From the December 01, 2011 issue of Futures Magazine • Subscribe!

The law of large numbers and avoiding the Siren’s song

New voyage

Neil is ecstatic. He’s heard the siren’s song and is ready to jump overboard. Along on this voyage are four other traders. Unfortunately, their ears are not filled with wax.

Tuesday, Oct. 4, 2011 arrives. Everyone is trading merrily along in either the E-mini S&P, the Russell or the Euro, and it is roughly 2:40 p.m. Chicago time. The stock market is in a downtrend on the hourly, daily, weekly and monthly. The five-minute just touched the moving average on a rally. The conditions set up for a trade and Martin yells to his devoted new acolytes: "Go!" All short one E-mini SP or Russell 2000 contract except Neil, chained to his personal mast. Neil refuses to enter a trade after 3:30 pm Eastern because another former guru told him not to. The market rises 20 ticks. They short three more. It rises another 20, they short 12 more. There does not seem to be any reason for the rise. It adds 20 more ticks, they short 48 more. Another 15 seconds later, it goes up another 20, so they add…wait for it… 192 contracts. The market goes up another 20 in less than 30 seconds. All four students are shut down by the brokerage firm.

Guru Martin, however, has a bigger account. Lucky for him. He adds — sit down before you read this — 768 contracts, giving him a total of 1,024 contracts! The market continues to rise 11 more ticks and the broker closes him down. "Road to ruin" (below) shows how it ended at 2:46 p.m. Chicago time.

Martin Gale lost $226,050 at $12.50 per tick in a six-minute period, plus commissions and slippage. And, it only took six failures of the hypothesis for Gale to be blown away. Even if his system has a respectable 60% success rate, it has a 40% chance of losing on any one decision. The chances of losing on six consecutive decisions are 0.41%. Although it sounds small, that is one time in every 200 series of tests. Roughly one time every six months of trading Martin will get wiped out. And, it’s good the broker stopped him out. The market continued to soar an additional 150 ticks thereafter (see "It only gets worse," below). All of Martin’s legendary profits were gone in one trade in under 10 minutes, because the "impossible" thing happened.

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