Should you Trade with the Kelly Criterion?
Find the optimal leverage and apply it to the S&P 500
The Kelly Criterion gives an optimal result for betting based on the probability of winning a bet and how much you receive for winning. If you check out Wikipedia or Investopedia, you’ll see formulas like this:
f*=p−(1-p)/(b-1)
which gives you the optimal amount to bet (f*) given the probability of winning (p) and the payout you’re given for the bet (b). For example, if you have a bet that gives you a 52% chance of winning and you have 1:1 odds (bet 1 to win 1 and your money back, so you get a total payout of 2), then you should bet 4% of your capital on each game (0.52–0.48/(2–1) = 0.04).
This is fine for a binary, win-lose outcome. The trouble is, investing in stocks don’t follow this simple model. If you make a winning trade, you could get a 10% return, 8% return, 6.23%, 214%, or any other value.
So how do we change our binary formula to a continuous model?
Continuous Kelly
Ed Thorpe and Claude Shannon (yes, the Claude Shannon for us nerds out there) used the Kelly Criterion to manage their black jack bankroll and clean up in Vegas in the 60's. Seeing the applicability of this method, Thorpe extended it to…
