Topic 6 · ~10% Allocation when the inputs are broken

Methods for Alternative Investing

Mean-variance optimisation assumes normality, a single period, known parameters and tradability. Alternatives violate all four. This topic is the catalogue of repairs.

Why MVO breaks on alternatives

Normality
Mean and variance fully describe a distribution only if it is normal. Alternative returns are negatively skewed and fat-tailed, so variance understates the risk that matters and the optimiser is blind to the exact loss profile the investor fears.
Single period
MVO optimises one period with no path dependency. Real institutions face intermediate drawdowns, spending, capital calls and the possibility of being forced to abandon the strategy — none of which appear in a one-period objective.
Known parameters
Inputs are estimated with error, and MVO is an error maximiser: it systematically overweights assets whose expected return is overestimated and whose correlation is underestimated. Small input changes produce wildly different, highly concentrated corner solutions.
Tradability
You cannot buy 12% of private equity today. You commit capital and receive an exposure that arrives over years and leaves on the GP's schedule — so the "weight" the optimiser outputs is not an instruction anyone can execute.

Add to these the input problem specific to alternatives: historical returns are smoothed, backfilled and survivorship-biased, so the raw inputs are not merely noisy but systematically flattering. Any answer that starts by fixing the inputs before fixing the optimiser is on the right track.

Robust allocation & Black–Litterman

Constraints. The crudest fix — minimum and maximum weights — works surprisingly well in practice because it prevents the optimiser from acting on estimation error. Its weakness is that the constraints, rather than the analysis, then determine the answer.

Shrinkage. Pull noisy sample estimates toward a structured target: expected returns toward the cross-sectional mean or toward equilibrium, covariance toward a single-factor or constant-correlation matrix. Shrinkage trades a small bias for a large reduction in variance and usually improves out-of-sample results.

Resampled efficiency (Michaud). Simulate many draws of the inputs consistent with estimation error, optimise each, and average the resulting weights. Produces smoother, more diversified, more stable allocations. Critiques: no clean theoretical foundation, results depend on the simulation design, and averaging can produce a portfolio that is optimal for no single scenario.

Black–Litterman. The most examinable repair. Two ideas combined:

1 — Start from equilibrium. Rather than forecasting returns, reverse-optimise the market-capitalisation portfolio to infer the expected returns that would make it optimal (Π = λΣwmkt). This becomes the neutral prior, so with no views the model returns the market portfolio — a sensible default that plain MVO never gives you.

2 — Blend in views with explicit confidence. The investor states absolute or relative views (P, Q) with an uncertainty matrix (Ω). The posterior expected returns are a precision-weighted blend of prior and views: a high-confidence view moves the allocation a lot, a low-confidence view barely at all, and every unexpressed asset stays at equilibrium.

Why it matters for alternatives: equilibrium market weights are hard to observe for private assets, so the neutral prior must be constructed judgementally — which is both the model's main practical limitation here and a good point to raise in an essay.

Risk parity & factor allocation

Risk parity equalises each asset's contribution to total portfolio risk rather than its share of capital. The motivation: a conventional 60/40 portfolio has roughly 90% of its risk in equities, so it is not diversified in any economically meaningful sense. Weights end up inversely related to volatility (and to correlation), which loads heavily on bonds; to reach an equity-like expected return the portfolio must be levered.

Critiques to have ready: it assumes leverage is available cheaply and continuously (funding risk); it implicitly assumes similar Sharpe ratios across assets, since it ignores expected returns entirely; its historical record is flattered by a four-decade bond bull market; and a rate shock hits both the bond sleeve and the leverage cost at once, as 2022 demonstrated.

Factor-based allocation goes further, allocating to underlying drivers — growth, real rates, inflation, credit, liquidity, and style premia such as value, momentum, carry and trend — rather than to asset-class labels. Advantages: it exposes double-counting (buyout and public equity load on the same factor), it makes risk contributions comparable across public and private sleeves, and it aligns the portfolio with the economic scenarios the institution actually cares about. Difficulties: factor definitions are not standardised, factor exposures of private assets must be estimated from lagged and smoothed data, and boards find factor language harder to govern than asset-class buckets.

Mean-CVaR optimisation belongs here too: replace variance with conditional VaR in the objective. It targets the left tail directly, is convex and therefore solvable as a linear program, and produces allocations that differ meaningfully from MVO whenever skewness is present — which for alternatives is always.

Stale pricing & unsmoothing

The mechanism. Private real estate and private equity are valued by appraisal or by model, not by transaction. Appraisers anchor on prior valuations and on comparable transactions that are themselves lagged, so reported returns are a weighted average of current and past true returns. The statistical signature is strong positive first-order autocorrelation.

The three consequences — memorise them as a set, because questions rarely ask for only one:

Volatility understated
Averaging suppresses period-to-period variation.
Correlation understated
The lagged series does not line up with contemporaneous public returns.
Sharpe overstated
Same numerator, artificially small denominator — and the optimiser over-allocates.

The repair. Un-smoothing (the Geltner / Fisher–Geltner–Webb approach) inverts the smoothing filter: if reported return rt = α·rt−1 + (1−α)·r*t, then the implied true return is r*t = (rt − α·rt−1) / (1 − α), where α is estimated as the first-order autocorrelation. The unsmoothed series has the same mean but a materially higher volatility and higher correlation with public markets. Always de-smooth before computing risk statistics or running an optimiser; note that unsmoothing corrects second moments, it does not correct a biased mean.

Related biases in alternative indices that must be adjusted alongside: survivorship (failed funds leave the index), backfill / instant history (a manager joins a database and contributes a favourable track record retroactively), and self-selection (reporting is voluntary in both directions — poor performers stop, closed stars never start).

Commitment pacing & the J-curve

Commitments are not allocations. A $100m commitment produces an average NAV far below $100m over the fund's life, because capital is drawn down over an investment period while earlier investments are already being distributed. To hold a target NAV exposure, an institution must maintain a rolling programme and commit more than the target — the over-commitment ratio — which is exactly where the risk sits.

The J-curve. Early years show negative returns: management fees are charged on committed capital, no value has yet been created, and conservative marks prevail. Value accrues later, and the curve turns up. Consequences: IRR in the first three years is meaningless as a skill signal; and vintage-year diversification is required so that a programme is not entirely in its J-curve phase at once. Secondaries and co-investments shorten the curve because capital is deployed into seasoned assets immediately.

Pacing models. The standard framework (Takahashi–Alexander) projects, period by period: capital calls as a declining rate applied to remaining uncalled commitment; distributions as a rate applied to NAV that rises with fund age (typically a power function of the fraction of fund life elapsed); and NAV evolving as prior NAV plus calls plus growth minus distributions. Feed several vintages through it and you get a projected exposure path against which annual commitment sizing can be set. The model's sensitivities — call speed, distribution timing, growth rate — are the honest place to stress it.

Cash-flow measures to keep straight: DPI (distributions ÷ paid-in) is realised return; RVPI (residual value ÷ paid-in) is unrealised; TVPI = DPI + RVPI is the total multiple. IRR adds a time dimension but is sensitive to the timing of early distributions and is not additive across funds. Report both, always.

Rebalancing & the denominator effect

Rebalancing policy comes in three forms: calendar (simple, predictable, may trade unnecessarily), percentage-range or corridor (trades only when a band is breached; corridors should be wider for illiquid and high-transaction-cost assets), and a hybrid that checks bands on a schedule. Rebalancing is implicitly a short-volatility, contrarian strategy: it sells what rose and buys what fell, which earns a rebalancing premium in mean-reverting markets and loses in strongly trending ones.

The denominator effect. When public markets fall sharply, private NAVs lag — both because of appraisal smoothing and because valuations are struck quarterly. The private allocation, as a percentage of a shrunken total portfolio, mechanically overshoots its policy range without a single private-market transaction. The institution then faces unattractive choices: breach the policy range, sell secondaries at a discount into a buyers' market, slow or stop new commitments (which damages vintage diversification precisely when vintages are most attractive), or sell liquid assets at depressed prices.

Exam trap
The denominator effect is not a valuation error to be corrected — it is a governance problem to be anticipated. The examinable answer is prevention: wide policy ranges for illiquid classes stated in the IPS, a liquidity budget stress-tested against a 2008-magnitude drawdown, and a pre-agreed protocol for what happens when a range is breached, decided before the market falls rather than during it.

Rebalancing in the presence of illiquid assets is therefore mostly done with the liquid sleeve — using the public book to offset unwanted exposure created by private-market drift, or using derivatives overlays to restore target beta cheaply while the private position self-corrects over the following quarters.

Portable alpha & overlays

The idea. Separate the decision about market exposure from the decision about skill. Obtain beta cheaply and capital-efficiently through futures or total return swaps, and deploy the freed capital in a diversifying alpha source. A plan wanting equity beta plus a market-neutral manager holds equity futures on a margin deposit and puts the rest with the manager — the alpha is "ported" onto the beta.

What makes it work
The alpha source must be genuinely uncorrelated with the ported beta, and it must be liquid enough to fund margin calls on the overlay.
How it fails
The classic failure is a liquidity spiral: the beta overlay loses, margin is called, and the alpha sleeve cannot be liquidated to meet it — so the plan is forced to unwind the overlay at the worst moment. Correlation between the alpha and the beta rising in stress makes it worse.
Governance
Requires derivatives authority in the IPS, collateral management capability, counterparty limits, and reporting that shows the true (levered) exposure rather than the capital allocated.

Overlays more broadly are how a large owner manages a portfolio it cannot trade. A rebalancing overlay uses futures to restore target exposure without selling illiquid assets. A currency overlay separates the hedging decision from the manager's security selection — hedge ratio, hedging instrument and rebalancing frequency become policy decisions. A completion portfolio fills the gap between the aggregate of the managers' actual exposures and the policy portfolio, neutralising unintended factor tilts.

Capital efficiency is the underlying theme. The exam's framing: the constraint is not capital but risk, and derivatives let an owner allocate risk and capital separately. The cost is operational complexity, counterparty exposure, basis risk between the derivative and the asset, and the discipline to hold enough liquidity to survive the margin path — not just the terminal outcome.

Confusion pairs

IRR vs TVPI/MOIC
Time-weighted on cash flows and manipulable by delaying the call vs a simple multiple that ignores time. Read them together; use PME to compare against public markets.
Commitment vs allocation
What you promised vs what is invested. Over-commitment is required to hold a target exposure — that is what pacing models size.
Risk parity vs equal weight
Equalised risk contributions (needs leverage and a covariance estimate) vs equalised capital.
Black–Litterman vs resampling
Blend equilibrium returns with confidence-weighted views vs average optimal portfolios across simulated input draws. Both attack estimation error, differently.
Smoothing vs unsmoothing
Appraisal lags suppress volatility and correlation; unsmoothing removes the autocorrelation and restores both — lowering the apparent Sharpe ratio.
Denominator vs numerator effect
Private weight rises because the public book fell vs private NAV itself rose. Same overshoot, opposite cause, different remedy.

Practice

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

1. Mean-variance optimisation is described as an "error maximiser" because it:

A. Maximises tracking error against the policy benchmark
B. Overweights assets whose expected returns are overestimated and correlations underestimated
C. Requires normally distributed returns
D. Cannot accommodate constraints
B. The optimiser treats estimates as certainties, so estimation error is precisely what it exploits — the assets that look best are usually those with the most favourable errors. The normality assumption (C) is a separate, real limitation.

2. In the Black–Litterman model, the neutral starting point for expected returns is obtained by:

A. Averaging historical returns over the longest available sample
B. Reverse-optimising market-capitalisation weights
C. Setting all expected returns equal to the risk-free rate
D. Shrinking the covariance matrix toward a single-factor structure
B. Equilibrium returns Π = λΣwmkt are the returns implied by the market portfolio being optimal. This is why, absent views, Black–Litterman returns the market portfolio rather than an extreme corner solution.

3. A reported private real estate series has first-order autocorrelation of 0.40. After unsmoothing, the series will most likely show:

A. Higher mean return and unchanged volatility
B. Similar mean return, higher volatility, higher correlation with equities
C. Lower volatility and lower correlation with equities
D. Higher Sharpe ratio
B. Unsmoothing corrects second moments, not the mean. Volatility and public-market correlation both rise, so the Sharpe ratio falls and the apparent diversification benefit shrinks — the reason de-smoothing must precede optimisation.

4. An institution wants a 15% NAV exposure to buyout funds in steady state. Relative to that target, annual commitments should be:

A. Equal to the target, since commitments equal exposure
B. Set so cumulative commitments exceed the target NAV, because capital is called and returned over time
C. Set below the target to avoid over-commitment
D. Made in a single vintage to maximise pacing efficiency
B. Because a commitment is only partially drawn at any moment and distributions return capital continuously, sustaining a target NAV requires an over-commitment supported by a pacing model. D is wrong: concentrating in one vintage destroys vintage-year diversification, one of the few free lunches in private markets.

5. Public equities fall 30% while private equity NAVs are unchanged for two quarters. The private allocation rises above its policy range. The best pre-planned response is:

A. Sell fund interests immediately to restore the range
B. Halt all new commitments until the range is restored
C. Rely on wide policy ranges and a pre-agreed breach protocol set out in the IPS
D. Reclassify private equity as a liquid asset
C. Forced secondary sales crystallise a discount (A) and halting commitments abandons what are often the strongest vintages (B). The examinable point is that this is anticipated in advance through range width, liquidity budgeting and a written protocol.

6. A fund reports TVPI of 1.8× with DPI of 0.4×. This indicates:

A. Most value is realised and returned to LPs
B. Most value remains unrealised in carrying NAV, so the multiple depends on valuation policy
C. The fund has generated a negative IRR
D. The fund is fully liquidated
B. RVPI = TVPI − DPI = 1.4×, so roughly 78% of the reported multiple is unrealised marks. Diligence should focus on valuation methodology and on whether comparable multiples used for marks are current. Nothing here determines IRR sign (C).

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 consultant presents an efficient frontier showing a 40% allocation to private real estate. Identify three reasons the result is unreliable, describe the corrections you would apply, and state how you expect the corrected allocation to differ.

Outline:
  • Reason 1 — smoothed inputs: appraisal-based returns understate volatility and correlation, inflating the asset's apparent Sharpe ratio. Correction: de-smooth using the estimated autocorrelation, then re-optimise.
  • Reason 2 — estimation error and corner solutions: MVO maximises error. Correction: shrinkage or Black–Litterman equilibrium prior, plus sensible constraints.
  • Reason 3 — tradability and path: the optimiser assumes the weight can be bought and held; in reality it must be built through commitments and cannot be rebalanced downward on demand. Correction: pacing model and a liquidity-budget constraint.
  • Expected effect: the corrected allocation is materially smaller and the frontier flatter, because the risk was always there — it was hidden in the valuation method.
  • Add the governance point: express the result as a range with a breach protocol, not a point estimate.

Prompt B (12 minutes). Explain the J-curve, why an institution must over-commit to reach a target private-markets exposure, and two risks that over-commitment creates. Recommend how each risk should be controlled.

Outline:
  • Define the J-curve mechanically — fees and conservative marks first, value later — and note the implication that early IRRs are uninformative.
  • Explain the exposure arithmetic: commitments are drawn slowly and returned continuously, so average NAV is a fraction of committed capital.
  • Risk 1 — a market drawdown coinciding with accelerating calls and halted distributions (the 2008 pattern). Control: liquidity budget stress-tested jointly, plus a committed credit facility.
  • Risk 2 — the denominator effect pushing the allocation through its policy range. Control: wide IPS ranges for illiquid classes and a written breach protocol.
  • Close on the pacing model: state its three key sensitivities (call rate, distribution timing, growth) and that commitments should be re-sized annually against the projected exposure path.
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