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Contrast the security market line with the capital market line, interpreting each.

FRM® Part I · Foundations of Risk Management · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM) · FRM1.FR.5.d

The idea

Both lines come from the CAPM but answer different questions. The capital market line plots expected return against total risk, the standard deviation. It applies only to efficient portfolios, which are combinations of the risk-free asset and the market portfolio. On it, Expected return = Rf + ((E(Rm) − Rf) ÷ σm) × σp. Its slope is the market portfolio's Sharpe ratio. The security market line plots expected return against beta and applies to every asset and portfolio, efficient or not. On it, Expected return = Rf + β × (E(Rm) − Rf). Its slope is the market risk premium. A fairly priced asset lies on the SML. One above it has a positive alpha and looks underpriced, and one below looks overpriced. The CML describes efficient combinations only. Under the CAPM assumptions, an individual stock or inefficient portfolio plots on the SML and below the CML because it carries diversifiable risk, but a mispriced asset can plot anywhere. Do not mix up the axes or the slopes.

Formulas

Capital market line

E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp

E(Rp)
the expected return of an efficient portfolio
Rf
the risk-free rate
E(Rm)
the expected return on the market portfolio
σm
the market portfolio's volatility
σp
the efficient portfolio's volatility

Only for efficient mixes of the risk-free asset and the market. An individual stock plots below it; use the SML, against beta, for those.

A practice question

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

Which pair of axes correctly describes the capital market line and the security market line?

  1. CML: expected return against beta; SML: expected return against standard deviationWhy not: Swaps the axes of the two lines.
  2. CML: expected return against beta; SML: standard deviation against betaWhy not: Puts beta on the CML axis and standard deviation on the SML vertical axis; both lines have expected return vertically.
  3. CML: expected return against standard deviation; SML: expected return against beta - correct
  4. CML: expected return against variance; SML: expected return against covarianceWhy not: Uses variance and covariance; the CML uses standard deviation and the SML uses beta, a standardised covariance.

The capital market line applies to efficient portfolios and measures risk as total standard deviation. The security market line applies to any asset and measures risk as systematic risk, beta.

A harder one

The risk-free rate is 3%, the expected market return is 9% and the market volatility is 15%. An efficient portfolio on the capital market line has a volatility of 24%. Its expected return is closest to:

  1. 12.6% - correct
  2. 14.4%Why not: Scales the market return by the leverage of 1.6 without paying the borrowing cost on the 0.6 borrowed.
  3. 9.6%Why not: Leaves out the risk-free rate, giving only the risk premium.
  4. 17.4%Why not: Uses the market return rather than the premium in the slope (9% / 15%), then adds Rf.

CML: E(Rp) = Rf + [E(Rm) - Rf] / sigma_m x sigma_p = 3% + (6% / 15%) x 24% = 3% + 9.6% = 12.6%. The portfolio holds 1.6 times wealth in the market, funded by borrowing 0.6 at 3%.

The hardest tier

The risk-free rate is 2% and the expected market return is 8%. Asset A has a beta of 0.5 and an expected return of 6.0%. Asset B has a beta of 1.5 and an expected return of 10.5%. Which statement is correct?

  1. A is overpriced because 6.0% is below the 8% market return; B is underpriced because 10.5% is above itWhy not: Compares each return with the market return instead of with the SML return for its own beta.
  2. A is overpriced and B is underpriced, because the SML requires 6.0% above its alphaWhy not: Reverses the sign of alpha: an asset above the SML offers more than its required return.
  3. A plots above the SML (SML return 5.0%) and looks underpriced; B plots below it (SML return 11.0%) and looks overpriced - correct
  4. Both are fairly priced because the line joining them slopes upward from the risk-free rateWhy not: Treats any upward-sloping line as the SML; the SML slope must equal the 6% market risk premium.

Required returns: A = 2% + 0.5 x 6% = 5.0%, so alpha = +1.0%. B = 2% + 1.5 x 6% = 11.0%, so alpha = -0.5%. Positive alpha means above the SML, underpriced; negative alpha means below, overpriced.

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