Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

Of percentages, decimals, SEC and Rosenberg

Whether interest rates, volatilities and other similar numbers are expressed as percentages (say 6%) or as decimals (say 0.06) is a trivial yet vexed issue in finance. I always remind students that when they use an online option pricing calculator, this is one common source of error (the other common source of error is to use an annually compounded interest rate where the software expects a continuously compounded rate).

But even I never thought that confusion between percentages and decimals could cause $216 million of losses and an enforcement action by the US SEC. And that too at Axa Rosenberg Group – the firm that (under its original name Barr Rosenberg Associates or BARRA) pioneered quantitative portfolio management and risk measurement for institutional investors.

The SEC described the coding error as follows. (BRRC stands for Barr Rosenberg Research Centre, a subsidiary of ARG which stands for Axa Rosenberg Group):

In April 2007, BRRC put into production a new version of the Risk Model. BRRC had assigned the task of writing the computer code that would link this new Risk Model with the Optimizer primarily to two programmers. Although BRRC tested the new Risk Model, it did not conduct independent quality control over the programmers’ work on the code. When these two programmers linked the Risk Model to the Optimizer, they made an error in the Optimizer’s computer code. …

Starting in 2009, a BRRC employee began work as part of BRRC’s effort to implement a new version of the Risk Model. In June 2009, this employee noticed certain unexpected results when comparing the new Risk Model to the existing one that was rolled out in April 2007. He learned that the Optimizer was not reading the Risk Model’s assessment of common factor risks correctly because an error in the code caused a failure to perform the required scaling of information received from the Risk Model. Some Risk Model components sent information to the Optimizer in decimals while other components reported information in percentages; therefore the Optimizer had to convert the decimal information to percentages in order to effectively consider all the information on an equal footing. Because proper scaling did not occur, the Optimizer did not give the intended weight to common factor risks.

The SEC goes on to describe the cover-up as follows:

The Senior Official and other BRRC employees met around the end of June 2009 to further discuss the error. The BRRC employee who discovered the error advocated that the error be fixed immediately. The Senior Official, however, disagreed and stated that the error should be corrected when the new Risk Model would be implemented. The Senior Official directed BRRC employees with knowledge of the error to keep quiet about the discovery of the error and to not inform others about it. The BRRC employee who discovered the error asked the Senior Official whether ARG’s Global Chief Investment Officer (“CIO”) should be informed, and the Senior Official instructed that he should not be told.

The SEC does not identify the “Senior Official” who tried to cover up the error, but last year Axa Rosenberg stated that Dr. Barr Rosenberg himself was involved in the cover-up and had resigned.

More than the trivial error itself, what is so tragic is that such a distinguished academic (whose papers I have been reading and enjoying for over 25 years) should try to cover up the error.

As an aside, in a case which is all about scaling errors, the SEC order itself contains a ridiculous scaling error – it states that the losses were $216,806,864 million. That would be $216 trillion which is well in excess of the total stock of financial assets in the world. I presume that the true losses were $216,806,864 or $216 million. I suppose this is fine unless the SEC tries to cover up this error.

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One response to “Of percentages, decimals, SEC and Rosenberg

  1. Richard Careaga February 4, 2011 at 11:50 pm

    All big numbers are the same big number without trying really hard. I’m sure that the supposedly significant digits, which are in the Magic Number Seven Plus or Minus Two range, were carefully checked, which is a shame because, of course, the “losses” were not measurements but differences between the outputs of two programs, which where themselves not measurements but models.

    We’d be less likely to fall into the big numbers trap if we still used powers of ten for anything over 9,999, say. Saying that the estimate of loss was 2 * 10^8 is both briefer and more informative than that “losses were $216,806,864.”

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