Sophisticated investors expressed shock at the alleged $50 billion fraud by New York-based broker and fund manager Bernard Madoff, yet even relatively simple quantitative analysis should have raised red flags, according to research by London-based software vendor Riskdata.A day after Madoff was indicted with securities fraud in a Manhattan court, US fund of funds Fairfield Greenwich issued a statement regarding its possible losses. As of November 2008, $6.9 billion of the fund's $14.1 billion in total assets under management were invested in Madoff.
"We are shocked and appalled by this news," said founding partner Jeffrey Tucker. "We have worked with Madoff for nearly 20 years, investing alongside our clients. We had no indication that we were the victims of such a highly sophisticated, massive fraudulent scheme."
Contrary to this, however, it seems there were a number of straightforward quantitative indications available.
One of these was looking at the fund's bias ratio. It is similar to Benford's Law, which is used in some countries to spot possible instances of tax fraud. Put simply, it holds that the distribution of leading digits within fabricated accounts tends to differ from those that occur naturally. But instead of digits, the bias ratio looks at distributions of small, medium and large returns at a given fund.
Riskdata examined the bias ratio of 2,281 funds in Chicago-based Hedge Fund Research's database that were in the same style category as Fairfield Sentry - a Madoff feeder fund operated by Fairfield Greenwich. Since August 2005, the fund's bias ratio was found to range between six and seven, while the bulk of the other funds in the same category had a maximum bias ratio of three. Of the 2,281 funds in the same style category, only 20 showed signs of suspicious activity - six of which were Madoff's fund and its feeders.
Riskdata also investigated the bias ratio of two other recent hedge fund frauds, including Connecticut-based Bayou Management, which was uncovered in 2005 and had a bias ratio of six. And mortgage-backed securities fund Connecticut-based Beacon Hill - found to be overstating returns in 2002 - had a bias ratio of seven.
"When a bias ratio indicates an individual fraud, you want to go further," said Ingmar Adlerberg, chief executive and founder of Riskdata. "Of course the due diligence process can be very lengthy and complex, but one next step is trying to understand the risk profile of the manager."
The firm simulated the possible returns of Madoff's strategy using information available to ordinary investors - namely, that he was running a split-strike conversion strategy using a basket of stocks that were highly correlated to the S&P 100 index.
Also known as collaring, split-strike conversion involves buying protective puts while selling covered call options. In this way, the strategy gains exposure to underlying stocks while limiting upside and downside.
By altering factors such as the strikes of the options bought and sold, as well as their maturity and the rolling frequency of the position, Riskdata produced a spectrum of possible return series for the Madoff funds.
But whatever the inputs, the firm was unable to replicate their reported returns - at best, only managing the performance of the underlying S&P 100 index.
Furthermore, an analysis of the factors driving these simulated returns - such as asset prices, the interest rate curve, market volatility and so on - were found to be very different from those driving the returns of the Madoff funds.
"If you take his description and you take a synthetic portfolio, it doesn't look at all like his for the time series. The fact that they're so different is another strong indicator of fraud," said Adlerberg.
While the simulation was largely exposed to market volatility and equity prices, for instance, the Madoff funds were little exposed to either of these factors. Over time, the factors driving returns also proved to be quite unstable, said Riskdata - an unusual result considering the narrowness of the strategy pursued by Madoff.
Other market participants, including at least one major European dealer, have encountered similar results while trying to replicate Madoff's purported returns. In a whistle-blowing letter to the US Securities and Exchange Commission in 2005, Harry Markopolos, former chief investment officer at Boston-based Rampart Investment Management, also reported difficulty in simulating Madoff's performance. The strategy was "wholly inferior to an all-index approach" and "should not be able to beat the returns on US Treasury bills", he wrote.
Meanwhile, Markopolos noted, there were not even enough listed S&P 100 options outstanding to support the strategy, given the size of the Madoff funds. There was also unlikely to be enough outstanding in the over-the-counter markets, he believed.
Combined with other factors, this led him to conclude that "the world's largest hedge fund is a fraud".
Although the measures used in the research by Riskdata were no replacement for the kind of rigorous qualitative investigation pursued by Markopolos, according to Adlerberg, they proved the worth of straightforward quantitative tools.
Among investors, Madoff's healthy and consistent returns were the main reason his services were so highly sought after. Ironically, even on a simpler level, some market participants thought they were an obvious giveaway. One risk manager at a bank that ended up trading with Madoff initially blocked the move several years ago, reportedly emailing his colleagues the words: "Too good to be true."
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