FINC3017 · Investments And Portfolio Management
The CAPM & its Empirical Tests
The CAPM & its Empirical Tests (Week 5) turns portfolio theory into an equilibrium pricing model. Under its assumptions every asset is priced on the security market line by its beta — only systematic risk earns a premium — and the equilibrium market risk premium equals A·σ_m². The empirical half asks whether the model survives the data: time-series tests check that alpha is zero, the GRS statistic tests it jointly, two-stage cross-sectional and Fama-MacBeth regressions estimate the price of beta, and the verdict (a too-flat SML, persistent anomalies, Roll's critique that the market is unobservable) is that the CAPM is rejected.
What this chapter covers
- 01CAPM assumptions: homogeneous expectations, price-takers, single period, mean-variance optimisers, frictionless, risk-free borrow/lend
- 02Security market line: E[R_i] = rf + β_i(E[R_m] − rf), with β_i = Cov(R_i, R_m)/σ_m²
- 03Only systematic risk is priced; idiosyncratic risk is diversified away
- 04Equilibrium market risk premium MRP = A·σ_m²
- 05Variance decomposition Var(R_i) = β_i²Var(f) + Var(ε_i)
- 06Jensen's alpha = 0 under the CAPM; time-series test of α = 0 and the GRS joint test
- 07Two-stage cross-sectional regression and Fama-MacBeth per-period λ_t
- 08Verdict: SML too flat (Black-Jensen-Scholes), anomalies, and Roll's critique
Beta, the SML required return, and Jensen's alpha
- 2 marks(a) Security market line: E[R] = rf + β(E[R_m] − rf) = 3% + 1.2 × (9% − 3%) = 3% + 1.2 × 6% = 3% + 7.2% = 10.2%.
- 2 marks(b) Jensen's alpha = realised − required = 12% − 10.2% = +1.8%, so the stock beat its beta-justified return.
- 2 marks(c) Equilibrium MRP = A·σ_m² = 2.5 × (0.18)² = 2.5 × 0.0324 = 0.081.
- 1 mark(c cont.) Convert to a percentage: 0.081 = 8.1%, the market risk premium consistent with that risk aversion and market volatility.
Key terms
- Security market line (SML)
- The CAPM pricing relationship E[R_i] = rf + β_i(E[R_m] − rf), plotting required return against beta. Every asset, efficient or not, should plot on it; positions above the line are underpriced (positive alpha) and below it overpriced.
- Jensen's alpha
- The intercept of an asset's excess-return regression on the market, equivalently realised return minus CAPM-required return. It should be zero under the CAPM, so a reliably positive alpha is evidence of skill or of a missing risk factor the model omits.
- Market risk premium (MRP)
- The expected excess return on the market over the risk-free rate. In CAPM equilibrium it equals the representative investor's risk aversion times market variance, MRP = A·σ_m² — linking the price of risk to how risk-averse the market is.
- Fama-MacBeth regression
- A two-stage cross-sectional test: estimate betas in the time series, then run a cross-sectional regression of returns on betas each period to get a series of risk-price estimates λ_t. The average and its standard error (σ(λ_t)/√T) test whether the factor is priced.
- Roll's critique
- The argument that the CAPM is untestable because the true market portfolio (all wealth, including non-traded assets) is unobservable. Any test really tests whether a chosen proxy is mean-variance efficient, so a rejection may just mean the proxy was wrong.
The CAPM & its Empirical Tests FAQ
Why does only beta, not total volatility, determine an asset's required return under the CAPM?
Because a well-diversified investor can eliminate idiosyncratic risk for free, the market refuses to pay a premium for it. Only the systematic component — how an asset co-moves with the market, measured by beta — cannot be diversified away, so the SML rewards beta alone and an asset's own volatility is irrelevant to its equilibrium expected return.
What does it mean that the empirical SML is 'too flat'?
Tests such as Black-Jensen-Scholes find that low-beta stocks earn more than the CAPM predicts and high-beta stocks earn less, so the fitted line is flatter than the theoretical SML. This shows up as positive alphas for low-beta portfolios and is one of the strands of evidence that the single-factor CAPM does not fully describe returns.
Is a non-zero alpha proof a manager has skill?
Not necessarily. Under the CAPM alpha should be zero, so a positive alpha could mean genuine skill, but it could equally mean the CAPM is mis-specified and the 'alpha' is really compensation for a missing risk factor (size, value, momentum). Multi-factor models exist precisely to absorb such alphas, which is why the exam links non-zero CAPM alpha to the need for richer models.
Exam move
Lock in the SML and the alpha = realised − required relationship so you can answer required-return and outperformance MCQs instantly, and memorise MRP = A·σ_m². On the empirical side, be able to name the tests (time-series alpha, GRS, Fama-MacBeth) and the verdict (flat SML, anomalies, Roll's critique) in a sentence each — these are reliable conceptual marks.
