is a testament to the power of its core insight — that in equilibrium, the only risk for which investors should be compensated is systematic market risk, because unsystematic risk can be eliminated through diversification at no cost.

Beta — The Measure of Systematic Risk

Beta is the central variable of the CAPM — the quantitative measure of an asset's systematic risk that determines its position on the security market line and therefore its expected return in the CAPM framework.

Beta measures the sensitivity of an asset's returns to movements in the overall market return — specifically the market portfolio represented by a broad equity index such as the S and P 500. A beta of one indicates that the asset moves in perfect lockstep with the market — when the market rises one percent the asset rises one percent, and when the market falls one percent the asset falls one percent. The asset has exactly the same systematic risk as the market portfolio.

A beta above one indicates greater systematic risk than the market — the asset amplifies market movements. A beta of one point five means the asset rises approximately one point five percent when the market rises one percent and falls approximately one point five percent when the market falls one percent. 

High-beta assets — typically smaller growth companies, technology stocks, and other economically sensitive securities — carry more systematic risk and therefore require higher expected returns in the CAPM framework.

A beta below one indicates less systematic risk than the market — the asset dampens market movements. A beta of zero point five means the asset rises approximately half a percent when the market rises one percent. Low-beta assets — typically utility stocks, consumer staples companies, and other defensive sectors — carry less systematic risk and therefore require lower expected returns. A beta of zero — theoretically achieved by the risk-free treasury bill — indicates no systematic risk at all.

A negative beta — exhibited by certain hedging instruments and assets that tend to rise when the market falls — indicates that the asset moves opposite to the market, providing negative correlation with systematic risk. Negative-beta assets are theoretically valuable portfolio diversifiers because they reduce systematic risk when combined with positive-beta holdings — though most financial assets exhibit positive betas and true negative-beta assets are uncommon.

Beta is calculated mathematically as the covariance of the asset's returns with the market's returns divided by the variance of the market's returns — or equivalently as the correlation between the asset and the market multiplied by the ratio of the asset's standard deviation to the market's standard deviation.

The Risk-Free Rate and the Market Risk Premium

The CAPM formula contains two market-wide parameters that are the same for every asset in the model — the risk-free rate and the market risk premium.

The risk-free rate — Rf — is the return available from an investment with zero risk — zero standard deviation and zero correlation with all risky assets. In practice the risk-free rate is proxied by the treasury bill rate — the yield on short-term United States government obligations that are effectively free of default risk and have negligible interest rate risk due to their short maturity.

The market risk premium — E(Rm) − Rf — is the excess return of the market portfolio above the risk-free rate — the additional return that investors collectively require to hold the market portfolio rather than the risk-free asset. 

Historically the United States equity market has provided an average annual return approximately five to six percentage points above the treasury bill rate — suggesting a long-run historical market risk premium in that range. Current forward-looking estimates of the market risk premium are derived from current equity valuations, earnings yields, and expected economic growth — and are a subject of significant academic and practitioner debate.

The product of beta and the market risk premium — βi × (E(Rm) − Rf) — is the risk premium specific to the individual asset — the additional expected return above the risk-free rate that the asset must offer to compensate investors for its specific level of systematic risk. 

A high-beta asset with a beta of two requires twice the market risk premium above the risk-free rate — it must offer twice as much compensation for systematic risk as the market portfolio itself.

The Security Market Line

The security market line is the graphical representation of the CAPM — a straight line plotting the relationship between beta on the horizontal axis and expected return on the vertical axis for every asset in a CAPM-consistent equilibrium market.

The security market line begins at the risk-free rate on the vertical axis at beta equals zero — the treasury bill earns the risk-free rate with no systematic risk. It slopes upward to the right — higher beta assets require higher expected returns. 

The slope of the security market line equals the market risk premium — the additional expected return per unit of beta. The market portfolio — with beta equal to one — lies on the security market line at the market's expected return.

Every asset in an efficiently priced market lies exactly on the security market line in CAPM equilibrium — meaning every asset offers precisely the expected return that compensates for its systematic risk and no more. Assets plotting above the security market line are underpriced — they offer higher expected returns than their systematic risk justifies, making them attractive buys that will be purchased until their prices rise and their expected returns fall back to the line. Assets plotting below the security market line are overpriced — they offer lower expected returns than their systematic risk justifies, making them unattractive holds that will be sold until their prices fall and their expected returns rise back to the line.

Jensen's Alpha — Measuring Performance Relative to CAPM

Jensen's alpha — developed by Michael Jensen in 1968 — is the performance measure that quantifies the difference between a portfolio's actual return and the return predicted by the CAPM given the portfolio's beta. Alpha equals the actual portfolio return minus the CAPM-predicted return.

Alpha equals actual portfolio return minus the quantity risk-free rate plus beta multiplied by the market risk premium.

Positive alpha indicates that the portfolio generated more return than the CAPM predicts for its level of systematic risk — evidence of superior investment management that has added value through active security selection, market timing, or other skills beyond what passive market exposure would have produced. Negative alpha indicates underperformance relative to the CAPM prediction — the portfolio manager has destroyed value relative to passive investment at the same systematic risk level.

Jensen's alpha is the most theoretically rigorous measure of active portfolio management performance because it explicitly adjusts for the systematic risk taken to generate the return — unlike raw return comparisons that do not account for the possibility that higher returns simply reflect higher beta rather than superior management skill. An active manager who generates a fifteen percent return with a beta of two has not necessarily added value — the CAPM may predict exactly fifteen percent for a beta-two portfolio in the given market environment. Only if the actual return exceeds the CAPM prediction does positive alpha emerge.

CAPM Limitations and the Multi-Factor Extensions

Despite its theoretical elegance and practical utility the CAPM faces substantial empirical challenges — anomalies in actual market returns that the single-factor CAPM cannot explain.

The size effect — documented by Rolf Banz in 1981 — finds that small-capitalisation stocks have historically earned higher returns than the CAPM predicts for their beta, suggesting that size represents a risk factor beyond systematic market risk that investors must be compensated for bearing. The value effect — documented by Fama and French in 1992 — finds that stocks with low price to book ratios have historically earned higher returns than high price to book stocks with the same beta, suggesting that the value factor represents additional compensation for a distress risk that the single-factor CAPM misses.

Fama and French responded to these anomalies by extending the CAPM into the three-factor model — adding size and value factors to the market factor — and subsequently further extended to a five-factor model incorporating profitability and investment factors. These multi-factor models have greater empirical explanatory power than the single-factor CAPM but at the cost of greater complexity and the theoretical challenge of identifying what economic risks the additional factors represent.

Examination Relevance and Key Takeaways

The Capital Asset Pricing Model is tested on the Series 65 examination in the context of beta, systematic risk, the security market line, the market risk premium, Jensen's alpha, and the evaluation of portfolio performance relative to risk-adjusted benchmarks.

The key points to retain are these.

The CAPM formula is E(Ri) = Rf + βi × (E(Rm) − Rf) — the expected return of any asset equals the risk-free rate plus the product of the asset's beta and the market risk premium. Developed by William Sharpe in 1964 building on Markowitz's modern portfolio theory — Sharpe received the Nobel Prize in Economics in 1990. The model assumes rational risk-averse investors with homogeneous expectations, frictionless markets, and unlimited risk-free borrowing and lending.

Beta measures systematic risk — the sensitivity of an asset's returns to market movements. Beta of one equals market-level systematic risk. Beta above one means more volatile than the market. Beta below one means less volatile. Beta of zero means no systematic risk — the risk-free treasury bill. The risk-free rate is proxied by the treasury bill rate. The market risk premium — E(Rm) − Rf — is the excess return of the market above the risk-free rate — historically approximately five to six percent annually for United States equities.

The security market line plots expected return against beta — all fairly priced assets lie on the line in CAPM equilibrium. Assets above the line are underpriced — offering more return than systematic risk justifies. Assets below the line are overpriced — offering less return than systematic risk justifies. Jensen's alpha — actual return minus CAPM-predicted return — measures portfolio management performance adjusted for systematic risk. Positive alpha indicates value added beyond passive market exposure. Negative alpha indicates underperformance relative to the risk-adjusted benchmark.