Topic 5 · ~10% Know what each measure hides

Risk & Risk Management

Every risk measure is a summary, and every summary discards something. The exam tests whether you know what each one discards — and which risk it cannot see at all.

The VaR family

Value at risk answers one question: over a stated horizon and at a stated confidence level, what loss will not be exceeded? Three ways to compute it, each with a different failure mode.

Parametric
(delta-normal)
Assume normally distributed returns and linear exposures: VaR = −(μ + zασ)·V. Fast, analytic, aggregates easily. Fails on fat tails, negative skew and optionality — precisely the characteristics of alternatives. The Cornish–Fisher expansion adjusts the z-score for skewness and excess kurtosis and is the standard patch.
Historical simulation
Re-price the current portfolio using actual historical return vectors and read the empirical quantile. No distributional assumption and it preserves observed correlations and tail shape. Fails when the window omits a relevant regime; the tail rests on very few observations; estimates jump discontinuously as extreme days roll out of the window.
Monte Carlo
Simulate from an assumed stochastic process, revalue the portfolio in each path. Handles non-linearity, path dependency and complex derivatives. Its risk is model risk: the output can only be as good as the assumed process and correlation structure, and it is computationally heavy.

Scaling and interpretation. Under an i.i.d. assumption, VaR scales with √T — an assumption that fails when returns are serially correlated, which is exactly the case for smoothed alternative returns (there the true multi-period risk is higher than √T scaling suggests). Also be precise about what VaR is not: it is not a maximum loss, it says nothing about the size of losses beyond the threshold, and a 99% one-day VaR should be breached roughly two or three times a year — a model with zero exceptions is miscalibrated, not conservative.

Coherence, CVaR & higher moments

The four axioms of a coherent risk measure: monotonicity (a portfolio that always loses more is riskier), translation invariance (adding cash reduces risk by the amount of cash), positive homogeneity (doubling the position doubles the risk), and subadditivity (the risk of a combined portfolio cannot exceed the sum of the parts).

VaR fails subadditivity. For non-elliptical distributions — discrete default risk, options, credit portfolios — combining two positions can raise measured VaR, so VaR can penalise diversification and can be gamed by moving risk just beyond the confidence threshold. Conditional VaR (expected shortfall, expected tail loss) is the expected loss given that VaR is exceeded. It is coherent, it uses information from the whole tail, and it is convex — so mean-CVaR optimisation is a tractable linear program, whereas mean-VaR optimisation is non-convex and riddled with local optima. For fat-tailed alternative portfolios, CVaR is the better default.

Memory hook — MoTHS
Monotonicity, Translation invariance, Homogeneity, Subadditivity. VaR has the first three; only subadditivity is missing, and that single failure is why CVaR exists.

Higher moments. Skewness measures asymmetry — most alternative strategies that earn a premium are negatively skewed, because they are effectively selling insurance. Excess kurtosis measures tail fatness. Reporting a Sharpe ratio for a strategy with strong negative skew is misleading, since the denominator treats upside and downside deviation identically; use Sortino, a drawdown-based ratio, or an explicit tail measure alongside it.

Drawdown measures deserve their own note: maximum drawdown, time to recovery, and the Calmar ratio speak directly to the institution's real constraint — the point at which a board loses its nerve or a redemption is forced. They are path-dependent and sample-dependent, so a maximum drawdown from a short history understates the plausible worst case.

Decomposing portfolio risk

Total risk tells you nothing about where the risk comes from. Three decompositions, each answering a distinct question:

Marginal VaR
∂VaR/∂wi — the change in portfolio VaR for a small increase in position i. Answers: what does the next dollar cost me in risk? Used for trade sizing and for finding the risk-minimising portfolio (where all marginal VaRs are equal).
Component VaR
Marginal VaR × position value. These sum exactly to total VaR, so they answer: how is my existing risk distributed? This is the basis of risk budgeting — allocating a risk budget rather than a capital budget.
Incremental VaR
The exact change in VaR from adding or removing the entire position. Answers the full add/drop question; unlike marginal VaR it does not rely on a small-change approximation, so it is the right measure for a large trade.

Risk budgeting proceeds by setting a total risk budget, allocating it across strategies or factors by component contribution, and monitoring utilisation. Note the important structural point: capital weights and risk weights diverge dramatically once leverage and volatility differ across sleeves — a 5% allocation to a levered volatility strategy can consume 25% of the risk budget. Risk parity is the limiting case of budgeting: equalise every component's contribution.

Factor-based decomposition is usually more informative than asset-class decomposition, because it reveals that ostensibly different sleeves share a driver. The classic finding: an endowment portfolio spread across public equity, buyout, venture and opportunistic real estate has one dominant factor — equity risk — no matter how many boxes the allocation table contains.

Liquidity & counterparty risk

Two kinds of liquidity risk, and they correlate. Funding liquidity risk is the inability to meet obligations as they come due — margin calls, capital calls, redemptions, benefit payments. Market (asset) liquidity risk is the inability to transact size at a fair price, visible as bid-ask spread, market depth, and price impact. The spiral that matters: a price fall triggers margin calls (funding), forcing sales into a thin market (market), pushing prices down further. Model them jointly, never separately.

Measurement and management. Liquidity-adjusted VaR adds an explicit liquidation-cost term; time-to-liquidation analysis classifies the book into tiers (days / weeks / quarters / years); cash-flow stress tests project calls, distributions, spending and margin under adverse scenarios simultaneously. Management tools: liquidity budgets and floors, committed credit facilities, staggered fund terms, gates and side pockets at the fund level, and diversification of funding sources.

Counterparty risk. Exposure has two parts — current exposure (mark-to-market replacement cost today) and potential future exposure (how large it could become before maturity). Mitigants examined: netting agreements, collateral and CSAs with variation and initial margin, central clearing through a CCP, downgrade triggers, and limits on rehypothecation. Remember the two second-order effects: wrong-way risk, where exposure rises just as the counterparty's credit deteriorates (buying protection on a bank's affiliate), and the fact that collateralisation converts counterparty risk into liquidity risk, since variation margin must be funded in cash at short notice.

Prime broker risk for hedge funds specifically: asset segregation, rehypothecation rights, cross-margining, and the possibility that a PB failure freezes assets. Multiple prime brokers and clear custody arrangements are the standard mitigants — and are a core ODD question.

Operational & model risk

Operational risk is the risk of loss from inadequate or failed internal processes, people and systems, or from external events. It is the leading cause of catastrophic hedge fund failure — a larger share of fund closures trace to operational failure and fraud than to investment losses. Crucially, it is uncompensated: there is no risk premium for weak controls, so the only rational exposure is zero, which is why ODD carries a veto rather than a score.

Categories to be able to name: valuation and pricing errors; unauthorised trading and limit breaches; settlement and reconciliation failure; misappropriation of assets; inadequate segregation of duties; key-person dependency; cyber and business-continuity events; and regulatory or compliance breaches.

Model risk has three sources — the wrong model, the right model with wrong inputs, and the right model implemented incorrectly. In alternatives it appears in valuation of Level 3 assets, in risk models calibrated on benign samples, and in systematic strategies where the model is the product. Governance response: independent validation separate from the model's developers, documented assumptions and limitations, backtesting against realised outcomes, sensitivity analysis across plausible specifications, version control and change management, and pre-agreed criteria for switching a model off.

Exam trap
Compensated versus uncompensated risk is the organising distinction. Market, credit, illiquidity and volatility risks carry premia and belong in the portfolio in deliberate amounts. Operational risk, model risk and counterparty risk carry no premium — they are to be minimised, not budgeted. A question asking "which risk should the allocator accept in exchange for return?" is testing this.

Stress testing & scenario analysis

Statistical measures estimate risk from the sample. Stress testing asks what happens outside it, which is where institutions actually fail. Three approaches:

Historical scenarios
Replay 1987, 1998 (LTCM), 2008, the 2020 liquidity shock, 2022 rates and the UK gilt/LDI episode. Concrete and credible to boards; limited to shocks that have already happened.
Hypothetical scenarios
Construct internally coherent shocks — a rate spike with credit widening and a dollar rally. Requires judgement about which variables move together and by how much; the coherence of the scenario is the whole craft.
Reverse stress tests
Start from failure and work backwards: what combination of events would breach our covenant, exhaust our liquidity, or break the funded ratio? Often the most useful, because it surfaces exposures no forward scenario thought to include.

The correlation assumption is the point. In a crisis, correlations across risk assets converge toward one and diversification disappears exactly when it is needed. Stress tests should therefore impose elevated correlations rather than estimate them from history. Include second-round effects: forced deleveraging by other holders, redemption cascades in crowded strategies, funding-market closure, and the withdrawal of dealer balance sheet.

For alternatives specifically: stress must run on cash flows as well as marks. A scenario that produces a survivable mark-to-market loss can still be fatal if it simultaneously triggers capital calls, halts distributions, and increases margin — the combination that broke over-committed endowments in 2008–09.

The risk management process

Measures are the easy half. The exam also tests risk management as a governed process, because the failures it studies were governance failures with adequate models attached.

1. Identify
Enumerate exposures by risk type — market, credit, liquidity, counterparty, operational, model, legal, regulatory, reputational. Include risks that are not in the return series: key person, valuation, financing, concentration in a prime broker.
2. Measure
Quantify what can be quantified (VaR/CVaR, stress losses, exposure limits, liquidity coverage) and describe what cannot. Never let unmeasurable mean unmanaged.
3. Set appetite & limits
Translate the board's risk appetite into hard limits: notional and exposure caps, VaR/CVaR limits, drawdown triggers, liquidity coverage minimums, counterparty caps. Limits without a breach protocol are decoration.
4. Monitor & report
Independent risk reporting to the board, escalation on breach, and periodic review of the limits themselves. Frequency should match the liquidity of the exposure.
5. Respond
Reduce, hedge, transfer (insurance, derivatives, reinsurance), or accept with documented rationale. Every response has a cost — state it.

Three lines of defence. The business owns its risk; an independent risk and compliance function sets the framework and challenges the business; internal audit tests that both work. The critical exam point is independence: a risk officer who reports to the portfolio manager is not a second line. The same logic drives operational diligence's insistence that valuation and cash movement sit outside the investment team.

Leverage and financing risk deserve separate treatment because they convert a survivable loss into a terminal one. Distinguish balance-sheet leverage (borrowed capital), notional leverage (derivative exposure per unit of capital), and embedded leverage (options, structured notes, levered funds). Then examine the funding: term of the financing versus term of the asset, margin terms and the counterparty's discretion to raise them, rehypothecation rights, and cross-default clauses. A portfolio financed overnight against assets that take months to sell is one margin call from liquidation regardless of its VaR.

Confusion pairs

VaR vs CVaR
A threshold loss at a confidence level vs the average loss beyond it. VaR is not subadditive; CVaR is coherent and convex, so it can be optimised.
Marginal vs incremental VaR
Sensitivity to a small change in a position (use for the next trade) vs the total change from adding or removing the whole position.
Component VaR vs marginal VaR
Component = marginal × position size, and components sum to total VaR — that is what makes it the risk-budgeting measure.
Funding vs market liquidity
Can you meet calls and margin vs can you exit at a fair price. They correlate precisely when it hurts.
Historical vs Monte Carlo VaR
No distributional assumption but hostage to the sample window vs any distribution you like and hostage to the assumed process.
Stress test vs scenario analysis
Shock one or more factors to an extreme vs a coherent, internally consistent narrative across all factors. Reverse stress testing starts from the failure and works backwards.

Practice

Six multiple-choice questions in exam style, with the reasoning — not just the letter.

1. A portfolio has expected monthly return 0.8% and monthly volatility 3.0%. Using the parametric method and z = 1.65, the 95% one-month VaR as a percentage of value is closest to:

A. 3.0%
B. 4.1%
C. 4.9%
D. 5.8%
B. VaR = −(μ − zσ) = −(0.008 − 1.65 × 0.03) = 0.0415, or about 4.1%. Note the drift is subtracted, which lowers VaR; over short horizons many practitioners set μ = 0, which would give 4.95% — read the question for which convention is required.

2. Which property does VaR lack, and what is the practical consequence?

A. Monotonicity — VaR can rank a dominated portfolio as safer
B. Translation invariance — adding cash may not reduce VaR
C. Subadditivity — merging portfolios can increase measured risk, penalising diversification
D. Positive homogeneity — doubling positions may not double VaR
C. VaR satisfies the other three axioms. Subadditivity fails for non-elliptical distributions, so a diversified book can show higher VaR than the sum of its parts and risk can be hidden just beyond the confidence level. CVaR restores coherence.

3. A risk manager wants to know how much of current portfolio risk is attributable to the credit sleeve. The correct measure is:

A. Marginal VaR
B. Component VaR
C. Incremental VaR
D. Standalone VaR of the sleeve
B. Component VaR decomposes existing total risk into additive contributions. Marginal VaR answers the next-dollar question, incremental VaR the full add/drop question, and standalone VaR ignores diversification with the rest of the book entirely.

4. A fund's monthly returns show first-order autocorrelation of 0.35. Scaling monthly volatility by √12 to obtain annual volatility will most likely:

A. Overstate annual volatility
B. Understate annual volatility
C. Produce an unbiased estimate
D. Have no effect, since autocorrelation affects only the mean
B. √T scaling assumes independence. Positive serial correlation means shocks persist across periods, so true multi-period variance exceeds T times single-period variance. Positive autocorrelation in a supposedly liquid fund is also a stale-pricing red flag in its own right.

5. An institution buys credit protection on a corporate borrower from a bank that is itself heavily exposed to the same sector. This is best described as:

A. Basis risk
B. Wrong-way risk
C. Gap risk
D. Rollover risk
B. Wrong-way risk is when exposure to a counterparty rises at the same time as the counterparty's own creditworthiness deteriorates. The protection is worth most precisely when the seller is least able to pay. Mitigants: collateral, central clearing, and diversifying protection sellers.

6. Which risk should an allocator seek to minimise rather than budget for?

A. Illiquidity risk
B. Credit risk
C. Operational risk
D. Volatility risk
C. Illiquidity, credit and volatility risks carry premia and can be taken deliberately in exchange for expected return. Operational risk is uncompensated — there is no market payment for weak controls — which is why ODD holds a veto over allocation.

Constructed-response practice

Write these under time. Each outline is the shape the rubric rewards, not a model answer to memorise.

Prompt A (15 minutes). An endowment's risk report shows 99% one-month VaR of 4% of assets and describes the portfolio as "well diversified across nine asset classes". Critique the report and specify three additions you would require.

Outline:
  • Attack the measure: VaR says nothing about tail magnitude, is not coherent, and for a portfolio containing private assets is computed on smoothed inputs that understate volatility and correlation.
  • Attack the diversification claim: nine asset-class boxes with one dominant factor is concentration, not diversification — require factor decomposition and component risk contributions.
  • Addition 1: CVaR plus a de-smoothed input series, so tail losses and true correlations are visible.
  • Addition 2: a joint cash-flow and mark-to-market stress test covering spending, capital calls, and a drawdown occurring together (the denominator effect).
  • Addition 3: liquidity tiering with time-to-liquidation and a reverse stress test identifying what would breach the spending policy.
  • Close on governance: state who reviews it, at what frequency, and what action thresholds trigger a response.

Prompt B (12 minutes). Distinguish funding liquidity risk from market liquidity risk, explain how they interact in a crisis, and describe two structural mitigants an institutional allocator can put in place in advance.

Outline:
  • Define both precisely, with an example of each specific to an alternatives portfolio (margin call vs inability to exit a fund interest).
  • Describe the spiral explicitly as a feedback loop: price fall → margin call → forced sale into thin market → further price fall.
  • Mitigant 1: a liquidity budget with tiered time-to-liquidation and a committed credit facility arranged before it is needed.
  • Mitigant 2: structural — staggered fund maturities and diversified vintages, secondary-market relationships, and a deliberate over-commitment limit tested against a 2008-style scenario.
  • Note what each mitigant costs (cash drag, facility fees, forgone return) so the answer is a trade-off, not a wish list.
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