Book: Hedge Funds: Insights in Performance Measurement, Risk Analysis, and Portfolio Allocation
Author: Edited by Greg N. Gregoriou, Georges Hübner, Nicolas Papageorgiou and Fabrice Rouah
Difficulty: Advanced
The Big Idea
A quiet return series can hide a dangerous investment. To judge a hedge fund, ask what generates its gains, which losses its record may conceal, whether valuations are timely, and whether the investor can actually implement the proposed allocation.
This edited research collection approaches those questions from several directions: allocation, index construction, incentives, performance measurement, statistical risk and structured products. Its chapters sometimes reach different conclusions because their data, models and questions differ. The useful skill is learning to compare those assumptions.
This is an independent reading companion with original exercises for all 29 substantive chapters. Keep the book beside you: the assignments ask you to inspect its methods, tables and qualifications. These lessons do not reproduce its studies, original tables or complete mathematical derivations.
Contents
- Quick revision sheet
- How to use this companion
- Seven flexible study blocks
- Complete chapter map
- Part I: portfolio allocation, Chapters 1–7
- Part II: management, Chapters 8–12
- Part III: risk and performance, Chapters 13–20
- Part IV: statistical properties, Chapters 21–27
- Part V: special classes, Chapters 28–29
- Reconciling conflicting research findings
- Pine indicator and observation lab
- Four reusable worksheets
- Capstone and assessment rubric
- Technical and current-context references
- Final Takeaway
Quick Revision Sheet
Use this after reading, then return to the linked lesson whenever you cannot explain a qualification in your own words. Every formula below uses consistent units and a stated observation horizon.
| Concept | Working definition or formula | Mistake to avoid |
|---|---|---|
| Diversification | Portfolio variance depends on weights, individual variances and covariances. Tail behavior also depends on how extreme outcomes occur together. | Assuming more funds necessarily eliminate a shared liquidity shock. |
| Alpha and beta | Excess fund return = alpha + Σ(beta × factor return) + residual. Alpha is conditional on the specification. | Equating every unexplained return with skill. |
| Tracking error | Standard deviation of active returns, where active return = portfolio return − benchmark return. Report its mean separately. | Calling high correlation or low active-return volatility an exact replica. |
| Net return | End wealth after the actual fee waterfall, divided by starting wealth, minus 1; handle external cash flows appropriately. | Subtracting a performance-fee percentage directly from gross return. |
| Drawdown | At time t: 1 − wealth(t)/highest prior-or-current wealth. Maximum drawdown is the largest such percentage over the chosen record. | Ignoring record length, the starting peak or recovery duration. |
| Survivorship bias | Difference arising from retaining survivors and omitting relevant nonsurvivors; its numerical size depends on the comparison. | Assuming a reporting exit always means fund failure. |
| Certainty equivalent | Wealth level with utility equal to expected utility of the risky wealth distribution; depends on preferences and scenario probabilities. | Treating a preference-sensitive number as a universal ranking. |
| VaR versus expected shortfall | For positive losses, VaR is a loss quantile at a stated confidence and horizon. Expected shortfall averages the worst tail fraction, with boundary handling for discrete samples. | Calling VaR the worst possible loss or using an unstated quantile convention. |
| Skewness and kurtosis | Skewness = E[(r−μ)³]/σ³. Pearson kurtosis = E[(r−μ)⁴]/σ⁴; excess kurtosis subtracts 3. Finite-sample estimators differ. | Mixing Pearson kurtosis (normal = 3) with excess kurtosis (normal = 0). |
| Stale pricing | A mark that inadequately reflects information relevant to current value can delay recognition of economic gains or losses. | Inferring either safety or fraud from smooth returns alone. |
Five formulas to keep beside the book
| Calculation | Formula | Assumption or limit |
|---|---|---|
| Compounded wealth | W(T) = W(0) × ∏[1 + r(t)] | No external cash flows; use simple returns consistently. Arithmetic average is not compound growth. |
| Sharpe ratio | Mean of (r − rf) / standard deviation of (r − rf) | Same frequency throughout. Multiplying a periodic ratio by √periods/year requires restrictive dependence assumptions. |
| Zero-target downside deviation | √{average[min(r, 0)²]} | This uses all N observations. It differs from standard deviation calculated only among negative observations. |
| Linear one-factor shock estimate | Portfolio allocation × estimated beta × factor shock | Local approximation; omits nonlinear exposure, other factors, financing changes and uncertainty. |
| Recovery after loss L | Required gain = L/(1−L) | L is a positive decimal drawdown less than 1; a 20% loss requires a 25% gain. |
How to Use This Companion
The supplied volume is Wiley’s 2005 collection, ISBN 9780471737438. The names in the opening are the editors; individual chapter authors are credited below. Page assignments use the printed page numbers in the book, not the PDF viewer’s page count. Blank pages, part introductions, references and the index explain gaps between assignments.
For each chapter, read the assigned pages, write down the objective, work the original example, then answer the exercise before expanding its answer key. Finish by locating one supporting passage or table in the book and recording a limitation the short lesson cannot settle. You need basic return arithmetic, probability, regression and a spreadsheet; revisit the revision sheet when notation gets in the way.
Study samples, fee surveys, industry sizes and regulation in this collection belong to its publication period. Historical optimizer weights are not current allocation advice. The chapters are not a single unified experiment.
All fictional numbers, exercises, worksheets, the capstone and indicator rules here are original teaching devices. They are not reported fund results or a reproduction of the authors’ empirical work.
A technical reading routine
- Define the object: individual fund, manager, index, fund of funds or structured claim.
- Find the information date: when was the NAV, ranking or factor actually available?
- Follow the transformation: excess return, unsmoothing, factor adjustment or optimization.
- Inspect feasibility: access, weights, notice, lockups, costs and cash requirements.
- State the inference: describe what the evidence supports, its uncertainty and what would change the conclusion.
Seven Flexible Study Blocks
These are blocks of work, not seven promised days. Several research chapters may take multiple sittings. Move on when you can explain the result and its assumptions without copying the text.
| Block | Read | Produce before moving on |
|---|---|---|
| 1 — Portfolio role | Chapters 1–3 | One comparison of direct and delegated exposure, plus a joint stress calculation. |
| 2 — Allocation assumptions | Chapters 4–7 | A dated exposure record, a locked-position calculation and a screening-score critique. |
| 3 — Product and manager design | Chapters 8–12 | A tracking diagnostic, explicit fee waterfall, loss waterfall and two drawdown paths. |
| 4 — Evidence and persistence | Chapters 13–17 | A bias audit and a timeline showing what a selection rule could know before investing. |
| 5 — Competing performance measures | Chapters 18–20 | A peer-set sensitivity check, a factor-proxy critique and a certainty-equivalent calculation. |
| 6 — Distribution and regime risk | Chapters 21–27 | A tail-sensitivity memo and one completed chart-observation worksheet. |
| 7 — Structures and valuation | Chapters 28–29, then cross-chapter review | A principal-protection gap calculation, valuation challenge and final capstone memo. |
Complete Chapter Map
Part I: Portfolio Allocation
Chapter 1: Integrating Hedge Funds into the Traditional Portfolio
Read: printed pp. 3–16. Chapter author(s): Harry M. Kat.
Learning objective: Separate a reduction in ordinary volatility from a reduction in crash exposure.
Work through the idea
Kat challenges the idea that a better mean–variance profile necessarily means a safer portfolio. A sleeve can reduce routine fluctuations while retaining losses during a shared funding shock. Adding managers may diversify security-specific noise faster than it removes a common exposure to liquidity or credit conditions.
Original worked example
Our fictional portfolio holds 70% in a traditional sleeve and 30% in a hedge fund sleeve. In one stress month they lose 10% and 8%, respectively. The portfolio loses 0.70 × 10% + 0.30 × 8% = 9.4%. The hedge fund sleeve softens this particular loss; it does not remove it.
A payoff resembling an option is an economic analogy. It does not prove that the fund actually holds that option or that its protection will work on every path.
Workbook exercise 1
Replace the hedge fund sleeve with a hypothetical managed-futures sleeve returning +6% in the same month. Calculate the portfolio return. Explain why this single scenario cannot establish reliable crash protection.
Show the explained answer — Chapter 1
The return is 0.70 × (−10%) + 0.30 × 6% = −5.2%. That is 4.2 percentage points better in this invented scenario. A different path could whipsaw the futures sleeve or produce losses in both sleeves. One chosen month says nothing about the probability of that favorable outcome.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 2: Hedge Funds from the Institutional Investor’s Perspective
Read: printed pp. 17–50. Chapter author(s): Noël Amenc, Felix Goltz and Lionel Martellini.
Learning objective: Connect allocation, benchmark choice and an investable implementation.
Work through the idea
The authors distinguish strategic exposure from active management and discuss the tension between representative indexes and investable products. An index may describe a broad universe while containing closed funds or terms an investor cannot obtain. Conversely, an accessible selection may poorly represent the universe. Their diversification findings must be read alongside Chapter 1 rather than treated as a universal rebuttal of it.
Original worked example
Our fictional fund earns 9%. A stated factor model attributes 5 percentage points to market exposure and 2 points to other compensated exposures. The remaining 2 points are a model residual in average performance, not independently proven managerial skill. If an omitted factor explains 1.5 points, the unexplained amount falls to 0.5 point.
The chapter’s favorable historical higher-moment findings and Chapter 1’s warnings use different empirical constructions. Compare periods, indexes, constraints and risk definitions before deciding that the authors disagree about the same experiment.
Workbook exercise 2
A replica has correlation 1 with an index because its returns equal twice the index return. If the index earns 1% in a month, what is the replica’s active return? Does perfect correlation establish accurate tracking?
Show the explained answer — Chapter 2
The replica earns 2%, giving active return of +1 percentage point. Perfect correlation measures linear co-movement, not equality of levels, volatility or mean returns. Inspect beta, active-return bias and tracking error as well as correlation.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 3: Funds of Hedge Funds versus Portfolios of Hedge Funds: A Comparative Analysis
Read: printed pp. 51–82. Chapter author(s): Daniel Capocci and Valérie Nevolo.
Learning objective: Design a fair build-versus-buy comparison without choosing winners in hindsight.
Work through the idea
The chapter ranks funds using prior returns, forms decile portfolios and compares their subsequent performance with funds of funds. Its results vary between directional and nondirectional groups; simply buying the previous winners is not a general solution. An investor also needs to price the work a fund of funds performs: sourcing, access, monitoring and operational review.
Original worked example
Our do-it-yourself basket earns 7% after underlying fund fees but before a separate 0.6% monitoring budget. Its simplified net return is 6.4%. A fund-of-funds product earns 6.2% after every fee. The apparent direct-investment advantage is only 0.2 percentage point before accounting for access differences and unrecorded liquidation costs.
Where the text associates outperformance with a negative intercept, inspect the displayed regression orientation. For fund return regressed on benchmark return, a positive intercept is the favorable direction, conditional on the model.
Workbook exercise 3
A researcher forms the 2001 portfolio using full-year 2001 returns and reports its 2001 result. Identify the timing error and give a permissible alternative.
Show the explained answer — Chapter 3
The portfolio uses information unavailable at the start of 2001. Rank eligible funds using information actually available before formation, such as a published 2000 record, then measure subsequent returns. Include reporting delays, closed funds, redemptions and funds that later disappear.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 4: Analyzing Style Drift in Hedge Funds
Read: printed pp. 83–104. Chapter author(s): Nolke Posthuma and Pieter Jelle Van der Sluis.
Learning objective: Distinguish a changing exposure estimate from evidence available in real time.
Work through the idea
A strategy label can remain unchanged while its market, size or credit exposure moves. The authors model time-varying betas with a state-space approach and a Kalman filter. This replaces a fixed rolling window with explicit assumptions about how exposures evolve; it does not eliminate model risk. Filtering uses information available up to the estimate date, while smoothing also uses later observations.
Original worked example
Our fictional sleeve has an estimated equity beta of 0.20 at one review and 0.65 later. On a $4 million allocation, a small −10% equity shock gives linear estimates of −$80,000 and −$260,000, respectively. This is a $180,000 difference before other exposures, nonlinear effects or estimation error.
A low model R² can reflect omitted factors, noise or pricing problems. It is not automatic evidence of active skill. Uncorrelated regression residuals are not necessarily independent or normally distributed.
Technical bridge: one scalar Kalman update
In a simple state-space measurement, predict exposure β with uncertainty P. For observation y = Fβ + noise with noise variance R, the scalar gain is K = PF/(F²P + R), and the update is β(new) = β(predicted) + K[y − Fβ(predicted)]. The state’s process uncertainty is added in the prediction step.
Our arithmetic illustration uses F = 1, P = 0.04 and R = 0.01. Then K = 0.8. A predicted exposure 0.30 and observation 0.50 yield 0.30 + 0.8 × 0.20 = 0.46. This toy observation is in exposure units, not a literal fund return. A multifactor return model needs the appropriate matrices, parameter estimation and diagnostics; a filter is not assumption-free.
Workbook exercise 4
A smoothed beta for March was calculated using data through December. Can it support a March allocation decision? What version should the researcher retain?
Show the explained answer — Chapter 4
No. December information was unavailable in March. Retain the contemporaneous filtered estimate, its uncertainty and the version of the data then available. Use the smoothed series for retrospective diagnosis and label it accordingly.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 5: Hedge Fund Allocation under Higher Moments and Illiquidity
Read: printed pp. 105–128. Chapter author(s): Niclas Hagelin, Bengt Pramborg and Fredrik Stenberg.
Learning objective: Account separately for valuation smoothing and restrictions on rebalancing.
Work through the idea
This study compares dynamic allocations under mean–variance and power-utility objectives, then changes assumptions about return smoothing and lockups. Its central implementation lesson is that the portfolio an optimizer requests may differ from the one the investor can actually hold. Unsmoothing changes an estimated return process; a lockup changes the feasible decision set.
Original worked example
Our $1 million portfolio contains $400,000 in a locked sleeve. After that sleeve loses 20% and everything else is flat, total value is $920,000 and the sleeve is worth $320,000, or 34.78%. An optimizer’s new 10% target would require reducing it to $92,000, a $228,000 redemption that the contract may prevent.
The study’s historical index allocations are outputs of its model and sample. They are not recommended portfolio weights. An assumed fixed bias adjustment or unsmoothing coefficient is a sensitivity assumption, not an observed truth.
Workbook exercise 5
If the locked sleeve instead rises 10%, calculate its new weight. Explain why buying more liquid assets is not the same as redeeming the locked position.
Show the explained answer — Chapter 5
Its value is $440,000 and total wealth is $1,040,000, so the weight is 42.31%. Without new capital, reallocating the remaining liquid assets does not reduce the dollar value of the locked sleeve. The original optimization needs feasible holdings and cash constraints.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 6: Revisiting the Role of Hedge Funds in Diversified Portfolios
Read: printed pp. 129–150. Chapter author(s): Jean Brunel.
Learning objective: Classify economic risks rather than treating every hedge fund as one asset class.
Work through the idea
Brunel separates broad strategy roles and emphasizes manager risk, nonnormal returns and the investor’s ability to stay with an allocation during losses. A sleeve with bondlike reported volatility may still have credit, leverage or liquidity risks unlike a conventional bond allocation. His alternative scoring objective also makes the investor’s preferences consequential.
Original worked example
Our fictional allocation has a $100,000 capital base and a policy limit of 15% loss under a joint stress. A proposed mix has excellent ordinary volatility but loses $19,000 in the chosen stress. It fails this policy condition even if a mean–variance optimizer ranks it first.
Market-environment partitions assembled using realized returns are retrospective diagnostics. They cannot demonstrate that an investor could identify the next environment in advance.
Workbook exercise 6
A score adds return measured as 0.08 to skewness measured as −1.2. What is missing before the result can guide a decision?
Show the explained answer — Chapter 6
The score needs explicit scaling and preference weights. These terms have different meanings and magnitudes; an arbitrary unit choice can dominate the ranking. Document the weights, test alternatives and assess whether the selected portfolios satisfy independent liquidity and loss limits.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 7: Hedge Fund Selection: A Synthetic Desirability Index
Read: printed pp. 151–162. Chapter author(s): Jean-Pierre Langevin.
Learning objective: Use a combined screening score without mistaking it for portfolio optimization.
Work through the idea
The D-Index combines a preference transformation of correlation with a transformation of the candidate’s risk-adjusted-return advantage. A modest stand-alone score can coexist with useful portfolio diversification. The index is a screening device: it does not encode every constraint, tail dependence or allocation weight.
Original worked example
Using the chapter’s functional form, take correlation ρ = 0 and Sharpe differential d = −0.30. Correlation utility is 1 − (ρ/2 + 0.5)² = 0.75. Return-differential utility is d/√(1+d²) = −0.2873. The illustrative D-Index is 0.4627, despite the negative Sharpe differential.
Use consistent, dimensionless Sharpe differentials. In the chapter’s numerical illustration, utility 0.447 corresponds to d = 0.5, not d = 5; substituting 5 gives about 0.981. This appears to be a decimal omission in the text.
Workbook exercise 7
Calculate the score for ρ = 0.5 and d = 0. Then explain whether a positive score specifies how much to invest.
Show the explained answer — Chapter 7
Correlation utility is 1 − 0.75² = 0.4375; return utility is zero, giving 0.4375. A positive score does not specify a position size or prove an improvement for every allocation. Test the resulting portfolio, constraints and stress behavior separately.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Part II: Hedge Fund Management
Chapter 8: Hedge Fund Index Tracking
Read: printed pp. 165–180. Chapter author(s): Carol Alexander and Anca Dimitriu.
Learning objective: Compare tracking error, cointegration and common-factor replication.
Work through the idea
These approaches target different properties. Tracking-error optimization seeks small return differences; cointegration seeks a stable long-run relationship between level series; principal-component replication seeks a shared source of variation. A good in-sample relationship can deteriorate, and a portfolio that requires frequent rebalancing may be incompatible with fund liquidity.
Original worked example
Our tracker’s active monthly returns are +0.1%, −0.1%, +0.1% and −0.1%. Their mean is zero and population standard deviation is 0.1%. A second tracker returns exactly 0.3 percentage point less than the benchmark each month. Its active-return volatility is zero, but its persistent shortfall is economically important.
The chapter labels a return/volatility statistic an information ratio. The conventional benchmark-relative information ratio uses mean active return divided by active-return standard deviation. Specify the definition rather than silently comparing unlike ratios.
Workbook exercise 8
Which tracker has lower tracking-error volatility? Does that settle which better replicates the benchmark?
Show the explained answer — Chapter 8
The second has zero active-return volatility, versus 0.1% for the first under the stated population convention. It still has a −0.3% monthly bias. Compare mean active return and cumulative tracking difference as well as volatility, turnover and costs.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 9: Designing a Long-Term Wealth Maximization Strategy for Hedge Fund Managers
Read: printed pp. 181–196. Chapter author(s): Keith H. Black.
Learning objective: Trace how fee terms alter incentives and investor outcomes.
Work through the idea
A performance fee gives the manager a nonlinear claim on gains while the investor bears losses. High-water marks, hurdles, deferral, caps and risk-adjusted compensation change that relationship. Each design can introduce new incentives: rewarding a reported Sharpe ratio, for example, can increase the value of artificially smooth marks.
Original worked example
Our one-year account starts at $100,000 and earns 12% gross. Assume a management fee of 1% of starting capital, then a 20% performance fee on the remaining gain above a hard 4% hurdle on starting capital. Management costs $1,000. The fee base is $12,000 − $1,000 − $4,000 = $7,000; the performance fee is $1,400. Ending wealth is $109,600.
A hard hurdle charges only on the gain above the hurdle; a soft hurdle may trigger a fee on a larger profit base once crossed. Never infer the legal fee mechanics from a short label.
| Step | Dollar calculation | Balance or result |
|---|---|---|
| Start | Initial capital | $100,000 |
| Gross profit | 12% × $100,000 | $12,000 gain |
| Management | 1% × $100,000 | $1,000 fee |
| Hard hurdle | 4% × $100,000 | $4,000 excluded from incentive base |
| Performance | 20% × ($12,000 − $1,000 − $4,000) | $1,400 fee |
| Net | 12,000 − 1,000 − 1,400 | $9,600 gain; 9.6% net return |
Workbook exercise 9
Under the same calculation order, remove the hurdle. Find total fees and net return. What contractual details could change the answer?
Show the explained answer — Chapter 9
The performance fee is 20% × $11,000 = $2,200. Total fees are $3,200 and net return is 8.8%. Fees on average NAV, soft hurdles, crystallization frequency, equalization, expenses and high-water-mark adjustments can change this simplified result.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 10: Profiles of Hedge Fund Indexes against Conventional Asset Style Indexes
Read: printed pp. 197–234. Chapter author(s): Barry Feldman.
Learning objective: Separate factor exposure, contribution to variance and index construction effects.
Work through the idea
Feldman examines daily and monthly profiles, including short sellers and managed futures. An aggregate low beta can hide short-lived style tilts, and similar index labels can contain different exposures. A large beta does not necessarily identify the factor responsible for most portfolio variance because factor volatility and covariance also matter.
Original worked example
Our first independent factor has beta 0.5 and volatility 20%, giving a 10% exposure-volatility contribution. A second has beta 2 and volatility 2%, giving 4%. With independent factors their combined factor volatility is √(10² + 4²) = 10.77%, before residual risk.
A fitted profile describes a return relationship, not a holdings audit. Daily sampling adds observations but does not automatically cure nonsynchronous pricing, sample selection or serial dependence.
Workbook exercise 10
Can you add 10% and 4% to obtain total volatility? What information is needed when factors are correlated?
Show the explained answer — Chapter 10
No. With independence add variances, not standard deviations. With correlated factors include covariance terms: 2 × beta₁ × beta₂ × covariance(F₁,F₂). The residual’s variance and its relationship to included factors also require appropriate model assumptions.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 11: Applying Securitization Technology to Hedge Funds
Read: printed pp. 235–244. Chapter author(s): Paul U. Ali.
Learning objective: Follow cash and loss priorities through a collateralized fund obligation.
Work through the idea
A CFO repackages hedge fund exposure into claims with different priorities through a special-purpose vehicle. Tranching redistributes losses; it does not eliminate losses in the underlying assets. Scheduled debt obligations can create a liquidity problem when the funds financing them cannot redeem in time.
Original worked example
Our fictional vehicle has assets of $100 million funded by $70 million senior debt, $20 million junior debt and $10 million residual capital. Ignore interest, expenses and recoveries. A $15 million asset loss wipes out the $10 million residual and causes a $5 million loss to junior debt; senior principal remains covered in this simplified waterfall.
A rating or bankruptcy-remote structure is not a guarantee of repayment or ready secondary-market liquidity. The chapter’s legal descriptions belong to its historical transaction context.
Workbook exercise 11
Increase the asset loss to $35 million. Allocate the principal losses and calculate the senior recovery percentage.
Show the explained answer — Chapter 11
Residual capital loses $10 million and junior debt loses $20 million. The remaining $5 million loss reaches senior debt, which recovers $65 million of $70 million, or 92.86%. Real structures require the actual waterfall, triggers, expenses and payment timing.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 12: Maximum Drawdown Distributions with Volatility Persistence
Read: printed pp. 245–256. Chapter author(s): Kathryn Wilkens, Carlos J. Morales and Luis Roman.
Learning objective: Explain why the order and clustering of returns matter to drawdown.
Work through the idea
The authors examine whether volatility persistence changes maximum-drawdown behavior, using fund data and simulation. Equal average return and unconditional volatility do not imply equal path risk. Their results also differ across fund groups, which is a reason to avoid turning an association into a universal rule.
Original worked example
Our two paths contain the same four returns. Path A is −10%, −10%, +10%, +10%; Path B is −10%, +10%, −10%, +10%. Both end at $98.01 from $100. Path A’s maximum drawdown is 19%; Path B’s is 10.9%, including the initial $100 peak.
A Ljung–Box test on squared residuals and an ARCH LM test are related diagnostics, not generally identical tests. A failure to reject randomness does not prove that returns are independent.
| Point | Path A wealth | Path B wealth |
|---|---|---|
| Initial | $100.00 | $100.00 |
| After return 1 | $90.00 | $90.00 |
| After return 2 | $81.00 | $99.00 |
| After return 3 | $89.10 | $89.10 |
| After return 4 | $98.01 | $98.01 |
| Maximum drawdown | 19.0% | 10.9% |
Technical bridge: a volatility recursion
A common GARCH(1,1) form is σ²(t) = ω + aε²(t−1) + bσ²(t−1), where ε is the prior return innovation after its conditional mean is removed. Under the usual finite-variance assumptions with a+b < 1, unconditional variance is ω/(1−a−b).
For our original parameters ω = 0.00008, a = 0.10 and b = 0.85, unconditional variance is 0.0016, giving 4% volatility. If the prior variance is 0.0016 and the prior innovation is −10%, the next variance is 0.00008 + 0.10 × 0.01 + 0.85 × 0.0016 = 0.00244, giving about 4.94% volatility. The shock changes the next conditional estimate; it does not make a loss certain. Our chart indicator uses rolling volatility and does not fit this model.
Workbook exercise 12
Calculate the return needed to recover from a 19% drawdown. Why should a comparison also control for record length?
Show the explained answer — Chapter 12
Recovery requires 1/0.81 − 1 = 23.46%. A longer record offers more opportunities to experience a severe path, so comparing maxima over unequal horizons can mislead. Match horizons and report drawdown duration as well as depth.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Part III: Risk and Performance Measurement
Chapter 13: A Literature Review of Hedge Fund Performance Studies
Read: printed pp. 259–272. Chapter author(s): Fabrice Rouah.
Learning objective: Explain why published performance and survival estimates differ.
Work through the idea
Rouah organizes research on data biases, persistence, factor models, diversification and survival. The definition of the sample changes the answer: live versus dead funds is a different comparison from survivors versus a historical universe containing both. Database disappearance is not necessarily liquidation.
Original worked example
Our equal-weight sample has three survivors returning 8% each and one failed fund returning −20% over the same period. The survivors-only average is 8%; the full-sample average is 1%. The 7-percentage-point gap illustrates one particular survivorship comparison, not an industry correction factor.
A historical estimate of bias is specific to its database, dates and estimator. Subtracting the same annual amount from every modern fund does not create an unbiased series.
Workbook exercise 13
A fund stops reporting after closing to new subscriptions. Should the researcher automatically record a −100% liquidation return? Explain the required treatment.
Show the explained answer — Chapter 13
No. Record its reporting exit and investigate the reason and later investor cash flows. Keep unknown terminal outcomes visible, distinguish censoring from verified failure, and run sensitivity cases rather than inventing a liquidation result.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 14: Investing in Hedge Funds through Multimanager Vehicles
Read: printed pp. 273–296. Chapter author(s): Meredith A. Jones.
Learning objective: Make a resource-aware choice between direct and packaged exposure.
Work through the idea
The chapter compares direct manager portfolios, funds of funds and index products in terms of access, fees, liquidity and oversight. Delegating selection can save work but creates a second manager to evaluate. A benchmark provider’s transparency is also different from the information actually delivered to the end investor.
Original worked example
Our institution budgets $3 million for alternatives. Twelve direct allocations of $250,000 use the whole budget before cash buffers, fees or monitoring resources. A packaged vehicle may solve the minimum-size problem, but its holdings, fee layers and redemption terms still need review.
The reading compares correlation 0.5 to a coin flip. That is incorrect: a correlation of 0.5 indicates a positive linear relationship; in a simple regression with an intercept, it corresponds to R² = 0.25, not statistical independence.
Workbook exercise 14
An index product advertises daily NAV while its assets redeem quarterly. List two questions that test whether daily reporting means daily access to cash.
Show the explained answer — Chapter 14
Ask whether the investor has a contractual daily redemption right and how the issuer funds redemptions when underlying assets are locked. Also examine gates, notice periods, financing lines, discounts and suspension clauses. A daily valuation is not a cash payment promise.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 15: Performance in the Hedge Fund Industry: An Analysis of Short- and Long-Term Persistence
Read: printed pp. 297–322. Chapter author(s): Sébastien Gyger, P.-A. Bares and R. Gibson.
Learning objective: Distinguish a short-horizon persistence finding from an executable selection process.
Work through the idea
The authors examine repeated peer outperformance and portfolios formed from past rankings. Persistence is mainly short-lived in their sample, with results changing as formation and holding horizons lengthen. An apparent monthly opportunity can be unusable when reporting is delayed and subscriptions or redemptions require notice.
Original worked example
Our fund’s January NAV becomes available on February 20. A study that forms a portfolio on February 1 from the January ranking uses unavailable information. Even February 20 may be too late for the next permitted subscription if the notice deadline was February 15.
Winner persistence and loser persistence are different phenomena. A contingency table can show persistence because losers keep losing, without identifying a profitable group of repeat winners.
Workbook exercise 15
Twenty prior winners include eleven subsequent winners. Calculate the repeat rate. Does that alone prove persistent skill?
Show the explained answer — Chapter 15
The repeat rate is 11/20 = 55%. It is only a descriptive result. Assess the appropriate null, sample size, repeated testing, risk exposure, overlapping periods, return smoothing and whether the rule could actually be implemented after delays and costs.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 16: Further Evidence on Hedge Fund Performance: A Calendar-Time Approach
Read: printed pp. 323–340. Chapter author(s): Maher Kooli.
Learning objective: Read abnormal performance as conditional on the benchmark and estimation method.
Work through the idea
Kooli compares several models, including market exposure, changing conditional volatility, Fama–French factors and a calendar-time approach. Positive historical residual performance remains a sample result rather than a promise. Aggregating funds into indexes does not automatically remove the biases inherited from the underlying reporting process.
Original worked example
Our fictional monthly excess return is 0.60%. A market factor contributes 0.20%, leaving an intercept estimate of 0.40% in a simple attribution. Add a size factor contributing 0.25% and the unexplained average falls to 0.15%. The observations have not changed; the explanation has.
Several passages use market-model and CAPM language loosely. Record whether both fund and market returns are excess of the same risk-free return before interpreting the intercept as a CAPM alpha.
Workbook exercise 16
A monthly alpha estimate of 0.15% has a standard error of 0.12%. Compute the t-statistic and interpret it cautiously.
Show the explained answer — Chapter 16
t = 0.15/0.12 = 1.25. Under a conventional two-sided large-sample 5% reference this is not statistically significant. That does not prove alpha is zero; the model, sample dependence and uncertainty still matter. Do not promote a point estimate as established skill.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 17: Investing in Hedge Funds: Risks, Returns, and Performance Measurement
Read: printed pp. 341–364. Chapter author(s): Francis C. C. Koh, Winston T. H. Koh, David K. C. Lee and Kok Fai Phoon.
Learning objective: Extend performance review to practical risks and institutional context.
Work through the idea
The authors connect return analysis with leverage, concentration, liquidity, style consistency and the historical development of Asian hedge funds. An attractive ratio may leave important operational risks unmeasured. Country, domicile, trading market and manager location describe different aspects of a fund and should not be collapsed into one label.
Original worked example
Our manager holds $12 million of a security trading an assumed $1 million per day. A 10% participation limit allows $100,000 of daily sales, requiring about 120 trading days to exit if volume and prices remain unchanged. A monthly redemption promise therefore needs a separate source of liquidity.
The chapter’s industry sizes, Asian market descriptions and regulatory observations are historical. They should not be used as current eligibility, registration, tax or jurisdictional guidance.
Workbook exercise 17
Halve the assumed trading volume. Recalculate exit time and identify two assumptions that could make even that estimate optimistic.
Show the explained answer — Chapter 17
At $500,000 volume and 10% participation, daily capacity is $50,000, giving 240 trading days. Volume may disappear in stress and selling may move prices; settlement, trading halts and competing sellers can add delay. This is a rough capacity calculation, not an executable liquidation schedule.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 18: Efficiency of Funds of Hedge Funds: A Data Envelopment Analysis Approach
Read: printed pp. 365–380. Chapter author(s): Greg N. Gregoriou and Kevin McCarthy.
Learning objective: Interpret DEA efficiency as relative to selected peers, inputs and outputs.
Work through the idea
DEA constructs a best-practices frontier from the sample rather than requiring a conventional market benchmark. This changes the benchmarking problem rather than eliminating it. The chosen measures and peer universe determine which funds appear efficient; an efficient score does not certify low absolute risk or future skill.
Original worked example
In our deliberately simplified one-output, one-input illustration, Fund A produces return 6 with risk input 3, ratio 2. Fund B produces 8 with input 5, ratio 1.6. Relative to A under a constant-returns ratio model, B scores 1.6/2 = 0.80. This is not a replication of the chapter’s multivariate BCC model.
The chapter uses a live, large-fund sample. Treat its ranking as conditional on that sample; do not infer that excluding dead funds is harmless or that inefficiency alone establishes failure.
Workbook exercise 18
Add Fund C with output 9 and input 3. What happens to A’s relative score in this simplified model? What does that teach?
Show the explained answer — Chapter 18
C sets ratio 3. A’s score falls to 2/3 = 0.667 without any change in A’s own data. Relative efficiency depends on the comparison set. Check peer selection, outliers, sensitivity to variables and whether failed funds were excluded.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 19: The Performance of Hedge Funds in the Presence of Errors in Variables
Read: printed pp. 381–402. Chapter author(s): Alain Coën, Aurélie Desfleurs, Georges Hübner and François-Éric Racicot.
Learning objective: Explain how noisy factors can distort estimated betas and alpha.
Work through the idea
The authors introduce a higher-moment estimator to explore measurement error in explanatory variables. Their deliberately limited factor models produce striking changes in attributed performance, but the chapter also cautions against blind application of the correction. More sophisticated estimation is not a substitute for selecting economically appropriate factors.
Original worked example
Under our single-factor classical measurement-error assumptions, true factor variance is 4 and independent measurement-error variance is 1. The reliability ratio is 4/(4+1) = 0.8. A true beta of 1 would be attenuated toward 0.8 in a large-sample OLS illustration. Multivariate cases need not follow this simple direction.
Measurement error, omitted variables and nonlinear exposure are related but distinct problems. Do not claim that a higher-moment estimator proves all hedge fund alpha is spurious.
Workbook exercise 19
Increase measurement-error variance to 4. Find the illustrative beta and explain why a small estimated beta need not establish successful hedging.
Show the explained answer — Chapter 19
Reliability becomes 4/(4+4) = 0.5, so the illustrative slope is 0.5. The lower estimate can arise from a poor proxy rather than lower economic exposure. Check factor construction, timing and alternative proxies, along with uncertainty and estimator assumptions.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 20: Alternative RAPMs for Alternative Investments
Read: printed pp. 403–434. Chapter author(s): Milind Sharma.
Learning objective: Use a certainty equivalent to make risk preferences explicit.
Work through the idea
AIRAP evaluates the certain return equivalent to a risky distribution under a chosen utility function. It can recognize features that a mean/volatility ratio misses, but its ranking depends on risk aversion and the distribution supplied. An empirical distribution containing no crash cannot reveal an unseen crash merely because a utility formula uses every observation.
Original worked example
Our one-period investment has equally likely gross wealth multipliers 1.20 and 0.90. Under log utility, the certainty-equivalent multiplier is exp[0.5 ln(1.20) + 0.5 ln(0.90)] = √1.08 = 1.03923. The equivalent return is 3.923%, below the arithmetic mean return of 5%.
Log and constant-relative-risk-aversion utility require a valid wealth domain. A leverage scenario producing zero or negative terminal wealth cannot be fed into the same formula as though nothing changed.
Technical bridge: the general power-utility calculation
With positive gross wealth multipliers G(i), probabilities p(i) summing to 1, and relative-risk-aversion parameter c ≠ 1, the one-period certainty-equivalent return is [Σp(i)G(i)1−c]1/(1−c) − 1. At c = 1 use exp[Σp(i)ln G(i)] − 1.
For the worked example’s 1.20 and 0.90 multipliers, c = 2 gives [0.5/1.20 + 0.5/0.90]−1 − 1 = 2.857%. The c = 1 calculation gives 3.923%. Greater risk aversion lowers this investment’s equivalent return under the stated preferences. Repeated historical observations, forward scenarios and excess-return constructions are different inputs; label which you use rather than mixing them.
Workbook exercise 20
For equally likely multipliers 1.30 and 0.80, compute the log-utility certainty equivalent. Compare it with the previous investment.
Show the explained answer — Chapter 20
√(1.30 × 0.80) − 1 = √1.04 − 1 = 1.980%. Both investments have the same 5% arithmetic mean, but the second has a lower log-utility certainty equivalent. This exercise illustrates preference-sensitive evaluation; it is not a full replication of the chapter’s implementation.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Part IV: Statistical Properties
Chapter 21: Volatility Regimes and Hedge Fund Management
Read: printed pp. 437–452. Chapter author(s): Mark Anson, Ho Ho and Kurt W. Silberstein.
Learning objective: Separate volatility level, volatility changes and other explanatory factors.
Work through the idea
The chapter relates fund returns to volatility and compares regimes, then adds other economic variables. A volatility coefficient can change when correlated risk drivers enter the model. This makes a univariate relationship an initial description rather than a complete account of how a fund earns returns.
Original worked example
Our fictional sample has ten high-volatility months averaging −1% fund return and ten low-volatility months averaging +1%. The unconditional average is zero. These conditional averages suggest an association worth investigating; they do not show whether high volatility caused losses or could have been predicted before allocation.
VIX is option-implied S&P 500 volatility. Our chart lab below uses trailing realized volatility of one price series, which is a different variable and does not replicate this study.
Workbook exercise 21
A researcher defines regimes using the full sample’s future median volatility. How would you make a forward-looking classification experiment fairer?
Show the explained answer — Chapter 21
Set thresholds from a training period or a strictly lagged rule, freeze them before the evaluation period and log when classification becomes available. Compare with an unchanged baseline. Use contemporaneous regimes for description only, not as if known before the return occurred.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 22: Does Extreme Risk Affect the Fund of Hedge Funds Composition?
Read: printed pp. 453–472. Chapter author(s): Laurent Favre.
Learning objective: Measure allocation sensitivity to tail models, confidence levels and crisis observations.
Work through the idea
Favre compares mean–variance, modified VaR and conditional VaR approaches and investigates the effect of extreme observations on selected weights. Removing a crisis can make a smooth-looking strategy attractive again, which exposes dependence on the estimation window. Deleting an uncomfortable observation is a sensitivity test, not a justification for assuming the event cannot recur.
Original worked example
Our 100 equally weighted monthly losses have five worst values of 20%, 8%, 6%, 5% and 4%. Define historical 95% expected shortfall here as their average: 43%/5 = 8.6%. Excluding the 20% observation would materially change the tail estimate and the effective sample.
Cornish–Fisher modified VaR is an approximation and can behave poorly for extreme estimated moments. Traditional stocks and bonds can also have nonnormal returns; nonnormality is not exclusive to alternative investments.
Workbook exercise 22
Only 36 monthly observations are available. How many observations represent a 1% tail in expectation? What problem does that create for a 99% historical tail estimate?
Show the explained answer — Chapter 22
36 × 1% = 0.36 observation. There is insufficient direct tail information for a stable estimate at that level. A model can extrapolate but introduces assumptions; report uncertainty, threshold sensitivity and additional stress scenarios.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 23: A Hedge Fund Investor’s Guide to Understanding Managed Futures
Read: printed pp. 473–490. Chapter author(s): Hilary F. Till and Joseph Eagleeye.
Learning objective: Evaluate the portfolio role and failure modes of trend-following exposure.
Work through the idea
The chapter examines managed futures, particularly systematic trend following, as a potential diversifier. Its optionlike profile can differ from strategies that collect small premia while bearing occasional large losses. Trend following nevertheless needs a price path it can follow; a rapid reversal can produce losses, and not every CTA follows the same approach.
Original worked example
Our illustrative process establishes a long exposure after an upward move, then reverses only after a later downward threshold. If price oscillates around those thresholds, repeated direction changes can accumulate costs and losses. The same process may benefit from a sustained decline only after it has actually established short exposure.
A long-lookback-option factor is a model for explaining some return patterns. It does not establish that a live trend system can buy the exact low, sell the exact high or replicate a perfect hedge.
Workbook exercise 23
Explain why a historical positive return during an equity crisis is not equivalent to owning a put with a contractual payoff. Name the evidence you would want next.
Show the explained answer — Chapter 23
A put has specified payoff terms; a trend process depends on signal delay, exposure changes, markets, leverage and execution. Inspect many crisis and reversal paths, costs, pre-existing exposures and out-of-sample behavior. Do not assume positive performance on the next abrupt shock.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 24: Fat-Tail Risk in Portfolios of Hedge Funds and Traditional Investments
Read: printed pp. 491–514. Chapter author(s): Jean-François Bacmann and Gregor Gawron.
Learning objective: Distinguish ordinary dependence from joint extreme losses.
Work through the idea
The authors use extreme value methods for portfolio tail risk and investigate dependence in the extremes. Their allocation results vary with the initial portfolio and the type of fund-of-funds exposure. The effect of a single crisis observation demonstrates how fragile a tail inference can be when data are scarce.
Original worked example
Our asset pair has ten observed stock-tail months. The hedge fund sleeve also breaches its own tail threshold in four of them. The finite-threshold conditional co-breach rate is 4/10 = 40%. This descriptive fraction is not the same as an estimated asymptotic tail-dependence coefficient.
The chapter’s large model-optimal hedge fund allocations are historical risk-minimization outputs, not personal recommendations. Expected shortfall measures tail severity; it does not remove liquidity, model or estimation risk.
Technical bridge: tail thresholds and finite moments
In a peaks-over-threshold model, fit the excess loss Y = L−u conditional on L > u. Under the common generalized Pareto convention, the excess mean is σ/(1−ξ) when ξ < 1. Its variance is finite when ξ < 1/2, and its fourth moment when ξ < 1/4. Positive ξ describes an unbounded heavy tail; ξ < 0 gives a finite upper endpoint under this convention.
The chapter’s sentence saying the mean exists only for ξ < 0 is inconsistent with its subsequent kth-moment condition. The mean condition is ξ < 1 in the parameterization just stated. Other sources reverse the sign of the shape parameter, so compare formulas as well as symbols. See NIST’s conditional mean exceedance reference.
Our example σ = 2% and ξ = 0.25 gives a mean excess of 2%/0.75 = 2.667% beyond the fitted threshold. With ξ ≥ 1 that mean is not finite under the model; reporting a precise finite expected shortfall would then be inconsistent. Threshold choice trades model approximation against the number of observations available. Ordinary correlation can still be defined for nonnormal variables with finite variances; it simply does not fully characterize their joint tails.
Workbook exercise 24
Removing one joint crisis month leaves nine stock-tail months and three joint breaches. Calculate the rate and explain why the deletion does not establish independence.
Show the explained answer — Chapter 24
The rate becomes 3/9 = 33.33%. The sample and denominator changed, but joint stress remains. Even a statistically insignificant coefficient would not prove independence; assess uncertainty, thresholds, serial clustering and the economic reason the observations moved together.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 25: Skewing Your Diversification
Read: printed pp. 515–526. Chapter author(s): Mark S. Shore.
Learning objective: Identify which side of the return distribution contributes to variability.
Work through the idea
Shore compares portfolios containing hedge funds and managed futures using skewness and separate positive- and negative-return dispersion. The S-ratio divides the standard deviation among positive observations by that among negative observations. It answers a different question from downside deviation relative to a target and is not a complete ranking of investments.
Original worked example
Our positive-return observations have standard deviation 3%, while negative-return observations have standard deviation 2%. The S-ratio is 1.5. That number alone says nothing about the fraction of losing periods, the average loss or the size of an unobserved disaster.
Skewness is the standardized third central moment; it is not simply a distribution shifting left or right. Kurtosis is the standardized fourth central moment and cannot be inferred from peak height alone. Standard deviation is the square root of the second central moment.
Workbook exercise 25
An investment has only one negative observation. Can a reliable negative-subset sample standard deviation and S-ratio be estimated? What else should you report?
Show the explained answer — Chapter 25
A sample standard deviation of that subset is undefined with one observation. Report the subset count, return distribution, target-based downside deviation where appropriate, drawdowns and stress sensitivity. Do not substitute zero and display an infinite ratio as proof of quality.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 26: Investable Equity Long/Short Hedge Funds: Properties and Behavior
Read: printed pp. 527–546. Chapter author(s): Edward Leung and Jacqueline Meziani.
Learning objective: Interpret rolling exposure estimates and their confidence intervals.
Work through the idea
The authors compare investable long/short indexes using constant and rolling factor exposures. Similar labels do not guarantee identical market, size or value tilts. A coefficient can lose significance in a short window because the estimate changed, because precision fell or both; those explanations have different implications.
Original worked example
Our monthly alpha estimate is 0.2%, with a 95% confidence interval from −0.3% to +0.7%. The interval includes zero. There is insufficient evidence against a zero-alpha null under that model, while economically meaningful positive and negative possibilities remain compatible with the estimate.
The reading reverses the null-hypothesis wording near its rolling-alpha discussion. When zero is inside the relevant confidence interval, the conventional conclusion is to fail to reject alpha = 0, not to accept that alpha is different from zero.
Workbook exercise 26
A beta estimate rises from 0.20 to 0.35, but the confidence intervals overlap. Does this prove a deliberate timing decision?
Show the explained answer — Chapter 26
No. Test the difference with an appropriate covariance estimate and examine holdings or mandate evidence. Overlap alone is not a formal test of equality, and an estimated shift does not identify intent. Sampling error, factor changes and valuation timing can also move the estimate.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 27: Hedge Funds and Portfolio Optimization: A Game of Its Own?
Read: printed pp. 547–566. Chapter author(s): Zsolt Berenyi.
Learning objective: Understand why a performance measure can improve without new investment skill.
Work through the idea
The chapter constructs hypothetical option portfolios to investigate whether performance ratios can be enhanced by changing the payoff shape. A ratio that ignores important distribution features can reward that reshaping. Higher-moment measures are explored as a defense, but favorable results in a constrained model are not a universal proof of manipulation resistance.
Original worked example
Our fictional premium-collection process gains 1% in nine periods and loses 15% in the tenth. Summing returns gives −6 percentage points, but compounded wealth is 1.01⁹ × 0.85 = about 0.92963, a 7.04% loss. The nine quiet gains alone would give a highly misleading picture.
Bootstrapped distributions and hypothetical option prices are model inputs. They cannot reconstruct every missing crisis or prove that a particular manager traded the model portfolio.
Workbook exercise 27
Would a positive Sharpe ratio calculated before the loss prove deception or prove a durable edge? Explain both limits.
Show the explained answer — Chapter 27
Neither. A short sample may omit the bad state even when all marks are honest. The ratio does not establish durable skill; nor does an optionlike pattern by itself establish fraud. Inspect payoff mechanics, complete records, costs and independent valuations before assigning a cause.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Part V: Special Classes
Chapter 28: Structured Products on Fund of Fund Underlyings
Read: printed pp. 569–606. Chapter author(s): Jens Johansen.
Learning objective: Separate option-based protection, dynamic protection and issuer credit risk.
Work through the idea
Johansen compares option-based principal-protected notes with constant-proportion portfolio techniques, including participation, leverage and path dependence. Dynamic protection changes exposure as the cushion above a bond floor changes. A floor-based algorithm can fail to rebalance before a gap or redemption delay; contractual issuer protection is a separate promise whose value depends on the issuer.
Original worked example
Our simplified portfolio has value 100 and a bond floor of 85. The cushion is 15. With risky exposure equal to four times the cushion, exposure is 60 and the rest is 40 in cash. An instantaneous 30% risky-asset fall loses 18 before rebalancing, leaving value 82, below the floor. Ignore financing, interest and fees for this illustration.
Protection normally has specified maturity terms; early exit and issuer default can expose the investor to loss. Do not confuse the chapter’s illustrative crash-size assumption with a proven maximum future decline.
| Item | Calculation | Meaning |
|---|---|---|
| Cushion | 100 − 85 = 15 | Wealth available above the fixed illustrative floor. |
| Risky exposure | 4 × 15 = 60 | Dollar exposure, not 4 times total wealth. |
| Gap loss | 30% × 60 = 18 | Loss occurs before a rebalance. |
| New wealth | 100 − 18 = 82 | Floor breach of 3; issuer obligation must be assessed separately. |
Workbook exercise 28
What one-step risky-asset loss exactly consumes this cushion? If the risky asset falls 20%, calculate the new value, cushion and target exposure with a fixed floor and multiplier.
Show the explained answer — Chapter 28
The break-even gap is 15/60 = 25%. A 20% fall loses 12, leaving value 88 and cushion 3. Target risky exposure is then 4 × 3 = 12, requiring a large reduction from the remaining risky holding of 48. Actual execution may be delayed or costly. An issuer guarantee, if present and enforceable, is not the same as the algorithm never breaching its floor.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Chapter 29: Hedge Funds and the Stale Pricing Issue
Read: printed pp. 607–614. Chapter author(s): Mohamed Gaber, Greg N. Gregoriou and William Kelting.
Learning objective: Connect stale marks to misleading risk estimates and unfair dealing prices.
Work through the idea
The authors examine delayed prices, fair-value estimation and valuation governance. A smooth reported NAV can lag economic losses and distort volatility, correlation and fee calculations. Autocorrelation is a warning to investigate, not proof of deliberate manipulation; legitimate economic persistence and nonsynchronous markets can also produce it.
Original worked example
Our fictional fund has 1,000 units reported at $100 each, although a supported current valuation is $95. A redemption of 100 units at the stale $100 pays $10,000 instead of $9,500. With true initial assets of $95,000, the remaining assets are $85,000 across 900 units, or $94.44 per unit: the remaining holders bear the $500 overpayment.
The reading’s statement that smoothing is the only alternative is too broad. Documented fair-value estimation and independent challenge are different from mechanically averaging returns. Its historical regulatory discussion is not current legal guidance.
| Item | Reported mark | Supported alternative mark |
|---|---|---|
| Initial units | 1,000 | 1,000 |
| Unit value | $100 | $95 |
| Payment for 100 units | $10,000 | $9,500 |
| Overpayment using stale mark | $500 | Borne by the remaining units in this example. |
Workbook exercise 29
A high price has not traded for weeks and the manager reuses it for a monthly NAV. Give an original three-step investigation that does not presume fraud.
Show the explained answer — Chapter 29
First reconcile the position, price timestamp and subsequent market events with independent records. Next challenge the valuation method using documented alternatives and escalate material differences to an independent reviewer. Finally assess corrections, fee consequences and investor dealing fairness under the governing documents. Keep an audit trail of evidence and unresolved uncertainty.
Return to the reading: identify the relevant method or evidence, record its page, and name one assumption that could change the result. Keep this note with your answer.
Reconciling Conflicting Research Findings
Several chapters favor hedge fund diversification; others emphasize what conventional allocation methods miss. Another set finds positive abnormal performance, while measurement-error and factor studies question how much should be called skill. These are useful comparisons because the relevant assumptions are visible.
| Reading pair | What to compare | Original research task |
|---|---|---|
| Chapters 1, 2, 5 and 24 | Risk definition; stock/bond starting mix; index selection; smoothing; rebalancing and lockups. | List these choices before comparing any optimal weight. Explain why a lower estimated ES and worse skewness are not logically impossible together. |
| Chapters 4 and 26 | Adaptive versus rolling estimates; filtering versus smoothing; factor set; window length. | Separate an actual exposure change from a loss of precision. Keep information available on the decision date. |
| Chapters 3, 9, 14 and 15 | Fee layers, capacity, access, reporting delay and the horizon over which persistence appears. | Build a subscription timeline. Test whether the supposed advantage lasts long enough to implement. |
| Chapters 16, 19, 20 and 27 | Benchmark specification, noisy factor proxies, leverage, utility and payoff reshaping. | Re-rank a fictional candidate after adding one omitted exposure and one adverse scenario. Label every change. |
| Chapters 12, 21 and 29 | Volatility persistence, volatility regimes, stale marks and delayed recognition. | Explain why these are three possible mechanisms, rather than one interchangeable diagnosis. |
| Chapters 11 and 28 | Underlying assets, legal claim, priority, guarantee terms and funding liquidity. | Draw a cash-payment timeline and identify who bears a gap loss, and who bears an issuer default. |
Five checks for mathematical language
- Distinguish population moments from finite-sample estimators and state the kurtosis convention.
- Failure to reject a null is not proof it is true. A confidence interval containing zero is not evidence that the coefficient is significantly different from zero.
- Correlation 0 does not imply independence; correlation 1 does not imply an accurate return replica.
- Under a standard normal model, a three-standard-deviation exceedance is about 0.135% one-sided and 0.270% two-sided. Those probabilities are model properties, not reliable forecasts for fat-tailed fund returns.
- A distribution of returns and an ordered return path answer different questions. Random shuffling can erase the clustering needed to study drawdown.
Pine Indicator and Observation Lab
The book’s research on changing risk motivates a narrow chart experiment: observe when a listed instrument’s trailing realized volatility rises relative to its earlier baseline. All signal thresholds and episode rules below are ours. This indicator does not reproduce the VIX regressions, GARCH models, hedge fund indexes or stale-NAV studies in the book.
What This Indicator Shows
Use a standard daily candlestick chart with positive closing prices. The indicator calculates daily simple returns and their 20-observation population standard deviation. It divides that by the previous day’s 60-observation average of the same volatility measure. Thus a ratio of 1.5 means the current trailing volatility estimate is 50% above that lagged baseline.
| Item | Default definition | Interpretation |
|---|---|---|
| Data | One standard 1D close series; simple returns; no cross-symbol or higher-timeframe requests. | Daily prices are chart observations, not a private fund’s economic returns. Split adjustments, dividends, futures rolls and feed revisions can affect the sample. |
| Episode begins | At a confirmed daily close, ratio ≥ 1.50 while no episode is active. | One START marker for that episode; no claim to predict a sell-off. |
| Episode persists | Remains active until confirmed ratio ≤ 1.10. | The two thresholds create hysteresis and reduce repeated starts near one boundary. No fixed expiry and no replacement of an active episode. |
| Episode ends | At a confirmed close, ratio ≤ 1.10. | One END marker. Loss of valid warmup data resets state without a tradable exit. |
| Downside observation | Daily return < −2 × previous day’s trailing return volatility. | Independent orange marker. It can occur inside or outside an episode; it is not a formal tail-probability estimate. |
| Data-window values | Daily simple return, population standard deviation and zero-target downside deviation, all in percent. | No annualization. The pane’s main ratio is dimensionless; do not compare its scale directly with these percentages. |
| Warmup and timing | Both rolling windows and a lag must be available; expect about 81 daily price observations at defaults. | No marker before ready. Current-day ratio is hidden until close; history can still change if the data feed is revised. |
What This Indicator Does Not Show
It does not measure a fund’s alpha, assets, leverage, liquidity, actual holdings, borrow costs, valuation quality or investor redemption capacity. It does not estimate VaR, expected shortfall, an ARCH test or a probability of a crash. It submits no orders, simulates no fills and produces no Strategy Tester performance. A high ratio can accompany a strong rally or a decline.
Validation status: the script has received static review for indicator-only declarations, lagged baseline use, close-confirmed markers and episode state. It has not been compiled in TradingView or chart-tested. The copy interface is generated for this page and checked structurally; successful browser clipboard operation has not been tested. Compile and inspect it in Pine Editor before relying on any display.
View Pine Script Indicator Code
//@version=6
indicator("CandleChasers: Realized Volatility Regime Lab", shorttitle="CC Vol Lab", overlay=false)
int volLength = input.int(20, "Return volatility window", minval=5, maxval=250)
int baselineLength = input.int(60, "Lagged volatility baseline window", minval=10, maxval=500)
float enterRatio = input.float(1.50, "Stress episode entry ratio", minval=1.01, step=0.05)
float exitRatio = input.float(1.10, "Stress episode exit ratio", minval=0.10, step=0.05)
float shockMultiple = input.float(2.0, "Negative return / prior volatility threshold", minval=0.5, step=0.25)
if not timeframe.isdaily or timeframe.multiplier != 1
runtime.error("Use a standard 1D price chart for this teaching indicator.")
if exitRatio >= enterRatio
runtime.error("The exit ratio must be below the entry ratio.")
// Simple close-to-close returns; no total-return or fund NAV reconstruction.
float ret = close > 0 and close[1] > 0 ? close / close[1] - 1.0 : na
float realizedVol = ta.stdev(ret, volLength, true)
float baselineNow = ta.sma(realizedVol, baselineLength)
float priorBaseline = baselineNow[1]
float ratio = not na(priorBaseline) and priorBaseline > 0 ? realizedVol / priorBaseline : na
float downsideSquared = not na(ret) ? math.pow(math.min(ret, 0.0), 2) : na
float downsideDeviation = math.sqrt(ta.sma(downsideSquared, volLength))
bool ready = not na(ratio) and not na(realizedVol[1]) and realizedVol[1] > 0
// Episode state changes only at daily close. No trade orders or exposure sizing.
var bool stressEpisode = false
bool newStress = false
bool endStress = false
bool downsideShock = false
if barstate.isconfirmed
if not ready
stressEpisode := false
else
if not stressEpisode and ratio >= enterRatio
stressEpisode := true
newStress := true
else if stressEpisode and ratio <= exitRatio
stressEpisode := false
endStress := true
downsideShock := ret < -shockMultiple * realizedVol[1]
plot(barstate.isconfirmed ? ratio : na, "Realized volatility / lagged baseline", color=color.teal, linewidth=2)
hline(1.0, "Baseline parity", color=color.gray)
hline(enterRatio, "Episode entry threshold", color=color.red, linestyle=hline.style_dashed)
hline(exitRatio, "Episode exit threshold", color=color.orange, linestyle=hline.style_dotted)
bgcolor(barstate.isconfirmed and stressEpisode ? color.new(color.red, 92) : na)
plotshape(newStress, title="New stress episode", style=shape.triangleup, location=location.bottom, color=color.red, size=size.tiny, text="START")
plotshape(endStress, title="Episode ended", style=shape.triangledown, location=location.top, color=color.teal, size=size.tiny, text="END")
plotshape(downsideShock, title="Large negative return relative to prior volatility", style=shape.xcross, location=location.bottom, color=color.orange, size=size.tiny)
plot(barstate.isconfirmed ? 100 * ret : na, "Daily simple return (%)", display=display.data_window)
plot(barstate.isconfirmed ? 100 * realizedVol : na, "Population return standard deviation (%)", display=display.data_window)
plot(barstate.isconfirmed ? 100 * downsideDeviation : na, "Zero-target downside deviation (%)", display=display.data_window)
alertcondition(newStress, "New stress episode", "Confirmed daily realized-volatility ratio entered the stress regime. Observation only.")
alertcondition(endStress, "Stress episode ended", "Confirmed daily realized-volatility ratio exited the stress regime. Observation only.")
alertcondition(downsideShock, "Large negative daily return", "Confirmed daily return breached the negative prior-volatility threshold. Observation only.")
A concrete observation experiment
- Freeze the question: does high realized volatility tend to persist in a selected listed-price series? This is an association study, not a profit test.
- Freeze the sample: choose one instrument and a dated training and holdout period before inspecting results. Record chart type, timezone, adjustments and missing sessions.
- Freeze the rule: use the defaults first. A START is known only after its close. For each START, record the next five daily simple returns, beginning with the following trading session.
- Make a fair comparison: compute the root mean square return, √average(r²), over those five observations. Compare with five-session windows after preselected non-START dates in the same holdout. This RMS is not a demeaned standard deviation; use the same calculation in both groups.
- Control overlap: retain the first eligible observation date and exclude later dates whose five-session evaluation windows overlap. Apply the same rule to controls. Record observations with incomplete future windows as pending, not zero.
- Report the sample: event count, control count, median next-five-session RMS, range and a dated list of exceptional paths. Nearby events may still be dependent. A tiny sample cannot settle the question.
- Challenge the result: repeat on a separate instrument and untouched dates; then make one clearly labeled sensitivity change to a window or threshold. Report weak or reversed findings as well as favorable ones.
Manual state check before research
| Confirmed ratio | Prior episode state | Required result |
|---|---|---|
| 1.40 | Inactive | No START; remains inactive. |
| 1.60 | Inactive | START; becomes active. |
| 1.30 | Active | No new START; remains active. |
| 1.05 | Active | END; becomes inactive. |
| 1.55 | Inactive | New START; starts a new episode. |
Also inspect a negative return threshold on a day that is outside an episode. Verify that its observation marker can still appear. After changing inputs, TradingView recomputes the whole historical series; changed historical markers under new parameters are a new experiment, not evidence that the previous parameter set predicted them.
Four Reusable Worksheets
Copy these field structures into your own notes or spreadsheet for each review. The writing areas are prompts for notes; this page does not autosave entries or contain a trade-order form.
Worksheet 1: Source and Evidence Audit
| Field | Record | Why it matters |
|---|---|---|
| Research claim | Chapter, printed page, claim in your own words, and whether it is descriptive or predictive. | Prevents a broad slogan replacing a specific study result. |
| Data scope | Provider, dates, frequency, live/dead coverage, first reporting date and missing records. | Identifies what the researcher could and could not observe. |
| Definition and method | Return convention, fee treatment, model, horizon, thresholds and uncertainty measure. | Makes comparisons reproducible. |
| Feasibility | Accessible funds, minimums, publication lag, subscription/redemption dates and costs. | Separates a paper portfolio from an implementable one. |
| Challenge | Alternative factor, crisis scenario, peer set or estimation window; predicted effect before recalculation. | Creates a falsifiable sensitivity test. |
| Conclusion | Supported finding, unresolved question and next evidence needed. | Allows “insufficient evidence” as a valid outcome. |
Worksheet 2: Portfolio and Cash Stress Review
| Field | Complete for each sleeve | Review question |
|---|---|---|
| Position | Capital weight, dollar value, gross and net exposure, economic driver. | Are several managers providing the same underlying risk? |
| Joint scenario | Simultaneous sleeve returns, spread shocks, financing changes and estimated dollar losses. | Do plausible losses occur together rather than independently? |
| Contractual liquidity | Notice, dealing date, settlement date, lockup, gate and suspension provisions. | When can cash actually arrive? |
| Cash obligations | Redemptions, margin, expenses and debt service by date. | Is a paper gain available to meet a near-term payment? |
| Feasible response | Allowed trades, available cash, limits and transaction assumptions. | Can the requested rebalance be implemented? |
| Decision | Pass, fail or more information; reviewer, evidence date and next review trigger. | Does the conclusion change under a second severe but different scenario? |
Worksheet 3: Chart Observation and Hypothetical Trade Review
For this book, the primary task is observation. If you also review a hypothetical trade, keep it separate and do not convert an indicator marker into an assumed fill.
| Field | Record | Boundary |
|---|---|---|
| Chart identity | Instrument, venue, 1D chart, timezone, price adjustments, dates and settings. | Avoid mixing revised or differently adjusted series. |
| Observation known | Confirmed START, END or negative-return event; close timestamp and ratio. | No earlier intraday knowledge is assumed. |
| Evaluation window | Next five completed sessions, five returns, RMS calculation and missing/pending data. | No overlapping windows under the specified sampling rule. |
| Control | Preselected non-START date and identical horizon/calculation. | A control is not chosen because its outcome looks favorable. |
| Optional hypothetical trade | Decision, later obtainable price, size, financing, fees, slippage and exit rule, recorded separately. | Not an actual fill or an output of this indicator. A marker alone provides no position-sizing rule. |
| Interpretation | Persistence, reversal or inconclusive result, with sample count and counterexample. | No claim about fund NAV risk or investment profitability. |
Worksheet 4: Valuation, Incentives and Review Log
| Field | Evidence to obtain | Escalation question |
|---|---|---|
| Valuation chain | Position records, independent price sources, timestamps, model inputs and reviewer sign-off. | What changes if the last traded mark is no longer representative? |
| Uncertainty | Alternative supported valuations, size of discrepancy and reconciliation status. | Who can challenge or override the manager’s mark? |
| Fee chain | Management basis, incentive basis, hurdle, high-water mark, crystallization and equalization. | Does a valuation revision alter fees or fairness between investors? |
| Operational review | Administrator, custodian, auditor scope, exceptions and unresolved findings. | Which evidence is independent, and what exactly was verified? |
| Action record | Question raised, supporting document, responsible reviewer, response deadline and outcome. | What would cause a pause, a correction or a formal independent review? |
| Follow-up | Actual evidence received and changed conclusion, separately from initial suspicion. | Did new facts resolve the issue, or just replace it with reassurance? |
Capstone: Review a Fictional Hedge Fund Allocation
You are reviewing a fictional $10 million portfolio: 60% traditional investments, 25% Fund A, and 15% Fund B. A has smooth monthly marks and quarterly dealing; B is a managed-futures sleeve with daily reporting but contract terms still to be checked. The committee asks whether the proposed diversification and fees are justified.
No historical fund returns are supplied. Do not invent a track record, Sharpe ratio, alpha estimate or tail model. The correct response can be a conditional assessment and a request for essential evidence.
| Item | Fictional assumption | Required calculation or response |
|---|---|---|
| Stress scenario | Traditional investments −12%; A −18%; B +8%. | Compute each dollar contribution and the portfolio return. |
| Cash demand | A $600,000 payment is due before either private sleeve can redeem. All traditional holdings are liquid in this simplified case. | State the cash source and how the sale changes portfolio composition. Ignore execution costs for the arithmetic, then discuss them. |
| A fee illustration | Starting allocation $2.5 million. Separate positive year: 10% gross return; 1% of starting capital management fee, then 20% on the remaining gain above a hard 4% hurdle. | Calculate management fee, incentive fee, net gain and net return. Do not apply this positive-year fee example to the stress-loss year. |
| Pricing discrepancy | A reports NAV 100; a documented alternative valuation is 94. | Ask for reconciliation, independent challenge and implications for subscriptions, redemptions and fees. Do not presume either value is correct without evidence. |
| Selection claim | The committee wants last month’s top fund, but its NAV is published after the next subscription cutoff. | Show the information and transaction timeline; reject unavailable-information implementation. |
| Structure proposal | A protected note is offered with a 100 maturity promise and a dynamic floor mechanism. No issuer terms are provided. | Separate floor mechanics from the issuer obligation; list missing guarantee, maturity, credit and early-exit information. |
Your deliverable
Write a two-page committee memo, or an equivalent structured note, plus one calculation sheet. Include a cross-chapter evidence matrix, the stress and fee calculations, a cash timeline, a valuation challenge and at least one sensitivity test. State a decision for each proposal: acceptable under explicit conditions, unacceptable under the given constraints, or insufficient information.
Show the capstone calculation key and model reasoning
Stress: traditional holdings lose $6 million × 12% = $720,000; A loses $2.5 million × 18% = $450,000; B gains $1.5 million × 8% = $120,000. Net loss is $1,050,000, or 10.5%, leaving $8.95 million. B helps in this assumed scenario; its future protection is not established.
Cash: the traditional sleeve is worth $5.28 million after stress. Selling $600,000 of it meets the payment under the simplified liquidity assumption and leaves $4.68 million of traditional assets. After the payment, investable portfolio value is $8.35 million: traditional 56.05%, A $2.05 million or 24.55%, B $1.62 million or 19.40%. The external payment is not an investment return. In practice assess settlement timing, costs, restrictions and continued margin needs.
Separate fee year: gross profit $250,000; management fee $25,000; hard-hurdle amount $100,000; incentive base $125,000; incentive fee $25,000. Total fees $50,000, net gain $200,000 and net return 8%. A different contract or calculation order changes the result.
Model reasoning: demand verified NAV records and their information dates, live/dead coverage, independently reviewed valuations, fee documents and actual redemption terms. Compare factor specifications and stress both sleeves losing together. A proposed note needs issuer and guarantee terms before an investor can assess principal protection. A defensible memo does not fill missing facts with optimistic assumptions.
| Area | Points | Full-credit evidence |
|---|---|---|
| Source and inference | 20 | Uses at least six chapters across three parts; separates historical findings, assumptions and original calculations. |
| Arithmetic and conventions | 20 | Correct stress, cash, fee and one additional chapter calculation; labels horizons, units and return conventions. |
| Risk and feasible cash | 20 | Accounts for joint losses, locked positions, reporting versus dealing, and payment/settlement dates. |
| Models and valuation | 20 | Explains omitted-factor or measurement uncertainty, valuation challenge and issuer versus algorithm protection. |
| Research discipline | 20 | Provides one predeclared sensitivity, information-date control and an evidence-based decision without invented performance. |
Completion criteria: finish all 29 chapter exercises, attach page-based evidence notes, complete the four worksheets at least once, and submit the capstone. Aim for 80/100 or better, then correct every material arithmetic, timing or valuation error even if the overall score passes. Completion shows study progress; it is not a professional credential or evidence of trading competence.
Final self-check
- Can I explain why a quiet return series may still contain a large economic loss exposure?
- Can I distinguish correlation, beta, alpha, active-return bias and tracking error?
- Can I identify the information date that makes a ranking implementable or impossible?
- Can I trace a fee, debt or principal-protection claim through an explicit waterfall?
- Can I state which missing evidence would stop me reaching an investment conclusion?
Technical and Current-Context References
The book is the required source for its empirical designs and findings. The external references below serve narrower purposes: current investor context and the chart indicator’s confirmation behavior. They do not validate the historical studies or our hypothetical outcomes.
- Investor.gov: Hedge Funds — current SEC investor guidance on valuation questions, fees and redemption limitations. Fund status and adviser obligations are separate questions; do not read the book’s historical “unregulated” descriptions as blanket exemptions from law.
- Investor.gov: Structured Notes with Principal Protection — a repayment promise depends on issuer creditworthiness. The label alone does not eliminate loss risk.
- TradingView: Pine Script bar states (paid link) — reference for close-confirmed indicator logic. Documentation review is not compilation or chart testing.
Final Takeaway
Evaluate the economic exposure, the data that describe it and the contract that delivers it together. This collection is most useful when its chapters become tests of assumptions: what changes if the bad month is retained, the factor is noisy, the mark is stale, the fee is different, or the requested redemption cannot happen?
Risk Disclosure
This material is for education and research, not personalized investment, legal, tax or financial advice. Trading and investing involve substantial risk, including loss of capital; leverage, short selling and derivatives can amplify losses and may create obligations beyond the initial investment. Hedge funds and structured products may involve illiquidity, financing, valuation, operational and issuer risks. Historical findings, hypothetical calculations and indicators do not predict future returns or establish profitability. Obtain appropriate independent advice and verify current terms and requirements before acting.
CandleChasers is not affiliated with the book’s editors, chapter authors, publisher or any investment manager discussed in the source. This is an independent educational companion and is not an authorized or endorsed edition.