COINCIDENCE II

COINCIDENCE  II

Before getting into this matter (lucky traders) further, it will be useful to consider the card game Chancy. The rules of Chancy are simple. Spread before you is a well-shuffled deck of cards, face down. You play by drawing a card from anywhere in the deck. If it is a seven you earn no points. If it is above seven, then you earn the value of the card less seven (e.g., a Queen earns you five). If the card is below seven then you lose seven less the value of the drawn card (e.g., draw five and you lose two). After each turn, the card drawn is returned to the deck, which is then reshuffled. The winner is the player with the highest score after an agreed number of draws by each player.

Over the long run, you should expect your average score to tend toward zero, since the likelihood and size of earnings and losses on each draw is equal. But there is no impossibility in having a run of luck and accumulating a large positive score. On the contrary, the probability of any such run of luck can be calculated.

For example, the probability of five consecutive draws being earners (i.e., above seven) is 2%, and the chance of five consecutive draws being big winners (Jack or better) is 0.065%. This means that if a large number of people sat down to play a five-draw game of Chancy, you would expect 2% of them to draw only earners and 0.065% of them (1 in 1,500) to draw only big earners. These winners possess no skill lacked by the other players; the game provides no way for skill to affect the outcome. The winners have just been lucky, as we knew in advance some would be. Just as the rules of Chancy guarantee that, in a large enough sample, the average score will be zero, so they also guarantee that some players will be big winners.

Now, let's return to bond trading. How much it resembles Chancy is hotly debated. Those traders with "high scores" will assure you it is a game of skill, not luck. But that is irrelevant for the point I wish to make. Even if bond trading is a game of skill, you can still win by luck. The prices of bonds go up and down, by lesser and greater amounts. Even if a trader made her buy and sell decisions by tossing a coin, given enough luck she could still be a big winner.

Suppose, then, that you own or manage an investment bank. One of your proprietary traders has five consecutive big wins and earns your bank a fortune. Deutsche Bank hears of this incredible feat and attempts to poach him from you, offering a salary of $750,000 and guaranteed minimum bonus of $2 million. Should you top this offer to keep your star trader or cheerfully say goodbye to someone who has just had a run of luck that there is therefore no reason to believe will be repeated?

There are two ways to answer this skill or luck question. One was suggested already. If it is skill rather than luck, then this successful trading should persist. Observe your trader at work. If his success continues over very many trades and through different market conditions (trending, volatile, and so forth), then the probability that it is just luck will approach zero: he is clearly a wizard of finance.

The second is to think about what information is available to your trader and how he makes his decisions. Could he possibly predict bond price changes or follow a trading strategy that beats the odds?

Answering the skill or luck question is not easy. The expected random distribution of performance in bond trading is harder to calculate than the distribution of Chancy scores; the bond markets are more complex than this simple card game. So it will be correspondingly harder to tell whether or not a trader's performance can reasonably be attributed to luck. And this complexity also makes it difficult to know whether or not a trader's decision-making processes could possibly give him any advantage. Yet, if you manage an investment bank, you should try to answer these difficult questions. Otherwise, for all you know, you are paying people enormous salaries merely for having been lucky.

Remarkably, investment banks make no serious attempt to answer the skill or luck question. They simply assume that a run of success is evident of financial wizardry, even when the success would require only moderate luck. When the sums involved are large enough, even one or two wins will do. "Look, she has just made us $500 million. That can't be luck!" This is precisely what was said about several traders of emerging markets government bonds in the late 1990s-- only days before they lost their banks millions of dollars when the Russian government defaulted.

The strongest evidence that investment banks just assume success is due to skill is their habit of offering successful traders from competitor banks vast sums of money to switch employer. The tactics of these traders are a mystery to the bank that court them. Perhaps they bought when the coin landed heads and sold when tails. Their new employer neither knows nor, apparently, cares.

Investment bankers seem to agree with those primitive tribespeople who assume that any good or ill fortune that befalls someone must be due to some quality of the person-- that there is really no such thing as luck at all. In this spirit, I suggest a new line of business for them. Investment banks should employ former winners of Lotto (Lucky Draw) jackpots to buy Lotto tickets for them. No salary could be too high for these wizards of ticket selection.

Credits: Much of this article is extracted from Crimes Against Logic, by Jamie Whyte, 2005.