Welcome back – it’s been far too long!

Hi simplex,

For the discrete formula, see the variables provided by gg53 two posts up.

For the continuous formula, you need an equity curve. Convert it to returns by taking the difference between each period. Compute the average return. Compute the variance of the returns. Apply the formula f* = average(returns)/variance(returns). To get half…[Read more]

Yes that’s the simplified version of the discrete Kelly formula. It assumes you have only two discrete outcomes. See the Thorp paper for more details on this. Try comparing the resulting f* in the formula above to the f* calculation for continuous Kelly.

Hi gg53,

Half Kelly is prudent as you reduce your variance of returns by 1/2 but your expected long-term growth rate is reduced by only by 1/4, so a good trade-off. Half Kelly is also prudent because by underestimating the maximum size that should be traded you protect yourself against an overly optimistic estimate of future system returns…[Read more]

You might try out a simple program posted on FF a while back called, “Mr Kelly” on FF as a means of doing some simple simulations to get a feel for how it places its bets according to account size and payout. I believe this simulation uses discrete Kelly.

http://www.ff.com/showthread.php?t=185228

When you describe “MAXIMIZE geometric return” it sounds like you’re referring to Kelly. Are you using discrete or continuous Kelly for your calculations?

The only other way that I know of to maximize return in some optimal sense is by using Markowitz. But Markowitz generally is thought of more in relation to a portfolio than to a single…[Read more]