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Hong KongCAPM: required return, beta, and the security market line
CAPM gives required return as the risk-free rate plus beta multiplied by the difference between the expected market return and the risk-free rate. Beta measures systematic risk, with the market at 1.0.
One formula, used constantly, and a graph that turns it into a mispricing test.
The formula
Required return equals the risk-free rate, plus beta multiplied by the equity risk premium - where the equity risk premium is the expected market return less the risk-free rate.
The risk-free rate is usually proxied by short-term Treasury securities. Beta comes from the security or portfolio.
What beta means
| Beta | Interpretation |
|---|---|
| 1.0 | Moves with the market |
| Above 1.0 | More volatile than the market - a 1.5 beta implies a 15 per cent move for a 10 per cent market move |
| Below 1.0 | Less volatile than the market |
| 0 | Uncorrelated with the market |
| Negative | Moves against the market - rare |
Beta measures systematic risk only, which is why it is the input CAPM uses. Unsystematic risk is diversifiable, so the model does not pay you for it.
Beta is only meaningful where the portfolio's movement is largely explained by the market. A low R-squared makes beta and any measure built on it unreliable, and the question is telling you to use standard deviation instead.
The security market line
Plot required return against beta and CAPM traces a straight line, intercepting at the risk-free rate. That line is the security market line.
A security plotting above the line is offering more return than its beta requires, so it is undervalued. Below the line, overvalued. That comparison is the examinable use.
Jensen's alpha is the vertical distance from the line: actual return less CAPM-required return. Positive alpha means outperformance on a risk-adjusted basis.
Security market line against capital market line
The security market line uses beta on the horizontal axis and applies to any security or portfolio. The capital market line uses standard deviation and applies only to efficient portfolios.
Questions swap them, and the axis is how you tell them apart.
The assumptions, and why they matter
A single period, no taxes or transaction costs, borrowing and lending at the risk-free rate, and homogeneous expectations.
CAPM is a model of required return rather than a prediction. Multi-factor models exist because beta alone explains less of the variation in returns than the single-factor model implies, and knowing that a limitation exists is enough for this exam.
Dollar limits and rate thresholds here are indexed annually. Confirm the current figure before relying on it, and expect the exam to test the rule rather than the number.
Common questions
What is the CAPM formula?
Required return equals the risk-free rate plus beta multiplied by the equity risk premium, where the premium is the expected market return less the risk-free rate.
What does a beta of 1.5 mean?
The security is expected to move one and a half times as much as the market - roughly a 15 per cent move for a 10 per cent market move, in either direction.
When is beta unreliable?
When R-squared is low, meaning the portfolio's movement is not well explained by the market. Standard deviation and the Sharpe ratio are the appropriate measures then.
How does the security market line identify mispricing?
A security plotting above the line offers more return than its beta requires and is undervalued. Below the line it is overvalued. The vertical distance is Jensen's alpha.
What is the difference between the security market line and the capital market line?
The security market line uses beta and applies to any security or portfolio. The capital market line uses standard deviation and applies only to efficient portfolios. The axis distinguishes them.