Saturday, November 14, 2009

Following Kelly

In professional gambling, the Kelly formula is frequently used to determine the proper wage size to maximize bankroll growth rate. The formula is:

f* = The fraction of a player's bankroll which should be wagered.
b = Odds the player is receiving on the wager. 1 to 1 odds would be 1.  2 to 1 would be 2.
p = The probability the player will win the wager.
q = The probability the player will lose the wager.

For even money bets, or 1 to 1 risk reward trades, formula can be simplified to:

f* = 2p - 1

Most gamblers view Kelly betting as being very aggressive and many gamblers like to bet half-Kelly to minimize variance.  Based on this formula, most good traders are underbetting their bankroll.  I would venture to guess very good traders have a 60% probability of winning on their 1 to 1 risk reward trades.

f* = 2(0.6) - 1 = 0.2.

So these traders should be willing to risk 20% of their bankroll in that case.  Or 10% in the case of half-Kelly.  Personally, half-Kelly seems to be appropriate given the tail-event risk of trading in the financial markets not found in blackjack.  But I often hear 2% or 3% of a bankroll should be risked on any one trade.  I believe that's way too low for good traders and it will take you too long to make good returns.  In order to make money fast, one has to bet big and deal with some drawdowns along the way.
There is a Kelly calculator that shows you the proper wager based on probability of winning and odds for winning.

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