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Can you try to maximize the Ln(k*E), instead of (k*E)? I think you'll have the same results as Visaria and myself with Ln(k*E). K*E maximizes the bankroll, while Ln(k*E) maximizes the rate of growth.

Haha. Now that we are both geniuses, let's compare the results on this one: http://www.iqtest.com/prep.html?test=final It's decidedly more difficult. I got 114 on that more difficult one.

What you set up is not the risk/reward parameters, but the target profit and target loss. These targets have different probabilities of being reached. The expected value of these parameters is zero gain, minus the commissions. If this game was as simple as setting up the target profit and...

Yours is the one that you stated in the opening post.

There are many ways, but yours is not one of them.

The Sharpe Ratio remains the standard, despite the criticism of its properties by some market practitioners. No. There is nothing in there that constitutes an "edge".

My Monte-Carlo simulation agrees. Here are the top 10 strategies, if betting on Red is not allowed: R16 R14 Score 8.4 5.7 8.009759 8.5 5.7 8.009752 8.4 5.8 8.009728 8.5 5.8 8.009715 8.3 5.7 8.009667 8.4 5.6 8.009662 8.5 5.6 8.009660 8.6 5.7 8.009647 8.3 5.8 8.009641 8.6 5.8 8.009606

One more adjustment needed, I think. In this particular problem, all betting strategies have the same number of betting opportunities. But what if we wanted to compare trading strategies with different number of trades? Since Sharpe increases with the square root of observations, I am adjusting...

Damn it, I had a bug in the calculation of standard deviation. After fixing it, here is what I get by maximizing Log(Sharpe): R16 R14 Red 7 5 11 7 5 10 7 5 12 7 5 9 7 5 13 8 5 11 8 5 10 8 5 12 8 5 9 7 5 8 Based on the results, my point is still valid (I think).

Okay, I think I am breaking new ground in computational finance. Let CK be the continuous Kelly, R be the return over a given period, s be the standard deviation of returns, r be the average return. First, I realized that my proposed performance metric: Performance Metric = CK * R = (R * r) /...

Yeah, that was the simplest thing to do, and it is a good approximation of the solution, which is 8.108% on R16, 5.405% on R14, 10.811% on Red.

My initial result of the Monte-Carlo came out nonsensical. I think that's because the quantity (R * r) / (s^2) does not make sense when r (average return) is negative. I need to figure out how to penalize it correctly, so that the average calculated metric over many trials makes sense.

Well, I am trying to convince myself, too. To this end, I am going to apply the metric (R * r) / (s^2) to the original problem, and see what I get. If I come up with {R-16: 8%, R-14: 5%, Red: 11%} as the top strategy using this metric, that would confirm its validity.

Thank you for your feedback, SplawnDarts. With regards to the "number of opportunities", I think it's already (implicitly) incorporated in the proposed metric: Performance Metric = CK * R = (R * r) / (s^2) That's because R is (in an arithmetic return sense) equivalent to r*N, where N is the...

Haha, yeah, you get used to familiar things. Okay, I think we nailed this problem, with a combined effort. What makes it very interesting is that it is related to the real-world trading strategy selection problem, which is this: Given N different trading strategies, which criteria (or...

What's the K*E for {R-16: 8%, R-14: 5%, Red: 11%} ?

Did you arrive at 1/5 to 1/10 Kelly analytically, or is it just a gut feel? Do you use discrete or continuous Kelly?

This should be: x + y + z <= 1

I managed to crash my machine twice, because I was doing so many simulations, but I think I've resolved the discrepancy. Your top result (maximizing the F(), numerically): {R-16: 8%, R-14: 5%, Red: 11%} My top result (Monte-Carlo, utility function is the average log(endingBankroll)): {R-16...

Actually, I know why. I am ranking the strategies based on the mean profit, while you rank them based on the compound rate of return.