Mpi Madoff Fraud Analysis 2008Q4

8/7/2019 Mpi Madoff Fraud Analysis 2008Q4

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2008, Markov Processes International, LLC

MPI Quantitative Research Series

BackgroundNow that the news of Madoffs $50B Ponzi scheme ison the front pages of news media around the world, theinvestment community is scratching their heads andtrying to understand how this could have happened.With all the advances in academic research, investmenttechnology and risk management tools it seemsimpossible to pull off an enterprise of such dimensions.The truth is that investors often prefer to ignore redflags and forgo analytical tools and techniquesspecifically designed to protect them from such a fraud.In 2006, at the request of a hedge fund manager, MPIperformed a returns-based quantitative analysis of oneof Madoffs funds and came to the conclusion that,most likely, the returns were not real. Moreover, intrying to explain the strategy we discovered that thefunds return pattern resembled that of a proven fraudcase the Bayou fund. This research article follows thefootsteps of our 2006 study.

Returns-Based ForensicsSince 19921 returns-based style analysis (RBSA)tools have become firmly entrenched in the investmentdue diligence process on the traditional side of theindustry. Institutional investors are presented withchoices either of fully trusting portfolio managers or ofperforming tests to understand whether the managersstories matched the results. Up until the early 90s thiswas a formidable and expensive exercise requiring thehelp of consultants or of investing heavily in holdings-based analytics technology and associated infrastructureto perform a laborious analysis of the portfolios entireholdings history. With the advent of RBSA the process

of reconciling performance with the stated managementstrategy became quick, inexpensive and very accurate.

This methodology gained widespread acceptance withinthe traditional side of the industry and provided

1 In 1992 MPI was the first to develop returns-based styleanalysis (RBSA) tool following the ideas of Nobel Prizewinner in Economics Prof. William Sharpe.

investors with inexpensive and effective means tounderstand inner workings of investment products byusing only performance data. It is worth mentioningthat such tools are used alongside holdings-basedanalytics as it is a known that holdings may not be ableto tell the whole story. This is because portfoliomanagers frequently use window dressing, use

complex derivative strategies such as portable alpha,which carry heavy risks, and, finally, may not providecorrect and full position information. The idea behindthe returns-based approach is relatively simple. On onehand there is a holding-based story describing theinvestment strategy and the instruments used. On theother hand theres a track recorda stream of monthlyinvestment returnsthat can often be closely mimickedby finding a combination of passive factors or indicesthat best explain the return movements. If the dynamicsof factor/index exposures agree with the informationderived from holdings, it reinforces the confidence inthe strategy. However, if theres a notable discrepancy,

it enables an investor to question the managers story.

Until recently, the applicability of returns-basedanalysis to alternative investment products wasrelatively limited. As compared with traditionalinvestments, hedge funds may take significant shortpositions, employ leverage, and engage in very rapid,almost instantaneous, strategy changes with the help ofderivatives. Unfortunately, traditional window-basedregression techniques are limited in their ability tohandle these complex investments. To address thelimitations of traditional RBSA in dealing with hedgefunds, a new methodology, Dynamic Style Analysis

(DSA), was specifically developed to improve thereturns-based analysis of hedge funds. For our analysisbelow we use MPI Stylus application utilizing DSAtechnique.

AnalysisOne of the main investment vehicles providing accessto Madoffs strategy was the Fairfield Sentry Ltd fundmanaged by the Fairfield Greenwich Group. The fundran a so-called split-strike conversion strategy. Below

Madoff: A Tale of Two Funds

A quantitative analysis of a Madoff hedge fund reveals a

striking similarity with another well-known case of fraud

December 2008

Michael Markov, CEOMarkov Processes International

Tel +1 908 608 1558www.markovprocesses.com


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2008, Markov Processes International, LLC Page 2

is the description of the funds strategy derived fromthe investment memorandum and published in BarronsMay 7, 2001 article.

"Typically, a position will consist of the ownership of

30-35 S&P 100 stocks, most correlated to that index,

the sale of out-of-the-money calls on the index and the

purchase of out-of-the-money puts on the index. Thesale of the calls is designed to increase the rate of

return, while allowing upward movement of the stock

portfolio to the strike price of the calls. The puts,

funded in large part by the sale of the calls, limit the

portfolio's downside."

While there are a number of funds following similarstrategy, Madoffs ability to generate stable returns overthe long run and in any market environment isperplexing. In this paper we will analyze this fund tobetter understand the return drivers. For our analysis,we used the returns of the Fairfield Sentry Ltd provided

by a third party. The funds monthly returns are shownin Figure 1.

Figure 1

Fairfield Sentry Monthly Returns

Created with mpi Stylus

Fairfield Sentry Ltd.

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One of the first striking observations one can make isthat the fund had very few down months over the 20-year period. The distribution of monthly returns inFigure 2 is positively skewed which is always attractiveto investors.

The chart in Figure 3 compares cumulativeperformance of the fund with the S&P 500 index over

almost a 20-year period through September 2008. Thefund produced an 11.6% annualized return vs. 9.3% forthe S&P 500 indexwith much lower volatility. Thedifference in annual volatility is striking: 2.8% forSentry and 14% for S&P.

Such a smooth return pattern usually results in a veryhigh Sharpe Ratio and, in fact, this fund and severalassociated feeder funds have the highest values of long-

term Sharpe Ratio in the entire 8,000+ hedge funduniverse.

Figure 2

Distribution of Monthly Return


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Total Return, %

Fairfield SentryLtd.

Financial ratios such as the Sharpe Ratio, mentionedabove as well as the Sortino and Omega ratios and

many other similar statistics are routinely used byinvestors to measure the attractiveness and efficiency ofhedge funds. The truth is that these statistics can bemisleading as they are academic abstracts and based oncertain theoretical assumptions such as normality, etc.As technical indicators, they provide no insight into theinternal workings of an active investment strategy,treating it the same way as an individual stock or assetclass. Moreover, by providing a false sense of securityto investors, such ratios can be very damaging. Thus,for anyone specializing in hedge fund quantitative duediligence, high, almost outlier values for such ratios,are immediately suspect.

Figure 3

Cumulative Performance



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Fairfield SentryLtd. S&P 500 Index

For our regression tests we use various U.S. marketindices: S&P 500 GIC sectors, S&P 500, S&P 100 andRussell Equity Style indices. To better detect the fundsoption-based strategy we use CBOE S&P 500BuyWrite indices: BMX (at-the-money) and BXY


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OTM (out-of-the-money), and the CBOE S&P 500PutWrite PUT index.

Once a reasonable set of factors is selected, MPIsDynamic Style Analysis (DSA) engine goes throughvarious combinations of selected indices to create adynamic portfolio that provides a reasonably good fit(usually measured by R-squared) and, moreimportantly, high predictability of results - thuspreventing over-fitting the data2. Thousands of indexcombinations were tried over various time intervals butnone produced result of any significant credibility. Weshould note that such a result (or rather lack thereof) isnot necessarily an indication of fraud. This could be anindication of missing factors, a strategy that is simplytoo difficult to model using monthly returns orsignificant errors in the data. Non-directional strategies,such as stat arbitrage, typically do not produce credibleresults using RBSA long-term. That being said, it isquite unusual for a fund to not have any credible results

over any time interval within a 20- year history.

One of the most interesting results was obtained byusing the CBOE options indices3 as factors. Thecombination of factors that best explained the Sentryreturns was a dynamic portfolio long PUT, S&P 100and Cash and short BXM and BXY. The weights of thistracking portfolio are shown in Figure 4.

Figure 4

Hypothetical Options Strategy


Factor Exposures

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BXM CallWrite PUT PutWrite BXY CallWrite OTM S&P 100 + Cash

2 We use MPIs proprietary Predicted R-squared statisticbased on the leave-one-out cross-validation popular in dataand image analysis applications. Any data analysis toolshould provide a means to prevent overfitting the data.Classical Theils Adjusted R-squared is not sufficient andcould be misleading.3 Although the fund had earlier data, the analysis starts in Jan2001 as this was the first date of S&P 100 series available tous.

In Figure 5 we compare the funds performance(labeled total) with the performance of the replication(tracking) portfolio shown above (labeled Style).Both performance lines virtually coincide, whichsignals that the replication portfolio produces nearlyidentical returns to the fund consistently through the 8-year history.

Figure 5

Sentry vs. Hypothetical Strategy



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Total Style

The result is quite interesting as it is the total oppositeof the Barrons description of the strategy: Madoff isbuying puts, selling calls and is also long S&P 100. Inour result, the replication portfolio is buying CBOEPutWrite Index, which is equivalent to selling puts andis selling BuyWrite Index which is equivalent to buyingcalls shorting the index. Note that we havent instructedthe system to place investments on the long or shortsidethe data analysis algorithms alone determined that

this combination provides the best replication of thefunds performance.

As mentioned earlier, these results were not deemedcredible by our DSA and its predictability measures.This means that small changes in input data could resultin significantly different factor exposures. This couldsignal that we are missing an important factor or notidentifying processes that affect fund returnssuch asfee deduction, return smoothing, etc. Regardless, theresults still raise immediate red flags. For example,given the enormous size of the fund (over $10B inSentry and other investments), was it possible to havesuch a significant volume of option contracts on thelong side? Why is the strategy matching the fundsperformance so different from its description by themanager? It is commonly said that RBSA is better atraising questions than it is at answering them, buthaving the right questions is the most important part ofthe due diligence process.


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Adding Missing FactorFailing to obtain any predictive explanation of thefunds performance using common equity andderivatives indices, we added an unlikely factormonthly returns of the Bayou fund. Bayou was one ofthe funds founded by Samuel Israel III, who defrauded

investors of hundreds of millions of dollars. As theinvestment world now knows, Bayous returns weresystematically falsified. Our reason for adding thisfactor was that characteristics of Madoffs fund andBayou were strikingly similarsmooth, positive returnsin any market environment.

One obvious drawback of our analysis is that data forBayou is only through June 2005, the last month Bayoureported its performance before filing for bankruptcy.However, the 2.5 years or 30 months used for theanalysis is sufficient to draw statistical conclusionsabout correlation coefficients, while not being too long(as we do not know the exact date that Bayou started

inventing its return numbers).

Analysis of both funds monthly returns in Figure 6finds that they do have similar patterns in magnitudeand the sign of returns: very few negative returns.

Figure 6

Bayou and Sentry Monthly Returns


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Further, we measured the correlation of the FairfieldSentry fund with various sector and style equity indicesalong with Bayou. Bars in Figure 7 represent thecorrelation coefficient of Sentry with a respective

factor. The rightmost bar represents Sentrys correlationwith Bayou, 0.41, which, although is not that high bytraditional standards, is still much higher than any otheranalyzed index. This result is perplexing as the fundsstrategy descriptions are strikingly different.

We then compared the returns of 8,000 funds andfunds-of-funds from the HFR database to the returnstreams of both Bayou and Fairfield Sentry Ltd.

Figure 7

Correlation with Fairfield Sentry


Correlation

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Healthcare Industrial Consumer, NCycl Technology Telecomm

Utilities R200 Value R200 Growth RMid Value RMid Growth

R2000 Value R2000 Growth Bayou Funds

The results are shown in the scatter chart in Figure 8below. Each red point represents a hedge fund plottedaccording to its correlation with the two funds: the X-axis represents correlation with Bayou, the Y-axis

correlation with Fairfield Sentry. The cluster circled inthe top right corner represents funds that correlatealmost perfectly with Fairfield Sentry (correlationsclose to 1.0). It is plausible to assume that these andother funds having extremely high correlation withSentry are the feeder funds for Madoffs strategy. Notethat these funds also have some of the highestcorrelation with Bayous returns.

Figure 8

Hedge Fund Correlation with Bayou & Sentry


Correlation w ith Bayou and Fairfield Se ntry

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It shouldnt come as a surprise that a DSA analysis ofMadoffs returns with an extended factor set displayeda portfolio made up of cash and the Bayou fund in avery stable combination of 60/40%, respectively,depicted in Figure 9. This also could be described asFairfield Sentry having beta 0.4 vs. Bayou.


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The system rejected any other factor or index as beingdetrimental to the predictive power of the analysis.Such a stable and simple combination tracked Madoffsfund return fairly closely as is shown in Figure 10.

Figure 9

Style Analysis using Bayou as a Factor


Style Analysis

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Bayou Funds Cash

One conclusion from this analysis is that Madoff was60% less aggressive in marking up numbers thanSamuel Israel. On another note, although the PredictedR-squared numbers for this analysis were somewhatlow, they were the only positive results obtained usingthousands of combinations of indices and factors overvarious time periods. One immediate question comes tomind: why did such different and unrelated operationsproduce such strikingly similar returns?

Figure 10

Sentry vs. Bayou+Cash Mix



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Fairfield SentryLtd. Bayou+Cash 40//60 Portfolio

Implications for Hedge Fund Indices andReplication StrategiesSome of the unlikely casualties of this case are hedgefund indices, which represent important benchmarks ofhedge fund performance. A number of hedge funddatabase vendors4 compile hedge fund indices by

4 Credit Suisse/Tremont, Hedge Fund Research (HFR), HedgeFund.NET, Barclay, CASAM CISDM, Eurekahedge, etc.

strategy. The performance of such indices is usuallymade public and is updated through the month as morefunds report performance. Each category indexrepresents a weighted average of a representative groupof funds in the category.

As Madoffs strategy was classified as Market Neutralby the industry, in Figure 11 we compare correlation ofthe Fairfield Sentry fund with various market neutralindices over the period Jan. 2001Sept. 2008. Thecorrelation of 0.53 with CS/Tremont Market Neutralindex is strikingly high and is, in fact, higher than withany other index.

Figure 11

Sentry Correlation with Hedge Fund Indices


Correlation with Fairfield Sentry Ltd.

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BarclayEquityMktNeutral Index

Correlation, representing a measure of lineardependency, is not an immediate indication of whetherthe fund and the index have similar performance. In

fact, even for highly correlated series the actualperformance could differ significantly. This was not thecase with CS/Tremont, however. In Figure 12 theperformance of hedge fund market neutral indices iscompared with that of the fund.

Figure 12

Performance of Major Hedge Fund Indices


Performance of Major Hedge Fund Indices

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Performance of the Fairfield Sentry fund represented bya red line consistently overlaps with the CS/Tremontindex and mimics it in variability and magnitude. Thefindings above shouldnt come as a surprise. Certainly,indices differ in coverage and classification. But themajor difference affecting index performance lies in itsweighting methodology. While most of the hedge fundindices are equal-weighted5, CS/Tremont index is asset-weighted, i.e., fund assets under management (AUM)are used as weights when computing index returns. Insuch an index a fund with significant assets could havea hundred times greater influence on the indexperformance than a fund with little AUM. This couldhave a tremendous impact on index performance. SinceMadoffs funds accumulated significant assets, anasset-weighted index of which it is a part should beexpected to have higher correlation with the fund thanan equal-weighted one.

One of the obvious implications for the industry is that

these indices will have to be restated. Once such acorrection is done, the CS/Tremont index will movecloser to the rest of the group.

This case brings both good and bad news to anemerging segment of the industry -- hedge fundreplicators. These strategies, available from about adozen asset managers, aim to track the performance ofmajor hedge fund indices using generic instrumentswith low fees and high liquidity. Many of these indexproducts have failed to outperform their benchmarksand produced a significant dispersion of results. It isalso well known that CS/Tremont indices are

notoriously difficult to replicate. And if Madoff relatedfunds returns contained in them are fraudulent, it isclear why it has been difficult to match their results, sosome of these managers should feel relieved.

The bad news is that nobody knows yet how manyMadoff and Bayou funds remain out there and areincluded in hedge fund indices. This reinforces the casethat replicating an index has its obvious drawbacks andpotential risks. Not only is one replicating a pool offunds where good ideas cancel out bad ones, but alsothe pool of funds can also contain nonexistent products.As such, it is our suggestion that nothing can replace

the thorough due diligence of individual hedge fundreturns. Only after such an analysis is performed canone determine if replication is possible and worthdoing.

5 Returns of all funds in the in the index are simply averaged.

The Anatomy of FraudThe focus of this section is building a plausible modelof behavior for a manager that is systematicallymarking up performance numbers. One strategy mightbe return smoothing, where positive returns aresubsidizing negative returns. Thus, in a month with a

negative return, the fund manager would adjust it in apositive direction and in a subsequent month having apositive return, deduct the amount of adjustment. Asimpler strategy would be to simply report returns asis when they are positive and report random positivenumbers when they are negative. This leads us to thefollowing model.

Lets assume that a manager follows a generic EquityHedge strategy represented by HFRI Equity Hedgeindex. From this index series we create two time series:HFRI EH + (plus) and HFRI EH (minus). The firstreturn series is equal to the original index if the returnis positive, and zero if the return is negative. The

second, the minus series, flips negative returns, i.e., isequal to zero when the index return is positive and tothe absolute value of the index return when it isnegative. It is easy to see that both time series producenon-negative returns in any market environment andthat their difference is equal to the original index.Figure 13 displays all three return series: the truncatedpositive, flipped negative returns, and original indexreturns.

Figure 13

Improved HFRI Monthly Returns


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HFRI EquityHedge Index(+) HFRI EquityHedge Index(-) HFRI EquityHedge Index

In other words, if R , R+

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A strategy that produces only positive returns in any

market environment Fcould be of the following form:

1 2F R R R + = + +

Where 1 and 2 are opportunistic adjustments that a

manager may apply to returns. The higher the numbers,

the more aggressive the manager in marking up returns.Our next step is to use this model to see if it couldexplain the behavior of Madoff in adjustingperformance numbers6. Thus, we will follow the abovemodel and perform an analysis of Fairfield Sentry

returns usingR+

, R

and cash as indices. The result isshown in Figure 14.

Figure 14

Sentry: Hypothetical Strategy Weights


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HFRI EquityHedge Index(-) HFRI EquityHedge Index(+) Cash

As is evident from the chart, such a strategy could beexplained by taking 30% of returns in up-months,flipping negative returns and applying a 20%adjustment in down months. The rest of the portfoliocould be invested in a short term instrument, whichcould also indicate a constant small upward adjustment.This Style portfolio tracks the manager fairly well asshown in Figure 15.

6 We realize that this model is simplistic. A better model canbe built only after obtaining sufficient details about thestrategy and the actual holdings. We use this model to detectthe trend but we dont expect to fully capture monthlyvolatility.

Figure 15

Sentry vs. Hypothetical Strategy



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We applied the same approach to Bayous returns. Theresults are shown in Figure 16. Note that Bayou appearsmore aggressive applying 50% markups in positive and

negative months.

Figure 16

Bayou: Hypothetical Strategy Weights


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ConclusionThe use of advanced returns-based style analysistechniques, like DSA, can be instrumental in alertinginvestors to return patterns and behavior that warrantfurther investigation. Tools like DSA cannot signalwhether a fund is actually engaged in fraudulentactivity, but it can definitely raise red flags that shouldtrigger skepticism and a call to action on the part of thehedge fund analyst or investor. Fund performance thatis not well explained through returns-based analysismay, of course, be due to missing factors or strategiesthat are simply too difficult to model with monthlyreturns. Some of the best hedge funds may not behighly correlated with any standard indices or factors. Itis critical that an attempt is made to understand if suchunexplained funds are simply difficult to model or ifsomething more sinister is at hand.


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Thus, it is our conviction that one must attempt areconciliation of stated manager strategy and actualfund performance in every case. The case of Madoffand its intriguing similarity and correlation with Bayouindicates that, in some cases, investors can indeed bealerted to potentially fraudulent activity in advance.This kind of early warning system is an important toolin the arsenal of a good analyst, but it must be followedup with solid due diligence and investigation on the part

of the analyst to determine if the fund is a keeper orticking time bomb.

Implications of the Madoffs case for the industry areenormous and may even reach hedge fund indexvendors and passive index replicators with both re-examining their rules and due diligence practice.

References

Erin Arvedlund, Don't Ask, Don't Tell, Barrons, May 7, 2001M. Markov, Why Would One Invest in an Outlier? - A Bayou Analysis, MPI Research, 3QTR 2005M. Markov, O. Krasotkina, V. Mottl, I. Muchnik. Dynamic Analysis of Hedge Funds. Proceedings: 3rd IASTED

International Conference on Financial Engineering and Applications, ACTA Press, Cambridge, October 2006.

Markov Processes International, LLC (MPI) is the leading provider of superior investment research and reportingsolutions. MPIs software applications and customized consulting services are employed by the worlds finestinstitutions and financial services organizations to enhance their investment research, reporting, data integrationand content distribution. MPI offers the most advanced platform available to analyze hedge funds, mutual funds,portfolios and other investment products, as well as asset allocation and portfolio optimization tools.

MPIs Stylus Pro software is utilized by alternative research groups, hedge fund of funds, family offices,institutional investors, consultants, private banks, asset managers, diversified financial services organizations aswell as marketing, product development and IT departments around the world. MPI also offers solutions for private

wealth advisors and high net worth professionals. Through its ground-breaking Dynamic Style Analysis modelMPI offers hedge fund analysts true due diligence and unparalleled insight. For more information on past MPIresearch articles visit www.markovprocesses.com.

Media ContactsLoretta Mock/Paul DamonCognito+1 646 395 [email protected]

Mpi Madoff Fraud Analysis 2008Q4

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