CFA Level II · Cheat Sheet
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| Concept | Formula / Definition | Key Point |
| Sharpe Ratio | (E(Rp) - rf) / σp | Higher = more efficient; ranks portfolios on CML |
|---|---|---|
| Capital Market Line | E(Rp) = rf + [(E(Rm) - rf) / σm] × σp | All investors hold mix of rf asset + tangency portfolio |
| Tangency Portfolio | Highest Sharpe ratio on efficient frontier | Identified as market portfolio in CAPM |
| Efficient Frontier | Maximizes return for given risk OR minimizes risk for given return | Only risky assets; dominates all other portfolios |
| Measure | Formula | Interpretation |
| CAPM Expected Return | E(Ri) = rf + βi[E(Rm) - rf] | Baseline return for security's systematic risk |
| Beta | Cov(Ri, Rm) / Var(Rm) | Sensitivity to market; βi > 1 = amplifies market moves |
| Jensen's Alpha | αi = Ri - [rf + βi(Rm - rf)] | Excess return above CAPM prediction |
| Alpha Interpretation | α > 0 | Outperformance (skill or luck); α < 0: underperformance |
| Metric | Formula | Use Case |
| Tracking Error (TE) | σ(Rp − Rbench) | Measures active risk; lower = closer to benchmark |
| Active Return (α) | Rp − Rbench | Gross excess return before risk adjustment |
| Information Ratio | α / TE = Active Return / Tracking Error | Efficiency of active alpha; higher = better risk-adjusted active return |
| Fundamental Law | IR = IC × √N × TC | IC = forecasting skill; N = breadth; TC = transfer coefficient |
| Model | Factors | Formula |
| CAPM | Market only | E(Ri) = rf + β(Rm − rf) |
| Fama-French 3F | Market, Size (SMB), Value (HML) | E(Ri) = rf + b₁(Rm−rf) + b₂(SMB) + b₃(HML) |
| Carhart 4F | Fama-French 3 + Momentum | Add b₄(MOM) |
| APT | k systematic factors | E(Ri) = rf + Σ λk × βik |
| Concept A | Concept B | Difference |
| Tracking Error | Active Return | TE is risk (volatility of excess return); active return is return (Rp − Rbench) |
| Alpha | Active Return | Alpha = CAPM excess; active return = any excess vs. benchmark (may differ if benchmark ≠ market) |
| Jensen's Alpha | Sharpe Ratio | Alpha: return after adjusting for beta risk; Sharpe: return per unit of total risk (no beta adjustment) |
| IC | IR | IC = forecasting skill (correlation); IR = scaled active return efficiency (depends on IC, breadth, TC) |
| Efficient Frontier | CML | Frontier = risky assets only; CML = efficient frontier + risk-free asset |
| Best-in-Class | Negative Screening | Best-in-class maintains sector neutrality; negative screening creates unintended sector tilts |
| Approach | Advantage | Disadvantage |
| Negative Screening | Simple; reduces ESG risk exposure | Increases tracking error; unintended sector bets |
| Best-in-Class | Maintains sector neutrality; lower sector TE | Within-sector concentration; reduced diversification; empirical return impact ambiguous |
| Factor Model | Quantifies ESG-return relationship | Assumes stable ESG-return correlation; may vary by cycle |
| Question | Rule | |
| Which portfolio is more efficient? | Compare Sharpe ratios; higher wins | |
| Did manager beat CAPM expectation? | Calculate Jensen's alpha; positive = yes | |
| Is active strategy worth higher costs? | Compare IR to |
Aligned to the CFA Institute Level II curriculum.
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