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Free FRM Risk Management & Investment Management Practice Questions & Answers
400 exam-style Risk Management & Investment Management questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 271
What is 'residual risk' (specific risk) in a portfolio model?
Select an option first.
Correct answer: B — The portion of a security's total risk that is uncorrelated with the market or factor returns — diversified away in a well-constructed portfolio. In a regression of security returns on factors: residual = total variance − explained variance (R²)
Explanation: B is correct. Residual/idiosyncratic risk = total σ² − β²σ²_market (in CAPM). A security with total σ = 25% and β = 1.2 in a market with σ = 15% has systematic variance = (1.2×15%)² = 324 bps² and residual = 625 − 324 = 301 bps². This residual is diversified away in a large portfolio. A is net risk after hedging. C is performance. D is model error.
Question 272
What is the 'geometric mean return' and when should it be used instead of the arithmetic mean?
Select an option first.
Correct answer: B — The compounded annualised return — the n-th root of the product of (1 + return) over n periods. It is always ≤ arithmetic mean and is the appropriate return measure for multi-period investments, as it reflects actual wealth accumulation. Arithmetic mean overstates long-term compound growth for volatile investments
Explanation: B is correct. Geometric mean: (1+r_geo)^n = (1+r₁)(1+r₂)...(1+rₙ). A volatile investment with +50% one year and −50% the next has arithmetic mean = 0% but geometric mean = √(1.5 × 0.5) − 1 = −13.4%. Actual compound return = −13.4%. The variance drag: r_geo ≈ r_arith − σ²/2. A is log-return calculation. C is only true when returns are identical. D is wrong.
Question 273
What is 'time-weighted return' (TWR) vs 'money-weighted return' (MWR)?
Select an option first.
Correct answer: B — TWR eliminates the effect of external cash flows (investor timing) by compounding sub-period returns — measures manager skill. MWR (IRR) reflects the actual investor experience including the timing and size of cash flows. MWR can differ significantly from TWR if large cash flows occur at unfavourable times
Explanation: B is correct. TWR vs MWR: if a manager earns 10% per year, TWR = 10% regardless of when investors added or withdrew cash. MWR differs if investors added cash before a down period (MWR < TWR) or before an up period (MWR > TWR). TWR is the standard for evaluating manager performance (GIPS). MWR measures investor experience. A conflates them. C and D are incorrect.
Question 274
What is 'correlation' vs 'covariance' and how are they related?
Select an option first.
Correct answer: B — Covariance measures the direction and magnitude of the linear relationship between two variables (in raw units of the variables). Correlation = Covariance / (σ_A × σ_B), standardising covariance to a dimensionless measure between −1 and +1. Correlation is easier to interpret and compare
Explanation: B is correct. Cov(A,B) = ρ_AB × σ_A × σ_B. Correlation is standardised: ρ = 1 (perfect positive), −1 (perfect negative), 0 (uncorrelated). Covariance depends on the units of the variables making it hard to interpret across different pairs. Portfolio variance uses covariance directly but correlation is more intuitive for diversification assessment. A conflates them. C: both can be negative. D is wrong.
Question 275
What is an 'alternative risk premium' (ARP)?
Select an option first.
Correct answer: B — Systematic, quantifiable sources of return that can be accessed through rule-based strategies — including: volatility risk premium (selling options), carry, value, momentum, quality, and merger arbitrage spread. These premiums are theoretically grounded in economic risk or behavioural biases and provide hedge-fund-like returns at lower cost
Explanation: B is correct. ARP: distinct from traditional beta (market) and alpha (skill). Alternative risk premiums: equity volatility risk premium (selling options earns a premium because implied > realised vol on average), FX carry (earning interest rate differential), commodity backwardation. ARPs provide diversification, are accessible via liquid instruments, and cost less than hedge funds. A is pure alpha. C is alternative asset beta. D is active return.
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Question 276
What is 'regression to the mean' in investment performance?
Select an option first.
Correct answer: B — The statistical phenomenon where extreme performance (very high or very low) tends to be followed by performance closer to the long-run average — important for investment manager evaluation: last year's top performer is likely to revert toward average, partly because past outperformance reflects both skill and luck
Explanation: B is correct. Regression to mean: managers who ranked in the top decile one year are more likely to rank near the median the next year. This is because: (1) some of their outperformance was luck; (2) their strategy may have been in favour and reverts; (3) capacity constraints emerge. Important implication: do not chase last year's winners without evaluating the source of performance. A is different. C and D are other regression concepts.
Question 277
What is 'marginal VaR' and how is it used in portfolio risk management?
Select an option first.
Correct answer: B — The change in portfolio VaR resulting from a small increase in the portfolio position in a specific asset — used to identify which assets are making the portfolio riskier or less risky, and to optimise the portfolio toward the maximum Sharpe ratio or minimum risk
Explanation: B is correct. Marginal VaR (MVaR): ∂VaR_p / ∂w_i. If adding more of asset i increases portfolio VaR, MVaR > 0; if it decreases (due to negative correlation), MVaR < 0. Portfolio optimisation: for a given expected return, reduce positions in assets with high MVaR and increase those with low or negative MVaR. A is a margin account concept. C is position VaR. D is a calculation difference.
Question 278
What is 'long-term capital allocation' for an institutional investor?
Select an option first.
Correct answer: B — Strategic asset allocation (SAA): determining the long-term target weights across asset classes (equities, fixed income, alternatives, real assets) based on: long-term return and risk expectations, liability structure, liquidity needs, regulatory constraints, and investment horizon. SAA determines approximately 90% of long-run portfolio return variation
Explanation: B is correct. SAA (Brinson et al. 1986): studies show SAA (asset class decisions) explains ~90% of return variation across time; security selection and timing explain much less. SAA should reflect the investor's fundamental objectives (e.g., pension fund: match liability duration), risk capacity, and long-term capital market assumptions. A is a duration decision. C is an alternative allocation decision. D is an interest rate risk decision.
Question 279
What are 'capital market assumptions' (CMAs) used for in SAA?
Select an option first.
Correct answer: B — Long-term estimates of expected returns, volatility, and correlations for major asset classes — inputs to the mean-variance optimisation or other portfolio construction process used to set the strategic asset allocation. CMAs typically look 5-10 years ahead and incorporate current market valuations, macroeconomic expectations, and historical data
Explanation: B is correct. CMAs (e.g., from BlackRock, JPMorgan, PIMCO): long-run expected returns by asset class, reflecting current valuation levels and macro outlook. Higher starting valuation → lower forward returns (mean reversion). CMAs are the key inputs driving SAA, so errors in CMAs translate directly into suboptimal allocations. A is regulatory. C and D are different assumption types.
Question 280
What is 'liability-relative investing' and when is it used?
Select an option first.
Correct answer: B — An investment approach that manages assets relative to liabilities rather than a market-cap benchmark — used by pension funds, insurers, and endowments where specific future obligations must be funded. The goal is to maximise surplus (assets − liabilities) or minimise the risk of funding shortfall
Explanation: B is correct. Liability-relative investing: traditional SAA maximises risk-adjusted return against a market benchmark. For pension funds, the 'liability' is the benchmark — assets should be managed to reduce funded status risk. LDI uses interest rate swaps and long bonds to hedge liability interest rate sensitivity. Equity can then be held in a return-seeking portfolio. A and C are asset-only approaches. D is too narrow.
Question 281
What is a hedge fund?
Select an option first.
Correct answer: B — A private investment vehicle that uses a range of strategies — including leverage, short selling, and derivatives — to generate absolute returns, typically accessible only to accredited investors
Explanation: B is correct. Hedge funds: private pools of capital using flexible strategies unavailable to mutual funds — leverage, short selling, illiquid assets, derivatives. They charge performance fees (typically 20% of profits above a hurdle) and management fees (typically 2% of AUM). A describes regulated vehicles with hedges. C and D are restricted investment strategies.
Question 282
What is the '2 and 20' fee structure in hedge funds?
Select an option first.
Correct answer: B — 2% annual management fee on assets under management and 20% performance fee on profits above a hurdle rate
Explanation: B is correct. '2 and 20' is the traditional hedge fund fee structure: (1) 2% management fee: charged on AUM annually regardless of performance; (2) 20% performance fee (incentive allocation): charged on profits above the hurdle rate or high-water mark. This aligns manager incentives with performance. A reverses the fees. C swaps them. D is incorrect.
Question 283
What is a 'high-water mark' in hedge fund performance fees?
Select an option first.
Correct answer: B — The previous peak NAV that the fund must exceed before it can charge performance fees — protects investors from paying fees on recovery of previously lost ground
Explanation: B is correct. High-water mark: if a fund falls from $100 to $80 NAV, the manager cannot charge performance fees until NAV recovers above $100 (the previous high-water mark). This prevents charging fees on simply recovering prior losses. A is about drawdown. C is the hurdle rate. D is a leverage constraint.
Question 284
What is a 'hurdle rate' in hedge fund performance fees?
Select an option first.
Correct answer: B — The minimum return a fund must earn before performance fees are charged — typically a risk-free rate or a fixed percentage
Explanation: B is correct. Hurdle rate: if the hurdle is LIBOR + 2% and the fund returns 15%, performance fees are charged only on the excess above the hurdle. Hard hurdle: fees only on returns above the hurdle. Soft hurdle: once the hurdle is cleared, fees apply to the entire return. A is a trading frequency requirement. C is a drawdown limit. D is a minimum AUM requirement.
Question 285
What is a 'lock-up period' in hedge funds?
Select an option first.
Correct answer: B — The minimum period after investing that an investor must wait before withdrawing capital
Explanation: B is correct. Lock-up period: typically 1-2 years, during which investors cannot redeem their shares. This allows managers to invest in illiquid assets without forced selling. After the lock-up, redemptions are typically allowed at quarterly or annual intervals with notice periods. A is not a standard hedge fund term. C is a soft close. D is settlement period.
Question 286
What is 'gate provision' in hedge funds?
Select an option first.
Correct answer: B — A restriction on the total amount that can be redeemed from the fund in any given period, typically expressed as a percentage of NAV (e.g., 20%)
Explanation: B is correct. Gate provisions (e.g., 20% quarterly gate): if redemption requests exceed the gate limit, each investor's redemption is pro-rated. This protects remaining investors from fire-sale liquidations during market stress. A is a minimum investment. C and D are different compliance requirements.
Question 287
What is a 'fund of funds' (FoF) in the context of hedge funds?
Select an option first.
Correct answer: B — A fund that allocates capital across multiple hedge funds, providing diversification but adding an additional layer of fees
Explanation: B is correct. FoF: diversifies across multiple hedge fund managers and strategies. Provides access to otherwise inaccessible funds with lower minimums. Disadvantage: double fee layer (FoF fee + underlying fund fees). AUM in FoF declined post-2008 due to fee transparency concerns. A is a direct fund. C is a liquid alternative. D is a PE fund of funds.
Question 288
What is 'global macro' as a hedge fund strategy?
Select an option first.
Correct answer: B — A strategy based on top-down analysis of macroeconomic trends, taking positions in currencies, interest rates, commodities, and equity indices across multiple countries
Explanation: B is correct. Global macro (e.g., George Soros, Bridgewater): trades based on views on global economies — e.g., shorting a currency expected to depreciate, buying bonds in a country expected to cut rates. Uses liquid instruments: futures, options, swaps, ETFs. A is equity-only. C is event-driven. D is a specific sub-strategy.
Question 289
What is 'managed futures' (CTA — Commodity Trading Adviser) as a strategy?
Select an option first.
Correct answer: B — A systematic or discretionary strategy that trades futures contracts across asset classes (commodities, currencies, rates, equities), typically trend-following
Explanation: B is correct. Managed futures/CTAs: primarily systematic trend-following — if an asset has been rising, go long; if falling, go short. Trades liquid exchange-traded futures across many markets. Often negatively correlated with equities in crashes, providing portfolio diversification. A is long-only commodity management. C is too narrow. D is a hedging strategy.
Question 290
What is 'relative value arbitrage' as a hedge fund strategy?
Select an option first.
Correct answer: B — Exploiting pricing discrepancies between related securities — buying the cheaper and shorting the more expensive — with minimal net market exposure
Explanation: B is correct. Relative value: profit from convergence of mispriced related securities. Examples: fixed income relative value (yield curve trades), convertible bond arbitrage, merger arbitrage. The paired nature of long/short positions eliminates most market risk. A is directional. C is country allocation. D is value investing.
Question 291
What is 'convertible bond arbitrage'?
Select an option first.
Correct answer: B — A strategy of buying convertible bonds (undervalued for their embedded equity option) and shorting the underlying stock to hedge the equity exposure, profiting from the option mispricing
Explanation: B is correct. Convertible arbitrage: convertible bonds embed a call option on the underlying stock. If the option is undervalued, buy the convertible and short the stock (delta hedge). Profit comes from the mispriced option premium as it converges to fair value. A conflates currency conversion. C is not arbitrage. D is cross-market arbitrage.
Question 292
What is 'merger arbitrage' (risk arbitrage)?
Select an option first.
Correct answer: B — A strategy of buying the stock of an acquisition target at a discount to the announced deal price, profiting if the merger completes, while risking a loss if the deal breaks
Explanation: B is correct. Merger arb: after a deal announcement, the target stock trades below the offer price (deal uncertainty discount). The arb buys at the discounted price and earns the spread upon completion. Risk: deal breaks — stock falls back to pre-announcement price. A is a regulatory risk. C is only one leg. D is incorrect.
Question 293
What is 'distressed debt' investing?
Select an option first.
Correct answer: B — Purchasing debt of companies in financial distress or bankruptcy at steep discounts, with the expectation that restructuring or recovery will return more than the purchase price
Explanation: B is correct. Distressed debt: investors buy bonds trading at 20-50 cents on the dollar during or approaching bankruptcy. In restructuring, bondholders may receive new equity or restructured debt worth more than the purchase price. Risk: the company liquidates and recovery is lower than expected. A is investment-grade. C is the borrower's perspective. D is short selling distressed debt.
Question 294
What is 'event-driven' as a hedge fund strategy category?
Select an option first.
Correct answer: B — A broad strategy that seeks to profit from specific corporate events — mergers, spin-offs, bankruptcies, earnings surprises — where the market may misprice securities before the event resolves
Explanation: B is correct. Event-driven: encompasses merger arb, distressed debt, activist investing, and special situations. The common thread is that a specific corporate catalyst will resolve an identified mispricing. A is reactive, not event-driven. C is technical analysis. D is global macro.
Question 295
What is 'activist investing'?
Select an option first.
Correct answer: B — Taking a significant stake in a company and using shareholder influence to push for changes — such as cost cuts, divestitures, board changes, or buybacks — that will increase shareholder value
Explanation: B is correct. Activist investors (e.g., Carl Icahn, Elliott Management) accumulate large stakes (often 5-10%) and publicly advocate for strategic changes. This is a form of event-driven investing where the investor creates the catalyst. A is passive. C is ESG investing. D is short activism (a related but different approach).
Question 296
What is 'private equity' as an asset class?
Select an option first.
Correct answer: B — Investment in companies that are not publicly traded — through venture capital (early stage), growth equity (expansion stage), or leveraged buyouts (mature companies), with the goal of improving operations and exiting at a profit
Explanation: B is correct. Private equity: long-term, illiquid investments in private companies. VC funds early-stage companies with high growth potential. Buyout funds acquire mature companies using leverage (LBO), improve efficiency, and exit via IPO or sale. Returns come from operational improvement, multiple expansion, and leverage. A is a different concept. C is index replication. D is a sovereign wealth vehicle.
Question 297
What is the 'J-curve effect' in private equity?
Select an option first.
Correct answer: B — The pattern of negative returns in early years (as capital is drawn down and fees are charged before investments mature) followed by positive returns in later years as portfolio companies are exited
Explanation: B is correct. J-curve: PE fund cash flows are negative in early years (capital called, fees paid, investments made) and positive in later years (exits generate returns). Net IRR appears negative initially before turning strongly positive. Important for LP cash flow planning. A is a yield curve. C and D are other PE concepts.
Question 298
What is a 'leveraged buyout' (LBO)?
Select an option first.
Correct answer: B — Acquiring a company primarily using borrowed money (debt), using the target company's assets and cash flows as collateral, with the goal of improving operations and exiting at a higher valuation
Explanation: B is correct. LBO: PE firm acquires a company with typically 60-80% debt and 20-40% equity. The target's free cash flow services the debt. Returns are amplified by leverage (equity return > total return) and operational improvements. A is an all-equity deal. C is a stock buyback. D is a minority investment.
Question 299
What is the 'vintage year' in private equity fund analysis?
Select an option first.
Correct answer: B — The year in which a PE fund makes its first capital call or first investment — used to compare funds across economic cycles
Explanation: B is correct. Vintage year classifies PE funds for performance comparison. Funds of the same vintage year faced the same macroeconomic environment, making comparisons more meaningful. Funds started at market peaks (e.g., 2007) generally performed worse than those started at troughs. A is exit year. C is investment period close. D is fundraising year.
Question 300
What is the 'IRR' (Internal Rate of Return) and why is it the primary PE performance metric?
Select an option first.
Correct answer: B — The discount rate that makes the net present value of all cash flows (capital calls and distributions) equal to zero — reflects both the timing and magnitude of cash flows
Explanation: B is correct. IRR: the time-weighted cost of capital that equates PV of outflows (calls) with PV of inflows (distributions). It is preferred in PE because it accounts for the irregular timing of capital calls and exits. A is an average return. C is a holding period return (NAV-based). D is the TVPI multiple.
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