FRM P2 Risk Management and Investment Management: practice questions with answers

Answer: D. Ang argues that alpha only has meaning relative to a benchmark, and that a good benchmark should be:

- well defined: specified in advance and transparent;
- tradeable: the investor could actually hold it as an alternative;
- replicable: it can be reproduced at low cost;
- adjusted for risk: it captures the systematic factor exposures the manager takes.

A manager with persistent small-cap and value tilts will appear to have alpha against a cap-weighted market index simply because it harvests the size and value premiums. A factor benchmark, built from index funds or tradeable factor portfolios with the same exposures, separates true skill from factor returns the plan could get cheaply. If the manager's returns are fully explained by factor exposures, the plan can capture them at lower cost through factor investing.

Answer: A. Annual breadth BR = 25 × 4 = 100 independent bets.

IR = TC × IC × √BR = 0.7 × 0.08 × 10 = 0.56.

Expected active return = IR × tracking error = 0.56 × 4.0% = 2.24%.

Constraints that lower the transfer coefficient directly reduce the value of the manager's forecasting skill.

Answer: D. Operational due diligence assesses the infrastructure and controls around the investment process: independent administration, valuation policies, custody, segregation of duties, compliance, auditors and key-person issues. A portfolio manager pricing hard-to-value positions without independent checks creates scope for misstated NAV and fraud, a recurring feature of hedge fund failures. Leverage, concentration and fees matter, but they are investment or commercial matters assessed separately.

Answer: A. Mean return = (8 − 4 + 12 + 1 + 6 − 2) / 6 = 3.5%.

Shortfalls below the 2% MAR: −4 − 2 = −6; 1 − 2 = −1; −2 − 2 = −4. Squared: 36 + 1 + 16 = 53.

Downside deviation = √(53/6) = √8.833 = 2.972%.

Sortino ratio = (3.5 − 2.0) / 2.972 = 0.50.

The Sortino ratio penalises only returns below the investor's target, which suits investors who care about shortfalls rather than total volatility, especially for skewed return distributions.

Answer: A. Active return = (β − 1) × R_B + ε, so tracking error has two independent parts:

TE² = (β − 1)² σ_B² + σ_ε² = (0.15 × 16)² + 4² = 2.4² + 16 = 5.76 + 16 = 21.76.

TE = √21.76 = 4.66%.

About a quarter of the active variance comes from an unintended beta bet, which a manager could remove cheaply with index futures if it is not part of the strategy.

Answer: B. Rearranging the smoothing model gives the unsmoothed (true) return:

r_t = (r*_t − ρ × r*_t−1) / (1 − ρ) = (−3.0 − 0.7 × 2.0) / 0.3 = −4.4 / 0.3 = −14.7%

Appraisal-based returns adjust slowly because appraisers anchor on previous valuations. Ang notes that this smoothing makes illiquid assets look less volatile and less correlated with public markets than they are. Unsmoothing gives a true return much closer to the fall in listed real estate, and unsmoothed series have higher volatility, higher betas and lower Sharpe ratios. Using reported returns in asset allocation would therefore over-allocate to illiquid assets.