CAL, CML, CAPM, and Performance Measures

How Level I tests risk-free combinations, systematic risk, CAPM, and the main portfolio performance measures.

Once Level I moves beyond pure risky-asset combinations, the portfolio question becomes more structured: what happens when a risk-free asset is available, which risk gets rewarded, and how do you judge portfolio performance after adjusting for risk?

Why This Lesson Matters

Candidates commonly miss these questions because they:

  • confuse the capital allocation line with the capital market line
  • mix total risk and systematic risk
  • use CAPM without understanding what beta measures
  • memorize Sharpe or Treynor mechanically without knowing when each makes sense

The stronger reader asks which risk concept the question is paying you for.

Combining A Risk-Free Asset With A Risky Portfolio Changes The Opportunity Set

If a complete portfolio combines a risk-free asset and a risky portfolio:

$$ E(R_c) = R_f + y\big(E(R_p) - R_f\big) $$

$$ \sigma_c = y\sigma_p $$

where (y) is the fraction invested in the risky portfolio.

This is why the capital allocation line is straight. Expected return and standard deviation both scale with exposure to the risky portfolio when the other asset is truly risk free.

LineWhat it connectsWhat it applies toCommon trap
Capital allocation line (CAL)Risk-free asset and any chosen risky portfolioOne investor’s chosen risky portfolio opportunity setTreating every CAL as the market line
Capital market line (CML)Risk-free asset and the market portfolioEfficient portfolios onlyApplying it to an individual security
Security market line (SML)Required return and betaIndividual securities and portfoliosConfusing beta-based pricing with total-risk tradeoffs

The CML is the special efficient CAL formed with the market portfolio.

Not All Risk Is Rewarded

Risk typeMeaningWhy it matters
Systematic riskMarket-related risk that cannot be diversified awayInvestors require compensation for bearing it
Nonsystematic riskSecurity-specific risk that diversification can reduceInvestors should not expect extra return for it in equilibrium

Level I often tests this through plain language: if a risk can be diversified away, it should not carry its own risk premium.

The Market Model And Beta Help Isolate Market Exposure

One common return-generating form is:

$$ R_i = \alpha_i + \beta_i R_M + \varepsilon_i $$

Beta measures sensitivity to market movements:

$$ \beta_i = \frac{\operatorname{Cov}(R_i, R_M)}{\operatorname{Var}(R_M)} $$

Interpretation matters more than computation alone:

  • (\beta = 1): asset tends to move with the market
  • (\beta > 1): asset is more sensitive than the market
  • (\beta < 1): asset is less sensitive than the market
  • negative beta: unusual hedge-like behavior

The CAPM equation is:

$$ E(R_i) = R_f + \beta_i\big(E(R_M) - R_f\big) $$

This is the Security Market Line in equation form. It says required return depends on the risk-free rate plus compensation for systematic risk.

CAPM And SML Questions Are Usually Interpretation Questions

SituationStronger interpretation
Actual return requirement is above CAPM returnSecurity may plot above the SML and appear undervalued
Actual return requirement is below CAPM returnSecurity may plot below the SML and appear overvalued
High total volatility but low betaThe security may still have limited systematic risk

The exam often cares more about whether the asset is priced relative to the SML correctly than about reproducing every assumption perfectly.

Risk-Adjusted Performance Measures Use Different Denominators

MeasureFormulaBest useCommon trap
Sharpe ratio(\dfrac{R_p - R_f}{\sigma_p})Comparing portfolios using total riskUsing it when the question clearly isolates systematic risk
Treynor ratio(\dfrac{R_p - R_f}{\beta_p})Comparing well-diversified portfolios using betaApplying it to a poorly diversified portfolio
(M^2)Sharpe-based return measure scaled to market riskTranslating Sharpe intuition into return termsForgetting it is built from Sharpe logic
Jensen’s alpha(R_p - [R_f + \beta_p(R_M - R_f)])Measuring return above or below CAPM-implied returnTreating positive alpha as proof of skill in every setting

The denominator tells you what kind of risk the measure is adjusting for.

How CFA-Style Questions Usually Test This

  • by asking what happens when a risk-free asset is combined with a risky portfolio
  • by testing whether a risk premium should attach to systematic or nonsystematic risk
  • by giving beta and market assumptions so you can apply CAPM
  • by asking which risk-adjusted performance measure fits the stated comparison

Mini-Case

A question asks which manager performed better. One manager’s portfolio is concentrated in a few names, while the other is broadly diversified. A weak answer goes straight to Treynor because beta sounds more advanced. A stronger answer asks whether systematic risk alone is the relevant denominator.

If the portfolio is not well diversified, Sharpe often gives the cleaner comparison because total risk still matters.

Common Traps

  • applying the CML to a single security
  • assuming beta measures total risk
  • forgetting that CAPM prices only systematic risk
  • using Treynor on a portfolio with large nonsystematic risk

Sample CFA-Style Question

An analyst says a stock should earn a higher return because it has high firm-specific litigation risk. Under CAPM, the strongest response is:

Best answer: Not necessarily, because firm-specific risk is nonsystematic and should not command a risk premium if investors can diversify it away.

Why: This is one of the cleanest ways Level I tests the difference between total risk and market-priced risk.

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