# Does better mathematics win in the markets?

Last week, the US District Court Southern District of New York issued a judgement dismissing the US CFTC’s complaint of market manipulation against Donald R. Wilson and DRW Investments (h/t Matt Levine). Describing the CFTC’s theories as little more than an “earth is flat” style conviction, the court wrote:

It is not illegal to be smarter than your counterparties in a swap transaction, nor is it improper to understand a financial product better than the people who invented that product. In the summer and fall of 2010, Don Wilson believed that he comprehended the true value of the Three-Month Contract better than anyone else, including IDCH, MF Global, and Jeffries. He developed a trading strategy based on that conviction, and put his firm’s money at risk to test it. He didn’t need to manipulate the market to capitalize on that superior knowledge, and there is absolutely no evidence to suggest that he ever did so in the months that followed.

In August 2011, DRW unwound its swap futures trade at a profit of $20 million, and the CEO of the biggest firm on the other side Jeffries emailed Wilson: “You won big. We lost big.”. The mathematics behind this trade is well described in a paper by a well known academic quant and two quants who worked for DRW:

Rama Cont, Radu Mondescu and Yuhua Yu “Central Clearing of Interest Rate Swaps: A Comparison of Offerings” available on SSRN.

The purpose of this blog post is to ask a different question: how common is it for traders make money simply by better knowledge of the mathematics than other participants. My sense is that this is relatively rare; traders usually make money by having a better understanding of the facts.

Perhaps the best known mathematical formula in the financial markets is the Black-Scholes option pricing formula, and Black has described his attempts to make money using this formula:

The best buy of all seemed to be National General new warrants. Scholes, Merton, and I and others jumped right in and bought a bunch of these warrants. For a while, it looked as if we had done just the right thing. Then a company called American Financial announced a tender offer for National General shares. The original terms of the tender offer had the effect of sharply reducing the value of the warrants. In other words, the market knew something that our formula didn’t know.

Black, F., 1989. “How we came up with the option formula”. Journal of Portfolio Management, 15(2), pp.4-8.

Many years later, Black did make money with superior knowledge of the mathematics of option pricing. A well known finance academic Jay Ritter has described the sad story of being on the losing side of this trade:

I lost more in the futures market than I made from my academic salary. … Years later, I found out who was on the other side of the trades in the summer of 1986. It was Goldman Sachs, with Fischer Black advising the traders, that took me to the cleaners as the market moved from one pricing regime to another. In the first four years of the Value Line futures contract, the market priced the futures using the wrong formula. After the summer of 1986, the market priced the Value Line futures using the right formula. The September 1986 issue of the Journal of Finance published an article (Eytan and Harpaz, 1986) giving the correct formula for the pricing of the Value Line futures. In the transition from one pricing regime to the other, I was nearly wiped out.

Ritter, J.R., 1996. “How I helped to make Fischer Black wealthier”. Financial Management, 25(4), pp.104-107.

One person who did make money by understanding the mathematics of option pricing was Ed Thorp who kept his knowledge secret till Black and Scholes discovered their formula and published it. Decades later Thorp said in an interview:

… with blackjack, … I thought it was mathematically very interesting, so as an academic, I felt an obligation to publicize my findings so that people would begin to think differently about some of these games. … Moving on to the investment world, when I began Princeton/Newport Partners in 1969, I had this options formula, this tool that nobody else had, and I felt an obligation to the investors to basically be quiet about it. … I spent a lot of time and energy trying to stay ahead of the published academic frontier.

Consulting Submitter, Journal of Investment, “Putting the Cards on the Table: A Talk with Edward O. Thorp”, PhD (July 1, 2011). Journal of Investment Consulting, Vol. 12, No. 1, pp. 5-14, 2011. Available at SSRN

Academics in general have been content to publish their results even when they think it is worth a billion dollars:

Longstaff, F.A., Santa-Clara, P. and Schwartz, E.S., 2001. “Throwing away a billion dollars: The cost of suboptimal exercise strategies in the swaptions market”. Journal of Financial Economics, 62(1), pp.39-66.

Using unpublished mathematical results to make money often has the effect of destroying the underlying market. Nasdaq (which owned IDCH) delisted the swap futures contract within months of DRW unwinding its profitable trade. Similarly, Fischer Black effectively destroyed the Value Line index contract through his activities. Markets work best when the underlying mathematical knowledge is widely shared. It is very unlikely that the option markets would have grown to their current size and complexity if the option pricing formulas had remained the secret preserve of Ed Thorp. Mathematics is at its best when it is the market that wins and not individual traders.

PS: One of the things that has puzzled me about the DRW case is that DRW was a founding member of Eris which offered a competing Swap Futures product. Why didn’t anybody raise a concern that DRW and Eris were conspiring to destroy IDCH? Of course, DRW would have the compelling defence that with $20 million of profits to be made from the arbitrage, they did not need any other motive to do the trade. But still it bothers me that the matter does not seem to have come up at all.

Posted at 15:42 on Thu, 06 Dec 2018 View/Post Comments (0) permanent link