The Mado Case FRUNZA Marius Cristian Schwarzthal Kapital · Financial crime in the hedge fund...

Financial crime in the hedge fund industryThe Madoff Case

FRUNZA Marius CristianSchwarzthal Kapital

Institute of Banking and Finance, University of Zurich , 19th of November 2016

Agenda

1 MotivationBackground

2 What is a ”Hedge Fund”?”Hedge fund” industryRisk assessment

3 Fraud indicators

4 The ”Madoff” caseBernard MadoffMarkopulos’s warningsFraud indicators

5 Q&A

6 Bibliography

Understanding structures to allow better researchSchwarzthal Kapital 2

Financial Crime

Introduction to theories and varieties of modern crimes [Frunza(2015a)] Solving modern crime in financial markets [Frunza(2015b)]

http://www.amazon.com/gp/product/B019K7CMUE?qid=1457293412

http://www.amazon.com/Solving-Modern-Crime-Financial-Markets/dp/0128044942

Key Figures

16 countries were visited for case studies, interviews andinvestigations

18 interviews were conducted with professionals, investigators,regulators

3.64 years is the average time spent in prison by the interviewedindividuals

22 institutions provided inputs: Barings, Europol, SAS, IOR, etc...

> 10 disciplines were used in studying the crimes on financial markets:economics, statistics, financial maths, accounting, data mining ,anthropology, criminology, law, sociology, psychology, history ...

> 100 case studies are described in the textbooks

3 R libraries were developed as analytic tools


What is a ”Hedge Fund”?

The term hedge fund a is in many ways inappropriate as the managerdo not hedge, but speculate, thereby implying risk taking strategiesthat could generate period with high losses.

Alfred Jones, an American financier form the post WW2 eraintroduced the term ”hedge fund”

Hedge funds are tools dedicated to wealthy individuals/organizations

Since the early 2000s hedge funds became a popular investmentvehicle amongst investors

aIn French hedge fund is translated as fond speculatif (speculative fund)emphasizing clearly the risk taking strategies of this type of funds



Figure: Hedge funds industry: Service providers in the hedge funds industry



Figure: Evolution of the total assets under management in the hedge fundsindustry



Figure: Hedge funds benchmark performance indexes Before the crisis Hedgefunds over-performed the classic market indexes. After the crisis the returns hadless traction compared to S&P 500 total return index


What can are the risks of a ”Hedge Fund”?

Shavings assets

Mis-representation of the returns

Ponzi schemes

Money laundering

Market manipulation


Performance metrics and their issues

Sharpe ratio

SX =E (RX − rf )

σδ(1)

Jensen’s alphaα = rx − (rf + βx(rm − rf )) (2)

Sortino’s ratio

S =E (RX − rT )√∫ rT

−∞(RX − rT )2f (RX ) dRX

(3)

Treynor measure

T =E (RX − rT )

β(4)


Sharpe ratio: Manipulation

For a set of m states

δ =m∑i=1

πiδi (5)

where πi are the probabilities of occurrence of state i and δi the excess returns under thephysical measure.Hence the Sharpe ratio can be reshaped as:

SX =

∑mi=1 πiδi√∑m

i=1 πiδ2i − δ

2(6)

Thus if the the manager had a better performance Sharpe ratio in the past then the

target future excess return should be lowered compared to the past excess. If the

manager had a poor past Sharpe ratio compared to the expected future ratio then the

expected excess return should be above the historical excess.


Sharpe ratio: Manipulation

Figure: Dynamic manipulation of the Sharpe ratio for a series of hedge fund returns


Performance manipulation indicators: Principles

There is no formula or statistical test to point if the performance isembellished

Each situation is different even for same type of fraud( i.e Ponzi)

Before doing a deep dive analysis, it is important to understand thebig picture

Always doubt the outcome of due-diligence

Statistical tools need to be customized depending on each situation


Too big to fraud...

Prior to the 2008 crisis many companies based their credit risk assessment

on the concept: "too big to fail". This trail persists today in the way

financial crime is assessed.

Too big to fraud: A big hedge fund will never enter in aperformance manipulation (Madoff.....)

(I)Moral hazard: The big hedge fund will never be investigated orliable for crime (Madoff, ....)

Eschatology: If this big hedge fund is involved in wrongdoings wewill have bigger issues at that times (Amaranth...)


Hedge funds: Due-diligence biases...

When analyzing credit ratings (S&P, Fitch, Moodys), big companies appear

to have a better creditworthiness than small companies. When assessing

financial crimes, some investigators tend to overlook big funds or banks

Size bias: A big organization has better means for corporate transparency and investorscommunication. In most of the cases they are perceived as less exposed to scams.[Liang(2003)] shows that audited funds have a much lower return discrepancy thannon-audited funds. Also it points that there is a significantly positive correlation betweenthe auditing dummy variable and fund size. Large funds tend to be audited while smallfunds tend not to be, because large funds can afford to have an auditor and there aremore needs for auditing their large money pools or complicated portfolio positions.

Reputation bias: If a hedge fund has a bond with a reputed bank, it is perceived as safer.Funds listed on exchanges, fund of funds (compared with hedge funds), funds with bothUS and non-US investors, funds open to the public, funds invested in a single sector(compared with multiple sectors), and unlevereged funds have better data quality than theother funds.

Geographic bias: Currently compliance processes deem companies incorporated in theWestern world as safer than those in the Eurasian Union. It might be true generally butnot for everything.

Safe harbor bias: Some funds or strategies were wrongly perceived like safe harbors.


Bias ratio

The Bias ratio, introduced by [Abdulali(2006)], is the most popularmetric used for assessing whether returns are manipulated or not.([Dimmock and Gerken(2014)], [Zask(2014)]).

The Bias ratio is similar to a test for randomness, as it is amathematical technique that identifies abnormalities in thedistribution of returns([van Dyk et al.(2014)van Dyk, van Vuuren, and Heymans]).

The Bias ratio metric is nothing else than the ratio of the frequencyof positive returns to the frequency of negative returns to within onestandard deviation of the observed return distribution, therebyassessing the asymmetry of the return’ distribution


Bias ratio

Let assume a given set of returns Ri with mean µR and standard deviation σR . Underthe discrete form the Bias ratio can be expressed as

BR =

∑Mi=1 Ri · 1(0 ≤ Ri ≤ σR)

const.+∑M

i=1 Ri · 1(−σR ≤ Ri ≤ 0)(7)

Under the continuous form of the return distribution is expressed as:

BR =

∫∞−∞ R · 1(0 ≤ Ri ≤ σR)dR

const.+∫∞−∞ R · 1(−σR ≤ Ri ≤ 0)dR

(8)

1 0 ≤ BR ≤ ∞2 if Ri < 0, ∀i > 0 then BR = 0

3 if Ri > σR , ∀i > 0 Ri > 0 then BR = 0

4 if E(Ri ) = 0 and E(R3i ) = 0 then BR → 1


Bias ratio

The Bias ratio for a highly liquid fund in an efficient market should beclose to one.

Highly illiquid securities have high serial correlation and hence thebias ratio of such a fund will be higher than 1.

High bias ratio for funds aimed to be invested in classic strategiesshould be an alarm signal.


Returns distribution discontinuity

When the performance indicators are manipulated by manager usually thefrequency of performance improvement is higher than the frequency of negativevariations, thereby generating discontinuities in the distribution of the performancevariation around the critical points ( ie. management target performance )

Discontinuity in performance metrics was discussed for the earning reporting by[Burgstahler and Dichev(1997)].

A straightforward statistical test to find discontinuities in returns is presented by[Takeuchi(2004)].



Let Ri i = 1, 2....,M be a set of independent random variables with distributionfunction F. Assuming equal spaced points −∞ = ζ0 < ζ1 < ζ2 < ...ζk =∞ ,where ζk − ζk−1 = z , the empirical frequency for each bin is given by :

Zj =M∑i=1

1(Ri ∈ (ζj−1, ζj)) for (j = 1, 2, ..., k) (9)

Zj follows a multinomial distribution an therefore it can be developed as:

pj = P(Ri ∈ (ζj−1, ζj)) = F(ζj−1)− F(ζj) (10)

where the expectation of Zj is E (Zj) = Mpj and the variance can be written asvar(Zj) = Mpj(1− pj)



The statistical discontinuity test is :

H0: In the bin j the distribution is smooth (pj−1 + pj+1)/2− pj = 0

Ha: Alternatively the distribution cannot be characterized as smooth in bin j

The statistics of the test can be expressed as:

τBD =(p∗j−1 + p∗j+1)/2− p∗j√

var((p∗j−1 + p∗j+1)/2− p∗j )(11)

the empirical probability of observation being in bin j is p∗j = Zj/M, with thevariance of the test being :

var((p∗j−1+p∗j+1)/2−p∗j ) =1

M(p∗j (1−p∗j )+p∗j ((p∗j−1+p∗j+1))+0.25(p∗j−1+p∗j+1)(1−(p∗j−1+p∗j+1)))

(12)Under the null hypothesis the test follows the normal standard distribution.

τBD ∝ N(0, 1) (13)

Based on this formulation it can be assessed on the base of the value of τBDwhether the smoothness hypothesis can be rejected for statistic value higher thenormal distribution at a given confidence interval level.


Benford’s law: Digit test

An empiric alternative to assess rogue performance reporting is through Benford’s law whichdeals with probability of occurrence of digit as a decimal in a set of numeric data([Benford(1938)]). It should be recalled that the Benford law states that the distribution of theis given by :

P(d) = log(d + 1)− log(d) = log(1 + 1/d) (14)

Figure: Benford law distribution. The first digit Benford law compared to the first digit of arandom variable generated from a t-Student law


Benford’s law: Digit test

Figure: First digit distribution for the Global Barclay Hedge Funds performance index.The observed distribution for this case follows the theoretical law.


The Madoff case

Quizz...


Bernard ’Bernie’ Madoff

Once upon the time Bernard Madoff was perceived as an experiencedprofessional with high authority in the Wall Street investmentcommunity.

His broker-dealer firm Madoff Investment Securities founded in the1960 was closely involved in developing the NASDAQ Stock Market,where Madoff served as chairman for many years.

Bernard Madoff was also a founding member of the InternationalSecurities Clearing Corporation in London.



Madoff employed a strategy referred to as a split-strike conversion, which isnothing else than a collar option structure on a basket of stocks.

This involved purchasing a basket of 30-35 large-capitalization stocks with ahigh degree of correlation to the main market index.

Once the stocks purchased out-of-the-money call options on index are soldand out-of-the-money put options index are bought, thereby forming a collarstructure aiming to reduce the variability of the investment.

The strike of the call is obviously greater than the strike of the put. Thusthe investment evolves in a tunnel established by the strikes of the call an ofthe put.

The aim of a collar is that on a long stock position, selling a call increasesthe return, and allows taking gains from bullish movements to the level ofthe short call strike price and the purchase of an out of the money putfunded with part or all of the call premium, protects the position against amarket downturn.



Figure: Collar payoff with a long position. The aim of a collar is that on a long stock position,selling a call increases the return, and allows taking gains from bullish movements to the level ofthe short call strike price and the purchase of an out of the money put funded with part or all ofthe call premium, protects the position against a market downturn.



Figure: Madoff’s investment process. Investors accessed Madoff’s strategy through feeder funds like Fairfield Sentry.Feeder funds generally did not mention Madoff’s name or his firm name on their materials. Madoff established a firm in theUnited States in charge with the market making and one in London United Kingdom more focused on family’s finances. JPMorgan was the bank keeping the funds of Madoff’s firm. Unusually Madoff’s hedge fund was not a hedge fund either de factoor de jure. It was nothing else than a broker dealer acting like a sophisticated prime broker for the feeders. Madoff Investmentsecurities was for sure not able to make the market for all the option he should trade OTC for his strategy, so he had somecounterparties allegedly UBS and the defunct Merrill Lynch.


The Madoff case: A family business

Madoff’s vehicle was not organized as traditional hedge fund ( see the Hedge fundchapter) and many of its functionalities (depositary, accounting, audit , brokerage etc...)were either internalized or provided by company managed by family and inner circlefriends.

Peter Madoff, Bernie’s brother was serving as Chief Compliance Officer for MadoffSecurities International Ltd, for more than 40 years, and ran the daily operations .He has served as vice chairman of the NASD, as member of its board of governorsand has been actively involved as his brother was in the NASDAQ Stock Market asa member of its board of governors and its executive committee and as chairmanof its trading committee.

Shana Madoff, Peter’s daughter worked for Madoff Securities International Ltd asa rules and compliance officer and attorney. She was married to Eric Swansonwhich was part of the team conducting a SEC review of Madoff’s firm in 2003

Mark and Andrew Madoff, both currently dead were serving as directors in thecompany in charge with trading floor and with sales activities

Ruth Madoff, Madoff’s wife was employed in the firm and she helped Bernie in thevarious illegal actions


The Madoff case: A family business

His closed friends going back together for more than 25 years involved were

Paul Konigsberg, was the accountant in charge of Madoff family Foundationtax returns

Davif Friehling the external auditor of the hedge funds

Frank di Pascali the direction of option trading which worked with Madoffsince the early 1980s

Jeffry Picower, a business man and investors in the fund who apparentlyknew about the scam and managed to pull out his funds with a very goodperformance

Stanley Chais was another investor with preferential treatment

This list is has more sophisticated ramifications and just give an image of how thescam was organized in order to form an inner circle that managed de facto theoperation from end to end. The way the firm functioned, its business model, thehuge reliance on family members and friends in the daily operations creates anunusual spectrum for a respected financial institution.


The Madoff case: Few questions remain not addressed until today II

1 Investors and mainly financial institutions do run extensive due diligences before placingfunds in a an alternative vehicle such a hedge funds . Reputed institutions mainly fromEurope which accounted for most than half of the Madoff contributions like AGF assetmanagement Oddo and Cie , Dexia Asset management, Santander, Union bancaire Privee,do regularly have in-depth review procedures of an investment vehicles, with teamspecialized in conducting such diligence. Why those procedures failed to signalirregularities?

2 Madoff’s scheme was too big and had many ramifications in various Wall Streetinstitutions to remained unnoticed to a trained eye. Harry Markopulos, the whistle-blowerthat alerted the SEC was for sure not the only person who remarked the big picture andmost likely other individuals with ambitions to earn fast money might have been informedabout the scam. Therefore the question is what was the real number of people aware ofthe scam that took part directly or indirectly from the very beginning or during theevolution of the scam, taking some juice from Madoff in order to keep the things lowprofile?

3 To reach out to such a huge amount of assets, most likely Madoff relied on some coreinvestors that knew all along the timeline of the scam about the true nature of thebusiness. They were probably paid preferentially by the funds like in every Ponzi scamthere are some winner. Were all those special clients identified?


The Madoff case: Few questions remain not addressed until today

4 The Madoff Securities was to big at leas theoretically speaking for not to be noticed bythe peers in the derivatives market making. For sure some trader from those institutionsknew that something does not look right from the volumes and types of trades Madoffwas engaged with. Why those Wall Street institution’s had preferred the Omerta insteadof denouncing a practice that would most likely be very harmful and disruptive to itsbusiness ?

5 For running such big scale operations any fund required a license which is submitted toregulators and authorities. They are supposed to carry in-depth review. Indeed MadoffSecurities was incorporate in the 1960s, when got its license, but regulators tend to doactivity reviews periodically especially for the systemic organizations. Why those reviewsdid not raise any signals and why they did not have the required detail level?

6 The ”Madoff” operation can be characterized as fully fledged ’mom and pop’ investmentboutique involving mainly members of his extended family. Nevertheless all big institutionsinteracting with other equivalent organization do require third party documents , auditsand reviews. Madoff managed to create an end to end operation whereas no externalparty was able to have a detailed view of his operations. Using a small audit firm Friehling& Horowitz, with an uncertain status relative to the US accounting authorities Madoffmanaged to manipulate its performances without catching the attention of any of itspeers. Why the regulators and its counterparties accepted those facts?


The Madoff case: Markopulos’s warnings

[...] I’ m turning this case in because it’s the right thing to do. Far better that the SECis proactive in shutting down a Ponzi Scheme of this size rather than reactive. Harry

Markopulos’s letter to SEC from November 2005

Harry Markopulos, the man who figured out Madoff’s scheme a send no less than five

letters to the Securities Exchange Commission between 2000 and 2008 warning about

the misrepresentations and incoherence’s in Madoff’s enterprise. The best known letter

is he sent in 2005 self titled : The World’s largest Hedge fund is a fraud containing a

detailed insight on the organization of the scam as well as no more than 29 red flags

that should alarm every investor.

aThe man who figured out Madoff’s scheme http://www.cbsnews.com/

news/the-man-who-figured-out-madoffs-scheme-27-02-2009/


http://www.cbsnews.com/news/the-man-who-figured-out-madoffs-scheme-27-02-2009/

http://www.cbsnews.com/news/the-man-who-figured-out-madoffs-scheme-27-02-2009/


Few of Markopulos a red flags are detailed below:

Madoff Investment Securities was to much secretive and did not allow proper externalauditors. The firm had also an unusual remuneration scheme, in which he perceived atransaction fee from the feeder which perceived also management fees and performancebonus from clients. Madoff Investment Securities was in fact a broker dealer which usedthe contributions from the feeder to finance the market making activity at a rate whichwas 3 times higher compared to its peers.

Madoff have mostly non-American investors (with few exceptions that apparently got theirgains fully) and collected funds mostly form Europe, fact that most likely bought him timein the eye of US regulators. Curiously many European fund managers consideredthemselves lucky if the could a special access to Madoff’s scam

The Madoff Investment Securities was a family business which made it unique in thesector. Furthermore only family members were induced to the secrets of the investmentstrategy

aMadoff Securities is the world’s largest Ponzi Scheme.https://www.sec.gov/news/studies/2009/oig-509/exhibit-0293.pdf


https://www.sec.gov/news/studies/2009/oig-509/exhibit-0293.pdf


If Madoff was really implementing his strategy he might have been involved as a broker inillegal front-running. Since the 1980 Madoff paid brokers to clear his customer’s orderthrough his broker-dealer firm. Those so called a ”legal kickback”, gave Madoff thereputation of being the largest dealer in trading about 15% of NYSE stocks volumea.Madoff used allegedly the orders that other broker placed through his firm to predict themarkets move and with this strategy to provide with superior returns. As a hedge fund itwould not represent an issue but as a broker dealer what Madoff Investment Securitieswas, this would be an illegal practice to take advantage of an information before sharing itwith the clients. His clients were the feeders (Figure 8, which had a proper hedge fundsstatus. This practice is in theory an offense called front-running.

The split strike conversion (collar) strategy cannot provide achieve 12% average annualreturns for many years with very less negative returns. His low volatility in returnsindicates that he probably used a narrow collar with options close to moneyness, which aremore expensive than the out-of the money ones. In this conditions his returns would haveeven more difficult to justify.

The volumes on the options market which Madoff allegedly used were not sufficient forimplementing his option based strategy. In addition he was not a counterparty with themajor option dealers from Wall Street like Goldman Sachs or Morgan Stanley.

Sharpe Ratio of 2.55 for Fairfield Sentry Ltd. was much high compared to the Sharperatios experienced by the rest of the hedge fund industry. The Fairfield’s Sharpe ratio is inthe 99th quantile in the distribution of the 5823 hedge funds performance from theBarclayhedge database

aTHE REGULATION OF PUBLICLY TRADED SECURITIES

http://www.sec.gov/rules/proposed/s71004/s71004-587.pdfUnderstanding structures to allow better researchSchwarzthal Kapital 35

http://www.sec.gov/rules/proposed/s71004/s71004-587.pdf

The Madoff case

Figure: Histogram of the Sharpe ratio. The Fairfield’s Sharpe ratio (red) is in the99th quantile in the distribution of the 5823 hedge funds performance from theBarclayhedge database (green)


The Madoff case: The Bias Ratio

During the Madoff events the Bias ratio had allegedly indicate abnormal values as presented bysoftware providers of the hedge funds industry 1.

Figure: In the Madoff case for the Fairfield fund the Bias ratio was 6.33 a very high value whichindicated that the returns might have not been genuine. Figure above shows the distribution ofBias ratios computed though a resampling approach from the initial target series of returns.

1Hedge Funds Risk And Replicationhttps://www.riskdata.com/resources/hedge_funds_risk_and_replication.html


https://www.riskdata.com/resources/hedge_funds_risk_and_replication.html

The Madoff case

Figure: Distribution of the monthly returns of Fairfield sentry returns. The redline indicated the zero returns

Parameter Value

Mean 0.0089Median 0.008

Standard deviation 0.0072Skewness 0.807Kurtosis 3.488

Sharpe ratio 2.67

Table: Basic statistics for Fairfield’s returns


The Madoff case

Figure: Maddoff scam. One of the points underline by many analysts is that Madoff’sreturns (Fairfields Sentry) did not look like any other hedge funds return and were notcorrelated with any other financial market. In addition Madoff’s strategy looked morelike a fixed income investment seemed with not correlation to any other index.


The Madoff case: Correlation drill

The correlation between Fairfields’s returns and other index is computes and represent ina distribution. The correlation level is inferior to 30 %, the highest being with the Belgianequity index (BEL 20 Index)A Granger causality test searching the cause effect relationship between the variousindexes and Fairfields returns rejects all causality with the exception of Barclay MergerArbitrage Index and Barclay Multi Strategy Index, which in practice are not indexes linkedto Madoff strategy.

Figure: Fairfield returns relationship with hedge funds benchmarks


The Madoff case: Benford test

To prove if the returns of the Madoff funds were handled manually one canapply the Benford test Figure below shows the first digit distribution forthe returns of the Fairfield funds which was Maddoff’s main feeding fund. .

Figure: First digit distribution for the returns of the Farifield funds which wasMadoff’s main feeding fund


The Madoff case

”If you want to do something, do it all.”

Carmine Persico, Boss of the Colombo Family


Q&A

More on our website ...www.schwarzthal.com


www.schwarzthal.com

Abdulali, A., 2006. The bias ratio: Measuring the shape of fraud.Protege Partners Quarterly Letter.

Benford, F., 1938. The law of anomalous numbers. Proceedings of theAmerican Philosophical Society, 551–572.

Burgstahler, D., Dichev, I., 1997. Earnings management to avoidearnings decreases and losses. Journal of accounting and economics24 (1), 99–126.

Dimmock, S. G., Gerken, W. C., 2014. Regulatory oversight andreturn misreporting by hedge funds. Available at SSRN 2260058.

Frunza, M.-C., 2015a. Introduction to the Theories and Varieties ofModern Crime in Financial Markets. Academic Press.

Frunza, M. C., 2015b. Solving Modern Crime in Financial Markets:Analytics and Case Studies. Elsevier.

Liang, B., 2003. Hedge fund returns: Auditing and accuracy. Availableat SSRN 968717.


Takeuchi, Y., 2004. On a statistical method to detect discontinuity inthe distribution function of reported earnings. Mathematics andcomputers in simulation 64 (1), 103–111.

van Dyk, F., van Vuuren, G., Heymans, A., 2014. The bias ratio as ahedge fund fraud indicator: An empirical performance study underdifferent economic conditions. International Business & EconomicsResearch Journal (IBER) 13 (4), 867–896.

Zask, E., 2014. Finding financial fraudsters: Quantitative andbehavioural finance approaches. Journal of Securities Operations &Custody 6 (4), 308–324.


The Mado Case FRUNZA Marius Cristian Schwarzthal Kapital · Financial crime in the hedge fund...

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