Madoff $65 billion Trap. A study in unlikely hedge fund economic returns

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Madoff $65 billion Trap

Gaetan “Guy” Lion

May 2010

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Introduction

Harry Markopolos wrote a book about his uncovering the $65 billion Madoff Ponzi scheme; and, his sharing with the SEC detailed findings in 1999, 2000, 2001, 2005, and 2007. But, the SEC never caught Madoff.

This presentation is an analytical review of Markopolos findings.

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Losses to InvestorsIn a Ponzi scheme, the earlier investors get repaid by the later ones. So, it is not like the entire $65 billion was lost.

Investors invested $36 billion in Madoff funds. They got back $18 billion. They lost $18 billion. They also thought they reaped $29 billion in gains that never existed.

Investments $36 billion

Redemptions $18 billionInvestors Madoff

Losses $18 billion Ponzi scheme$65 billion

Fantazy gains $29 billion

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A few unlikely Madoff victims

• Henry Kaufman: economist, former Managing Director at Salomon Brothers and economist at the Federal Reserve.

• Eliot Spitzer’s family. • Madoff Family Foundation to the tune of $19

million.

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Let’s look at a couple of fraud detection methods that would not have worked…

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Benford’s Law used in Fraud Detection Software

This test would not have uncovered Madoff’s Ponzi scheme.

The Gateway Fund (GATEX) used a strategy most similar to Madoff. It is a benchmark on how Madoff’s fund should have looked if it had been legit.

Benford's Law frequenciesLOG(1+1/FirstDigit)

FirstDigit Frequency1 30.1%2 17.6%3 12.5%4 9.7%5 7.9%6 6.7%7 5.8%8 5.1%9 4.6%

100.0%

Benford's Law test: Madoff vs GATEX distribution of monthly returns first digit

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

1 2 3 4 5 6 7 8 9

First Digit of monthly return

Fre

qu

ency

Benford

Madoff

GATEX

Error vs Benford's LawMadoff GATEX

Avg. error 2.9% 3.2%

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Detecting Fraud using Serial Correlation

Serial Correlation of monthly returnsMadoff (0.22) GATEX (0.01) S&P 500 0.02

The greater the serial correlation of monthly returns the more probable such returns are manipulated.

Madoff’s low negative correlation does not raise a red flag.

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To catch this Ponzi scheme, you had to understand what Madoff was claiming to do…

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Bernie Madoff claimed strategy

His “split strike conversion” strategy amounted to reducing stock returns volatility. He (supposedly) did this in three steps:

1)He bought 35 large cap stocks.

2)He bought S&P 100 Put options to reduce losses.

3)He sold S&P 100 Call options to finance the premium he paid for the Puts.

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So, he has a long position in stocks

He bought stocks at prices where the two lines cross. If stocks go up on the horizontal line he makes money (on the blue line) and vice versa.

Stock returns, long position payoff profile

Value

Gains +

Stock price

Losses -

Stock purchase

price

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He buys Puts to reduce losses

The Put strike price is at the red line inflection point. If stock prices along the horizontal line decline (moving to the left) of the strike price, the Put is in the money and will cover additional losses. Buying a Put establishes a floor on losses.

Put pay off profile

Value

Stock price

Strike price

Current stock price

Premium

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He sells Calls to finance the Puts premium

The Call strike price is at the green line inflection point. If stock prices along the horizontal line increase (moving to the right) of the strike price, the Call is in the money. This creates a cap on returns because you are forced to sell the stock at the strike price. This is to earn a premium on the Call to finance the Put premium.

Selling Call pay off profile

Value

Stock price

Strike price

Current stock price

Premium

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Net result is much lower volatility

Value

Stock price

Selling the Calls sets a low Ceiling on stock returns gains.

Buying the Puts sets a Floor on stock return losses.

Now the return profile looks very different than simply being long the stocks.

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Problem: Skewness

For the same premium level, you have to retain greater losses on the Put (red box top graph) than the gains you can retain on the Call (green box below). Skewness is really bad for a split strike conversion strategy.

Skewness implication:

Premium paid = Premium earned

Losses retained > Gains retained

Put pay off profile

Value

Stock price

Call pay off profile

Value

Stock price

Current Stock price

Put strike price

Current Stock price

Call strike price

Losses retained

Gains retained

Premium paid

Premium earned

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Skewness on S& P 100 Options on May 24, 2010

24-May-10S&P 100 level 493.925 days to expiration

PutStrike price Distance Quote Strike price Distance Quote

490 3.9 14.60$ 495 1.1 14.05$ 485 8.9 12.85$ 500 6.1 11.10$ 480 13.9 11.35$ 505 11.1 8.70$ 475 18.9 10.05$ 510 16.1 6.45$ 470 23.9 8.95$ 515 21.1 4.60$ 465 28.9 7.95$ 520 26.1 3.20$ 460 33.9 7.05$ 525 31.1 2.00$ 455 38.9 6.25$ 530 36.1 1.23$ 450 43.9 5.55$ 535 41.1 0.80$ 445 48.9 4.95$ 540 46.1 0.41$ 440 53.9 4.40$ 545 51.1 0.24$ 435 58.9 3.90$

Call

For about $6 you could sell a Call with a strike price of 510 on the S&P 100. This is 16.1 points away from the S&P 100 current level at the time of 493.9. You could use this $6 to buy a Put with a strike price of 455 or 38.9 points away from the current S&P 100 level. The distance of the Put strike price is more than 2 x the one of the Call strike price (38.9/16.1). That’s bad.

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Skewness = Asymmetry

At all option premium prices, the respective Puts’ strike prices are much further away than the Calls’ strike prices. We highlight the difference in strike price distance for a Call and a Put with a premium close to $6 as shown on the previous slide.

Puts and Calls Strike Price Distance vs Premium

$-

$2

$4

$6

$8

$10

$12

$14

$16

-80 -60 -40 -20 0 20 40 60

Distance from S&P 100 current level

Op

tio

n P

rem

ium

Puts strike price (negative) distance Calls strike price (positive) distance

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Another Problem: mismatch between the risk basis (specific stocks)

vs the hedge basis (Puts S&P 100 Index)

• Madoff was long 35 stocks;• He bought Puts on the S&P 100 index;• It would be inevitable that he would run into

losses on specific stocks;• He was not hedged vs any specific stock losses.

He was only protected against the index dropping. This should have caused Madoff to incur monthly losses more frequently than he did.

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Percent of month with loss?!

Markopolos states that Madoff’s record from 1993* to 2008 is unheard of in the hedge fund industry. 93.5% month gain… only 12 months losses out of 186 months. His loss frequency is only a fraction of the Gateway Fund (GATEX) that followed a similar strategy. And, that was during a wrenching time for capital markets including the 1997-1998 Asian currency crisis, the three year dot.com crash (2000-2002), and the onset of the financial crisis (2007 onward).

*Data for GATEX goes only back to 1993. So, we cut off the time series at this point to make it comparable between Madoff and GATEX.

Madoff GATEX% of month with loss 6.5% 26.3%" " " with gain 93.5% 73.7%

100.0% 100.0%

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Madoff Expected Returns: Near Risk Free Rate

To avoid almost all monthly losses, Madoff’s Put strike price should have been very close to the current price. This takes him almost out of equity returns and leaves him barely with a Risk Free Rate (even less if you factor skewness and basis risk).

Value

Stock price

Very short distance between Put and Call strike price.

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Returns are way too high to be legit

Madoff split strike conversion strategy should have earned close to the Risk Free Rate. Instead, it earned nearly three times that.

Madoff vs 90 dayT-Bills annual returns

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Madoff

90 day T-Bills

Madoff avg. 10.8%

T-Bill avg. 3.9%

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That’s Consistency!?

Madoff perfectly side steps the Dot.com and housing bubbles.

Madoff vs S&P 500 annual returns

-50%

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

Madoff

S&P 500

Standard deviation:Madoff: 3.8%S&P 500: 20.3%

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No one can duplicate his returns!?

Gateway Investment Fund (GATEX) used a similar but superior strategy to Madoff, but it did not come close to replicating Madoff risk-adjusted returns.

Madoff vs GATEX annual returns

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Madoff

GATEX

Returns; Standard deviation:Madoff: 10.8%; 3.8%GATEX: 6.4%; 7.5%

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An Efficient Frontier Map

This shows the combination of volatility (x axis) and return (y axis). GATEX that was expecting to do better than Madoff is already above the Efficient Frontier, reflecting a strong performance.

But, Madoff’s returns are way above the Efficient Frontier. Can you beat the Efficient Frontier? Yes, but not by that much!

Efficient Frontier (1990 - 2008)

3%

4%

5%

6%

7%

8%

9%

10%

11%

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22%

Yearly volatility or Standard Deviation

Yea

rly

retu

rn o

n C

AG

R b

asis S&P 500

GATEX

Madoff

T-Bill

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Madoff had to earn 15% before fees!

Madoff was giving away the entire Hedge fund fee structure to Fund of Funds. This includes a 20% performance fee of returns and a yearly 1% management fee.

Madoff gross return 15.0%Fund of Fund fees:a) Performance fee 20% -3.0%b) Management fee -1.0%

Clients' net return 11.0%

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Markopolos knew this was a Ponzi Scheme

Investors thought Madoff’s returns were due to:

1) Market timing based on a proprietary model; and

2) Front-running (placing his orders ahead of his clients to extract illicit gains).

Markopolos knew it was a Ponzi scheme for a simple reason. Madoff’s equity positions were much larger than the entire market for S&P 100 index options that he claimed to use for hedging.

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How did Madoff succeed for so long?

• As an investor wouldn't you like to earn 11% nearly risk free with the former Chairman of the NASDAQ?.

• As a feeder fund wouldn’t you like to retain the entire hedge fund compensation (1%/20%) and market to your

client a world beating manager (11% nearly risk free)?

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Who did not invest with Madoff?

The vast majority of large U.S. investment and commercial banks did not invest with Madoff. The head of derivatives at such institutions all concurred it had to be a Ponzi scheme.

This is not true for European banks. Many of them got caught with exposures ranging from $200 million to $2 billion.

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Financial Crisis & Lehman Chapt. 11 take out Madoff

$8 billion investors redemption requests

Lehman Chapt. 11 on 9/15/08

Lehman files chapter 11 on September 15, 2008. Within next couple of months, the S&P 500 loses 30% of its value. Investors flee to Treasuries. Their resulting yield drop by 175 bp. Investors request $8 billion in redemptions from Madoff. He is arrested on December 11, 2008.

S&P 500 level Sept 15 - Dec 11

700

800

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1000

1100

1200

1300

9/12/2008

9/19/2008

9/26/2008

10/3/2008

10/10/2008

10/17/2008

10/24/2008

10/31/2008

11/7/2008

11/14/2008

11/21/2008

11/28/2008

12/5/2008

- 30%

10 Year Treasury yield

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

2008

-09-

12

2008

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19

2008

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2008

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2008

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2008

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2008

-12-

19

- 175 bp

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The Four Red Flags summary

1) This option strategy should have earned close to the risk free rate. T-Bills over the period earned less than 4%. Madoff earned close to 11%. Impossible.

2) His mismatch between his risk on specific stocks and hedges using S&P 100 options should have caused frequent monthly losses. Instead, he incurred losses in only 6% of the months. Impossible.

3) The skewness in option prices dictates he could not simultaneously achieve: i) net zero hedging costs; and ii) avoiding nearly all losses on the S&P 100. Impossible.

4) The size of his equity portfolio was a high multiple of the entire market for S&P 100 options he claimed to use for hedging. Impossible.