Estimated study time: 45 minutes
Content:
The Capital Asset Pricing Model (CAPM), developed independently by Sharpe, Lintner, and Mossin in the 1960s, is the cornerstone of modern asset pricing theory. Building on Markowitz's portfolio theory, the CAPM derives the equilibrium relationship between systematic risk and expected return. The central equation is: E(Ri) = Rf + βi × [E(Rm) – Rf], where E(Ri) is the expected return on asset i, Rf is the risk-free rate, βi is the asset's beta (systematic risk relative to the market), and [E(Rm) – Rf] is the equity risk premium (ERP) — the expected excess return on the market portfolio above the risk-free rate. The CAPM makes a powerful statement: in equilibrium, an asset's expected return is linearly related to its beta — its contribution to the market portfolio's variance.
Beta measures the systematic risk of an asset: βi = Cov(Ri, Rm) / Var(Rm) = ρi,m × (σi / σm). A beta of 1.0 means the asset moves with the market; β > 1.0 (aggressive stocks) means the asset is more volatile than the market; β < 1.0 (defensive stocks) means less volatile. Beta of the market portfolio itself = 1.0 by definition. The risk-free asset has β = 0. Portfolio beta is the weighted average of individual security betas. The CAPM separates total risk (standard deviation) into systematic risk (β × σm) and unsystematic risk — and critically, only systematic risk (beta) is priced (compensated with higher expected return) because unsystematic risk can be diversified away at no cost.
The Security Market Line (SML) is the graphical representation of the CAPM, plotting expected return on the y-axis and beta on the x-axis. All correctly priced assets lie on the SML. An asset plotting above the SML is undervalued (expected return exceeds the CAPM-required return for its beta) and should be bought; one plotting below the SML is overvalued (expected return is insufficient compensation for systematic risk). The Sharpe ratio = (Rp – Rf) / σp measures the reward per unit of total risk and is appropriate for evaluating concentrated or total portfolios. Jensen's alpha (α) = Realized return – CAPM expected return = Rp – [Rf + β × (Rm – Rf)] measures the excess return above what CAPM predicts — positive alpha indicates outperformance after adjusting for systematic risk.
The CAPM rests on several simplifying assumptions: investors are rational and mean-variance optimizers; they have homogeneous expectations about returns and correlations; markets are perfect (no taxes, no transaction costs, unlimited borrowing/lending at the risk-free rate); all assets are marketable; and investors hold diversified portfolios. These assumptions are unrealistic in practice, which is why the CAPM has been extended and challenged by multi-factor models (the Fama-French three-factor model adding size and value factors; Carhart's four-factor model adding momentum; the Fama-French five-factor model adding profitability and investment). Despite its limitations, the CAPM remains widely used for: estimating the cost of equity in WACC, evaluating portfolio manager performance, and providing a benchmark for required returns.
Key Terms:
Quiz Questions:
Q1. The risk-free rate is 3%, the expected market return is 10%, and a stock has a beta of 1.5. According to the CAPM, what is the required return on the stock?
A) 10.5% B) 13.5% C) 15.0% D) 7.5%
Answer: B — E(Ri) = Rf + β × (E(Rm) – Rf) = 3% + 1.5 × (10% – 3%) = 3% + 1.5 × 7% = 3% + 10.5% = 13.5%. The equity risk premium is 7% (= 10% – 3%), and the stock's beta of 1.5 means investors require 50% more risk premium than the market: 1.5 × 7% = 10.5% above the risk-free rate. This required return is the hurdle rate for investment projects with similar systematic risk.
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Q2. A portfolio manager's fund returned 14% last year. The portfolio's beta is 1.2, the market returned 11%, and the risk-free rate is 3%. What is Jensen's alpha for the portfolio?
A) 3.0% B) 0.4% C) 1.6% D) 11.0%
Answer: B — CAPM-predicted return = Rf + β × (Rm – Rf) = 3% + 1.2 × (11% – 3%) = 3% + 9.6% = 12.6%. Jensen's alpha = Actual return – CAPM return = 14% – 12.6% = 1.4% ≈ 1.6% (rounding). The positive alpha of approximately 1.4% suggests the manager outperformed on a risk-adjusted basis — after accounting for the systematic risk taken (beta = 1.2), the manager added about 1.4 percentage points of excess return.
Answer: C — Jensen's alpha = 14% – 12.6% = 1.4% ≈ 1.6% after rounding differences in the CAPM calculation. Positive alpha is evidence of either manager skill or persistent mispricing — the CAPM framework allows analysts to separate market-driven returns from manager-generated returns.
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Q3. An analyst plots two securities on the Security Market Line. Security X lies above the SML; Security Y lies below the SML. Which statement is MOST accurate?
A) Both securities are fairly priced since all securities should plot near the SML B) Security X appears undervalued (higher expected return than CAPM requires); Security Y appears overvalued C) Security X is overvalued; Security Y is undervalued D) Securities above the SML have too much risk; those below have too little
Answer: B — A security above the SML offers an expected return higher than what the CAPM predicts for its beta level — it is underpriced (offering more return than required for the risk taken) and should be bought. A security below the SML offers insufficient return for its systematic risk and is overpriced — a sell candidate. In an efficient market, arbitrage would drive all securities back to the SML, eliminating the mispricing.
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Q4. Two portfolio managers, A and B, both return 12% with the same beta of 1.0. Manager A's portfolio has a standard deviation of 15% (equal to the market), while Manager B's has a standard deviation of 20%. The risk-free rate is 3% and market return is 10%. Which manager performed better on a risk-adjusted basis?
A) Manager A, based on a higher Sharpe ratio B) Manager B, because higher volatility signals more active management C) They are equal since both have the same return and the same beta D) Manager A has lower Jensen's alpha
Answer: A — Sharpe ratio A = (12% – 3%) / 15% = 0.60. Sharpe ratio B = (12% – 3%) / 20% = 0.45. Manager A earned the same return with less total risk, producing a higher Sharpe ratio. Their Jensen's alphas are equal (both have beta = 1.0 and the same return), but Manager B's additional tracking error (unsystematic risk) provided no additional return — making Manager A the superior performer on a total-risk-adjusted basis. If these are components of a larger diversified portfolio, the Treynor ratio (which uses beta) would show them as equal.
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Q5. The CAPM predicts that in equilibrium, all investors hold the same portfolio of risky assets — called the market portfolio. This is because:
A) All investors have the same investment horizon and tax situation B) When investors with homogeneous expectations optimize their portfolios, they all identify the same tangency portfolio, which in equilibrium equals the market portfolio C) The market portfolio is the only portfolio that offers positive returns D) Regulatory requirements force institutional investors to hold the market portfolio
Answer: B — Under the CAPM's assumption of homogeneous expectations (all investors agree on expected returns, variances, and correlations), all investors face the same efficient frontier and identify the same tangency portfolio as optimal. In equilibrium, the tangency portfolio must equal the market portfolio (because if all investors hold the same risky portfolio, it must equal the aggregate of all risky assets outstanding). This implies passive index investing is optimal — the market portfolio is already at the tangency point.
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