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?
Candidates commonly miss these questions because they:
The stronger reader asks which risk concept the question is paying you for.
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.
| Line | What it connects | What it applies to | Common trap |
|---|---|---|---|
| Capital allocation line (CAL) | Risk-free asset and any chosen risky portfolio | One investor’s chosen risky portfolio opportunity set | Treating every CAL as the market line |
| Capital market line (CML) | Risk-free asset and the market portfolio | Efficient portfolios only | Applying it to an individual security |
| Security market line (SML) | Required return and beta | Individual securities and portfolios | Confusing beta-based pricing with total-risk tradeoffs |
The CML is the special efficient CAL formed with the market portfolio.
| Risk type | Meaning | Why it matters |
|---|---|---|
| Systematic risk | Market-related risk that cannot be diversified away | Investors require compensation for bearing it |
| Nonsystematic risk | Security-specific risk that diversification can reduce | Investors 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.
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:
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.
| Situation | Stronger interpretation |
|---|---|
| Actual return requirement is above CAPM return | Security may plot above the SML and appear undervalued |
| Actual return requirement is below CAPM return | Security may plot below the SML and appear overvalued |
| High total volatility but low beta | The 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.
| Measure | Formula | Best use | Common trap |
|---|---|---|---|
| Sharpe ratio | (\dfrac{R_p - R_f}{\sigma_p}) | Comparing portfolios using total risk | Using it when the question clearly isolates systematic risk |
| Treynor ratio | (\dfrac{R_p - R_f}{\beta_p}) | Comparing well-diversified portfolios using beta | Applying it to a poorly diversified portfolio |
| (M^2) | Sharpe-based return measure scaled to market risk | Translating Sharpe intuition into return terms | Forgetting 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 return | Treating positive alpha as proof of skill in every setting |
The denominator tells you what kind of risk the measure is adjusting for.
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.
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.