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March 9, 2009

A Dollar and a Dream

Why P&L doesn't always tell the whole story

By Dan Mathisson

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Everyone still loves a winner. Even in these dark times on the Street, as careers grind to a halt, deferred compensation plans wither on the vine, and politicians and editorial writers rail against bonuses, Wall Street remains proud of its strict merit pay model. We are rightfully disdainful when we read of how the teacher unions fight merit pay, terrified of being

individually judged by objective criteria. Wall Street, on the other hand, has long thought of itself as the polar opposite. Sought out by the ambitious as the ultimate meritocracy, it is a place where a rock star on the trading floor can make 10 or 100 times what the next guy gets. Firms brag about their "eat what you kill" culture: Make money and get paid a lot, lose money and get shot.

The Fittest

Traders choose their counterparties with a similar ruthlessness. Algorithms and crossing systems that produce regular good results get richly rewarded with flow, while weak algorithms are shunned like the money-losing traders, with volume gradually drying up as the business unit inevitably atrophies.

And mostly this system of "survival of the fittest" works, until you confront something known as the "reverse lottery" problem, and realize that there is a hole in the logic of paying people and allocating flow based strictly on results you can see. The hidden flaw is that in probability games, observed outcomes often obscure an ugly reality.

For example, let's say I walk into my friendly local casino. I wander over to the blackjack table and begin playing, betting $50 at a time. I have a very simple strategy: As soon as I am up $100, I will immediately stop playing, get up from my seat, and walk out of the casino for the day. But if I am losing, I will doggedly continue playing, digging myself into a deeper and deeper hole until I either rally back and make my $100, or until I bankrupt myself by blowing my full $100,000 credit line.

The asymmetrical payouts in this game make it far more likely that I'll be a winner. Win two quick hands and I've made my money for the day. But to lose, I need to lose 2,000 more hands than I win. So while my expected profit for the long run is exactly zero, on any given day, I have a 99.9 percent chance of walking out up $100 (making a few simplifying assumptions). If I played every workday, there is a 78 percent chance of wrapping up the year having made $100 each day for all 250 business days, producing $25,000 in profits. And since most days I will have barely dipped into my credit line, my likely return on average capital would be well north of 100 percent.

Reverse Lottery