Capital market hypothesis: the Sharpe–Lintner CAPM

Financial Management · Unit I · Topic 4 of 16 · 5 min read

Systematic and unsystematic risk, the assumptions of the capital asset pricing model, its derivation from Markowitz through the capital market line to the security market line, beta worked from five years of returns (1.6, giving 15%), the efficient market hypothesis, and the empirical tests from Black–Jensen–Scholes and Fama–MacBeth to Roll and Fama–French.

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On this page

1. Risk and diversification
2. The model and its authors
3. Assumptions
4. Derivation in outline
5. Worked example: beta and cost of equity
6. The efficient market hypothesis
7. Empirical evaluation
How this is examined

Cases checked to exist. Read the judgment before quoting a holding.

Every case cited here has been checked to exist — the citation resolves and names the right parties. The propositions attributed to each case have not been verified line by line against the judgment. Case names link through to the full judgment: read it before quoting a holding in an examination answer, and never carry a proposition from notes into court on trust.

The examinable core. “Write a short note on the Sharpe–Lintner model” (February 2025, 6 marks). The answer is one equation — E(R_i) = R_f + β_i[E(R_m) − R_f] — with its assumptions, a line on how it is derived, and a line on whether the evidence supports it.

1. Risk and diversification

The risk of a share has two parts. Unsystematic (diversifiable) risk belongs to the company: a strike, a lost contract, a fraud. It can be removed by holding many shares, because the bad luck of one is offset by the good luck of another. Systematic (market) risk comes from forces that move all shares: interest rates, inflation, recession, war. It cannot be diversified away. Harry Markowitz (“Portfolio Selection”, Journal of Finance, 1952) showed how combining assets reduces risk for a given return.

Since unsystematic risk can be removed at no cost, the market pays a premium only for systematic risk. The capital asset pricing model (CAPM) measures that risk by beta (β).

2. The model and its authors

The CAPM was developed independently by William Sharpe (“Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”, Journal of Finance, 1964) and John Lintner (Review of Economics and Statistics, 1965), with Jan Mossin (1966). Sharpe shared the 1990 Nobel Prize in Economics with Markowitz and Merton Miller.

E(R_i) = R_f + β_i[E(R_m) − R_f], where R_f is the risk-free rate (Government Treasury bills), E(R_m) the expected return on the market portfolio, and β_i = Cov(R_i, R_m) ÷ Var(R_m). The bracket is the market risk premium.

β = 1: the share moves with the market;
β > 1: an aggressive share, moving more than the market;
β < 1: a defensive share; β = 0: a risk-free asset.

3. Assumptions

Investors are rational, risk-averse and choose portfolios by mean and variance of return.
They have the same expectations (homogeneous expectations) over a single period.
They can borrow and lend without limit at the risk-free rate.
Markets are perfect: no taxes, no transaction costs, assets infinitely divisible, information free to all.
No investor can affect prices (perfect competition).

4. Derivation in outline

(1) Markowitz’s efficient frontier gives the best risky portfolios. (2) Add a risk-free asset: every investor holds a mix of the risk-free asset and the one tangent risky portfolio, which in equilibrium must be the market portfolio M. This gives the capital market line: E(R_p) = R_f + [(E(R_m) − R_f) ÷ σ_m] σ_p, for efficient portfolios. (3) A single share adds to the risk of M only through its covariance with M; its contribution is Cov(i, m) ÷ σ_m. In equilibrium every share must offer the same reward per unit of that contribution, so E(R_i) − R_f = [(E(R_m) − R_f) ÷ σ_m²] Cov(i, m) = β_i[E(R_m) − R_f]. Plotted against β, this is the security market line. A share above the line is underpriced (it offers more than its risk demands); one below is overpriced.

5. Worked example: beta and cost of equity

Year	R_m %	R_i %	d_m	d_i	d_md_i	d_m²
1	10	12	0	0	0	0
2	12	16	2	4	8	4
3	8	8	−2	−4	8	4
4	14	18	4	6	24	16
5	6	6	−4	−6	24	16
Total	50	60			64	40

Means: R_m 10%, R_i 12%. β = 64 ÷ 40 = 1.6. With R_f = 7% and an expected market return of 12%: k_e = 7 + 1.6(12 − 7) = 15%. This k_e can be used in the WACC.

6. The efficient market hypothesis

The CAPM assumes prices reflect information. Eugene Fama (1970) classified market efficiency in three forms: weak (prices reflect all past prices, so charts cannot beat the market), semi-strong (prices reflect all public information, so analysing published accounts cannot), and strong (prices reflect even inside information). Evidence broadly supports the weak and semi-strong forms in large markets; the strong form fails, which is why insider trading is prohibited (in India by the SEBI (Prohibition of Insider Trading) Regulations, 2015).

7. Empirical evaluation

Support: Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) found that average returns rise with beta and the relation is roughly linear.
But the line is flatter than the model predicts: low-beta shares earn more, and high-beta shares less, than the CAPM says.
Roll’s critique (1977): the true market portfolio (all assets, including property and human capital) cannot be observed, so the model cannot be properly tested with a share index.
Fama and French (1992) found that size and book-to-market ratio explain returns better than beta, leading to their three-factor model; Ross’s arbitrage pricing theory (1976) also allows several factors.
Even so, the CAPM remains the most used method of estimating the cost of equity, because it is simple and links return to market risk.

How this is examined

The 6-mark short note on the Sharpe–Lintner model (February 2025) needs sections 2, 3 and a few lines from 4 and 7. Older papers also asked for k_e by CAPM from a given beta; the one-line calculation in section 5 does it. Draw the security market line in words: return on the vertical axis, beta on the horizontal, starting at R_f and passing through the market at β = 1.

Now try the real questions: Financial Management past question papers.