FINS5513 Chap.4 CAPM and the Security Market Line
CAPM and the Security Market Line
Week 4 derives an equilibrium relation between expected return and systematic risk. CAPM assumes rational mean-variance investors, common expectations, one holding period, price-taking behaviour, unrestricted borrowing and lending at one risk-free rate, tradable assets and no relevant taxes or transaction frictions. With those assumptions, investors converge on one optimal risky fund and it becomes the market portfolio.
Beta measures an asset's covariance with the market divided by market variance. It is the asset's marginal contribution to diversified market risk, not its total volatility. CAPM required return equals the risk-free rate plus beta times the market risk premium. The security market line plots that relationship against beta.
A point above the line has positive alpha and is underpriced conditional on the model; a point below has negative alpha and is overpriced. The capital allocation line must remain separate because it uses total standard deviation on its horizontal axis. Empirical interpretation is conditional on an unobservable true market portfolio and the proxy chosen for it.
What this chapter covers
- 01
CAPM assumptions and the separation result
- 02
Market portfolio as the common optimal risky portfolio
- 03
Beta from covariance with the market divided by market variance
- 04
Systematic risk versus diversifiable firm-specific risk
- 05
CAPM required return from risk-free rate and market premium
- 06
Security market line intercept, slope and beta axis
- 07
Positive and negative alpha as model-relative pricing signals
- 08
Roll critique and the joint test of CAPM with a market proxy
Worked example · free
Required return and an SML pricing verdict
- +1The market risk premium is 9.5% minus 3.5%, which equals 6.0%.
- +1CAPM required return is 3.5% plus 1.20 times 6.0%, which equals 10.7%.
- +1Alpha is 12.0% minus 10.7%, which equals positive 1.3%.
- +1The asset plots above the SML and is underpriced conditional on CAPM and the return forecast.
Key terms
- Market Risk Premium
- Expected market return above the risk-free rate, forming the slope of the security market line.
- Beta
- An asset's covariance with the market divided by market variance.
- Systematic Risk
- Common market-related risk that remains in a diversified portfolio.
- Unsystematic Risk
- Firm-specific risk that can be reduced through diversification.
- Security Market Line
- The CAPM schedule linking beta to required expected return.
- Alpha
- Expected or realised return above the model-required benchmark, conditional on the chosen model.
CAPM and the Security Market Line FAQ
Why is total volatility not priced?
Investors can diversify firm-specific volatility without giving up expected return. CAPM therefore rewards only the covariance an asset contributes to the market portfolio, summarised by beta.
What does beta greater than one mean?
A beta above one indicates that the asset's return tends to respond more than proportionally to market movements under the estimated relation. It does not directly state total standard deviation.
How is alpha interpreted?
Positive alpha places expected return above CAPM required return and suggests underpricing conditional on the model. Negative alpha suggests overpricing. Either sign can also reflect model error or a poor benchmark.
How does the SML differ from the CAL?
The SML uses beta and applies to individual assets and portfolios. The CAL uses total standard deviation and describes combinations of a risk-free asset with a particular risky portfolio.
Why is CAPM testing a joint test?
The true portfolio of all assets is unobservable, so empirical work uses a proxy. A rejection may reflect the pricing relation, the proxy, or both rather than CAPM alone.
Exam move
Keep a two-column comparison between CAL and SML. Write standard deviation and complete portfolios under CAL; write beta and all assets under SML. For every CAPM calculation, isolate the market risk premium before applying beta. Draw the SML with the risk-free intercept and market-premium slope, then use vertical distance to read alpha.
Practise converting covariance and market variance into beta and explain why beta can be low even when total volatility is high. For assumptions, connect each simplification to the derivation instead of listing generic criticisms. Close pricing answers with the phrase conditional on CAPM and the expected-return estimate.
That wording preserves the investment conclusion while recognising that the market proxy and omitted risks can change alpha.
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