Bernie Madoff’s con rested on an illusion of terrifying simplicity: returns that were too perfect. Stock market performance that defied all logic, rising smoothly, year after year. Investors fought over his products, believing in a financial genius able to tame the markets.

So could Madoff’s Ponzi scheme have been spotted earlier? The answer is an unambiguous yes, and very simply. Running the full method took me a few dozen minutes.

1 - The data

Let’s take one of the last reports from one of the Fairfield Sentry Ltd funds, handed out to clients. And look more closely at the performance.

Drop that into a spreadsheet and you can lay it out month by month, easily.

Just doing that already reveals something very unusual.

Performance of Madoff’s fund and of the S&P500 from December 1990 to October 2008

What is strange is not so much that the fund beats this arbitrarily chosen index… it is that no index and no fund grows in such a straight line. That alone should have alarmed anyone, but the point has long been documented.

Because Madoff’s fund used a split strike strategy, also known as a protective collar, which limits losses. Roughly²⁶:

• You buy shares: if they go up, great; if they go down… you get the idea;
• You protect yourself with a PUT option as insurance: if they fall too far, you can sell at a minimum price;
• You sell a CALL option: you set a maximum selling price, so you cap your gain, but you pocket a premium as soon as you sign;

So inevitably, all this costs a bit and seriously caps performance… but above all, the strategy depends heavily on the market, and on the equity market in particular… since the fund was buying shares in the S&P100²⁷.

2 - Applying Benford

So what does Benford say? Well… he is adamant.

First Digit Test - Madoff’s blue curve does not look consistent with Benford’s reference figures (pink bars)

Second Digit Test - Madoff’s blue curve clearly shows a statistical anomaly at 7.

First & Second Digit Test - Once again, the anomaly in Madoff’s curve is glaring.

Obviously you cannot conclude there is fraud on this basis alone, but this little manual calculation, done in a few dozen minutes with public data and any old spreadsheet, should have pushed any regulator to ask the question.

All the more so as running the same exercise after 5, 10 or 15 years of performance gives the same result: there is a clear statistical anomaly. And several studies have shown that this had been the case for quite a few years, and across several funds²⁸²⁹.

More thorough tests, including Pearson’s chi-square and the Kolmogorov-Smirnov goodness-of-fit test, applied to Madoff’s returns, confirmed that his data did not follow Benford. These tests showed statistically significant gaps from the expected distributions, further strengthening the case for system(at)ic manipulation ³⁰.

Benford could therefore have been a key tool in detecting this monumental fraud. Yet it was not the only red flag. There were other signals: the lack of transparency about trades, the feeder fund structure that kept investors away from the real performance, and Madoff’s refusal to be independently audited. On top of that, several investigations showed that the SEC had known for years, and did nothing.

The numbers were already screaming fraud. If only someone had taken the time to listen.