Models
Almost every question follows one pattern: identify the model, identify which of its assumptions the scenario breaks, and say what the analyst should do instead.
Three families of factor model
CAPM prices one factor. Its residuals turned out to be systematically related to firm characteristics, which is why every extension adds factors. Know which family a question is describing, because the estimation procedure and the failure mode differ.
(cross-sectional)
(macro / return-based)
(PCA)
Model selection logic for the exam: need interpretable attribution to a committee → fundamental. Need to replicate or benchmark a return stream → time-series. Need to compress a huge covariance matrix for risk estimation → statistical, with the caveat stated.
Alpha decomposition & benchmarking
Ex-ante vs ex-post. Ex-ante alpha is a genuine forward expectation of abnormal return, arising from skill or an exploitable inefficiency. Ex-post alpha is simply the intercept of a realised regression — it will be non-zero whenever the model omits a priced risk factor. The two are routinely conflated in marketing material, and separating them is a recurring exam task.
Beta expansion / alternative beta. Much of what hedge funds sold as alpha in the 1990s was reclassified as systematic exposure once the right factors were specified — merger-arbitrage's short deal-break put, trend-following's time-series momentum, carry trades' short-volatility profile. The practical consequence: a strategy's benchmark should include the factors it actually loads on, otherwise the manager is paid performance fees on beta.
Benchmark quality. A usable benchmark is specified in advance, unambiguous, investable, measurable, appropriate, reflective of current opinion, and owned by the manager. Alternative-investment benchmarks fail several of these routinely: peer-group indices are unopinable and biased; absolute-return targets ("cash + 5%") are unambiguous but carry no risk information; public-market proxies ignore leverage and illiquidity. For private markets, the defensible comparison is a public market equivalent that puts the same cash flows into an index (see the formula sheet), not an IRR-vs-index comparison.
Attribution. Distinguish allocation effect (weights differing from benchmark) from selection effect (security choice within a class) and interaction. For alternatives, add a timing component: because capital is called and returned at the GP's discretion, the LP's realised money-weighted return can diverge sharply from the fund's time-weighted return.
Structural credit models
The Merton insight. A levered firm's equity is a European call option on the firm's assets, struck at the face value of debt. If assets exceed debt at maturity, shareholders repay and keep the residual; if not, they hand over the firm. Equivalently, risky debt = risk-free debt − a put on the firm's assets. Default occurs when asset value falls below the default barrier.
Consequences worth memorising. Equity value rises with asset volatility (it is an option), which is the formal statement of the shareholder–bondholder conflict: increasing risk transfers value from creditors to owners. Credit spread widens with leverage and with asset volatility, and the model links the equity and credit markets — a jump in equity volatility should show up in spreads.
KMV/Moody's implementation. Asset value and asset volatility are unobservable, so they are inferred iteratively from observable equity value and equity volatility. Then compute distance to default — how many standard deviations the asset value sits above the default point (typically short-term debt plus half of long-term debt) — and map it to an empirical expected default frequency using a historical default database rather than the normal distribution.
Weaknesses to state. Because asset value follows a continuous diffusion, default is predictable: the firm can only default after drifting to the barrier, so very short-horizon spreads collapse to near zero — contradicted by observed short-dated spreads (the "credit spread puzzle"). There is no jump-to-default. Capital structures with covenants, multiple debt maturities and off-balance-sheet items are hard to represent. And it requires an observable equity price, which excludes private borrowers unless comparables are used.
Reduced-form credit models
The intensity approach. Default is not modelled as an economic event but as the first jump of a Poisson process with hazard rate (intensity) λ. Over a short interval, the probability of default is approximately λ·Δt; survival to time T is e−λT. Recovery is an assumption, usually a fraction of face or of market value.
The key relationship. To first order, the credit spread ≈ λ × (1 − recovery rate), i.e. the spread compensates for expected loss. Two consequences the exam tests: (a) λ and recovery cannot be separately identified from spreads alone — the same spread is consistent with high PD and high recovery or low PD and low recovery; (b) observed spreads exceed expected loss by a wide margin, and the excess is a default risk premium plus liquidity and tax components, not a pricing error.
Choosing between families. Structural when you have a balance sheet and want economic intuition or a private-borrower estimate; reduced-form when you must fit observed market prices exactly, price derivatives consistently, or handle entities with no meaningful asset value (sovereigns). Hybrid models make the intensity a function of firm fundamentals, aiming to capture both.
Portfolio credit risk adds default correlation, which is what turns a diversified pool into a systemic exposure. Copula approaches (notably the Gaussian copula) model the dependence structure separately from the marginals; their catastrophic failure in structured credit came from assuming a stable, low correlation parameter estimated in benign conditions. Know the lesson: in credit portfolios, the correlation assumption, not the individual PD, drives tranche risk.
Valuation & real options
DCF and its private-market variants. For cash-flowing assets, value is the present value of expected free cash flow at a risk-adjusted discount rate. In private markets the practical work is in the inputs: normalising EBITDA, choosing an exit multiple, and modelling the capital structure. Note that for a levered buyout, the return decomposes into EBITDA growth, multiple expansion, and deleveraging — and the exam likes to ask which portion is genuine value creation (growth and operational improvement) versus market beta (multiple expansion) or financial engineering (leverage).
Comparables and precedent transactions are fast but inherit the market's mispricing and require adjustment for size, growth, margin and control. A control premium applies when acquiring control; a marketability discount applies to illiquid minority stakes.
Real options. Where management has genuine flexibility, standard DCF understates value because it assumes a fixed plan. The main types: option to delay (natural resource projects, development land), to expand (staged venture financing), to abandon (a put on the salvage value), and to switch inputs or outputs (flexible power generation). The defining property: option value rises with volatility, which reverses the usual intuition that uncertainty destroys value. This is the analytical justification for staged venture investment — each round buys the option, not the obligation, to continue.
Cautions. Real-option valuation requires that the flexibility be real (management can and will act), that the underlying be reasonably tradable or at least estimable, and that the option not be duplicated by competitors, who can pre-empt a delay option. Applied loosely, it becomes a machine for justifying any price.
Term structure models
Vasicek. The short rate mean-reverts to a long-run level at speed κ with constant volatility σ. Tractable, produces closed-form bond prices, and generates realistic curve shapes. Its known flaw: with constant volatility, the process can produce negative rates — once considered a fatal defect, later a feature that matched observed markets.
Cox–Ingersoll–Ross. Same mean reversion, but volatility scales with √r, so volatility falls to zero as the rate approaches zero and the rate stays non-negative (given the Feller condition). More realistic conditional volatility behaviour; slightly less tractable.
Shared limitation. Both are one-factor models: all points on the curve are driven by the short rate, so the curve can only shift and twist in restricted ways, and they cannot fit an arbitrary observed curve exactly. Multi-factor and no-arbitrage models (Ho–Lee, Hull–White) are calibrated to fit today's curve exactly, which matters when the model is used to price derivatives rather than to forecast.
Why an alternatives candidate cares. Term-structure models feed the discount curve used in liability valuation for pensions and insurers, the pricing of structured products with embedded rate options, and scenario generation for asset-liability studies. The exam usually tests recognition — which model allows negative rates, which has state-dependent volatility, which fits today's curve by construction — rather than derivation.
Replication & model validation
Hedge fund replication asks whether a strategy's returns can be reproduced with liquid, cheap instruments. If they can, the manager's fee is buying beta you could rent. Three approaches:
Rolling and conditional betas. Static regression on a dynamic manager produces a meaningless average. Use rolling windows, or condition on a regime variable, to reveal exposure that switches — and remember that a manager who times beta well will look like an alpha generator in a static model and like a factor timer in a conditional one.
Validating any model — a repeatable four-part answer the exam accepts anywhere:
Confusion pairs
Practice
Six multiple-choice questions in exam style, with the reasoning — not just the letter.
1. A convertible-arbitrage fund shows a statistically significant positive intercept against a market-and-size model over 2012–2019. The most likely explanation is:
2. Under the Merton model, an increase in the volatility of firm assets, holding asset value constant, will:
3. A bond trades at a 300bp spread. Assuming a 40% recovery rate, the approximate risk-neutral annual default intensity is:
4. Which model characteristic prevents negative nominal short rates?
5. A buyout returns 2.5× over five years. Analysis shows EBITDA grew 20%, the exit multiple rose from 9× to 12×, and net debt fell by 40%. The strongest claim of value creation by the GP is:
6. An oil-sands project has negative NPV at the current spot price but management can delay development indefinitely. Standard DCF most likely:
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). A manager reports 4.2% annualised alpha against the S&P 500 over eight years for a systematic multi-strategy fund. Describe the analysis you would perform to determine whether this represents skill, and state what evidence would change your conclusion.
- Reject the single-factor benchmark immediately and say why: the fund's exposures are not the index's.
- Expand the factor set — size, value, momentum, carry, credit, term, volatility, trend — and re-estimate; report whether the intercept survives.
- Test for non-linearity: regress on option-like payoffs to detect a hidden short-volatility or short-put profile.
- Interrogate the data: backfill, survivorship, self-reporting, and serial correlation indicating stale marks; de-smooth and re-run.
- Assess statistical significance honestly — eight years of monthly data gives low power; adjust for multiple testing if many models were tried.
- State what would change your mind: a surviving intercept across specifications, out-of-sample persistence, and a coherent economic rationale tied to an identifiable edge.
Prompt B (12 minutes). Contrast structural and reduced-form credit models for valuing a portfolio of private middle-market loans. Recommend one, with justification, and identify the single largest source of model risk in your choice.
- Set out the two families in one sentence each — endogenous default from asset value vs exogenous default intensity calibrated to prices.
- Apply to the context: private borrowers have no traded equity and no traded debt, so neither family's natural input is observable.
- Recommend structural using comparable-company asset volatility and the borrower's actual capital structure, since the balance sheet is available and the loan is unquoted.
- Largest model risk: the asset-volatility proxy taken from listed comparables, which understates volatility for smaller, less diversified borrowers — plus default correlation across a sponsor-concentrated portfolio.
- Mitigation: sensitivity analysis across volatility assumptions, and stress the correlation parameter explicitly rather than estimating it from a benign sample.