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Apply the security market line to spot assets that are mispriced

CFA® Level I · Portfolio Management · Portfolio Risk and Return: Part II · PM.4.d

The idea

The security market line plots required return against beta, and under the CAPM every correctly priced asset lies on it. An asset whose expected return plots above the line offers more than its systematic risk warrants and is undervalued. One below the line is overvalued. The vertical distance between an asset's expected return and the line is its alpha. The test is only as good as the expected return estimate, so a plot far above the line usually means the forecast is wrong rather than that the market has left money on the table.

Formulas

Alpha against the security market line

α = expected return − required return

expected return
the return the analyst forecasts for the asset
required return
what the capital asset pricing model says it should return for its beta
α
the difference between them

Positive alpha plots above the security market line and the asset is underpriced; negative plots below and it is overpriced. It is only ever as good as the forecast, which is why two analysts get two alphas for the same share.

A practice question

From the question bank, with the reason each wrong option is wrong.

An asset plots above the security market line. What does this indicate?

  1. It is undervalued — correct
  2. It is overvaluedWhy not: Assets offering less than their beta requires plot below the line, not above it.
  3. It has zero betaWhy not: A zero-beta asset plots at the line's intercept. Its position relative to the line is a separate matter.

It offers more return than its systematic risk requires. Above the line means the expected return exceeds what the CAPM demands for that beta, which is a positive alpha.

A harder one

The risk-free rate is 3%, the market risk premium is 5%, and a stock with a beta of 1.2 is expected to return 10%. What is its alpha?

  1. 2.0%Why not: Uses a required return of 8%, which is the beta-of-one figure. With beta 1.2 the requirement is 9%.
  2. 1.0% — correct
  3. 1.2%Why not: The beta itself, reported as though it were a return.

Required return is 3 + 1.2(5) = 9%, and the expected 10% exceeds it by one percentage point. That gap is the alpha.

The hardest tier

Why should a large apparent alpha prompt scepticism rather than immediate investment?

  1. Because alpha is not observable for listed securitiesWhy not: It is computed readily; the difficulty is that one of its inputs is a forecast rather than an observation.
  2. Because the CAPM applies only to portfoliosWhy not: It is applied to individual securities routinely, which is what the security market line plots.
  3. Because estimation error is more likely — correct

The calculation depends on an estimated expected return, and an error there is a likelier explanation than a large mispricing. The line itself is nearly observable; the asset's expected return is not, so a result implying the market has badly misjudged a widely followed stock usually indicts the forecast.

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