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This had been done countless many times in various forms and shapes. What's new?

-- If the optimization time period is too short, there would be too few trades, and thus the statistical significance would be low. -- If the optimization time period is too long, you get statistical significance because of the large number of trades, but lose on the "adaptation", because...

You are trading about 10 times too large. Look up the term "volatility drag".

I used to be uncomfortable with that notion of the constantly changing risk/exposure. But then it occurred to me that this is how it should be. Your total exposure *should* be proportional to the payoff probability/magnitude. There is nothing wrong with it. I run an automated system which...

Here is a recent paper on the subject: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2259133 The author makes use of the Kelly criterion to numerically figure out the asset weights. That is, he is looking for the maximization of log(R), where R is the portfolio return. Interestingly...

I agree there is no easy answer. What's special about case (b) is that some strategies may want to be long instrument I, while other strategies may want to be short the same instrument I, at the same time. This makes it unclear how to to approach this from the capital allocation angle. If...

In the classic case (Merton-Markowitz), you allocate your capital to N assets simulteneously, and hold these assets until the next optimization period. This is different from allocating capital to N trading strategies, because it doesn't make sense to allocate capital to any strategy before it...

I will try to simplify the problem statement for the OP. Consider two trading strategies, S1 and S2. They trade in different time frames, so the frequency and duration of trades produced by S1 and S2 are different, but possibly correlated (positively or negatively). Given the finite amount of...

Here is an interesting math problem. If the average survival rate among daytraders is 5%, what would that rate be among those who take a 26% APR loan to get started in this business?

"Reg T EWL" = Regulation T Equity with Loan Value. Depending on your account size, you have certain rules to follow. The greater the account size, the less restrictive the rules are. These rules are put there by regulators to presumably protect yourself from blowing your account. "SMA" =...

After a ton of testing of various return distributions, I believe I came up with something sensible. The balance between the risks and the gains is found in what I call optimal leverage, which can be calculated as follows: Let R be the distribution of trade returns: R: {r(1), r(2), r(3), ...

The difference between the geometric and arithmetic means becomes large (and one might say it becomes profound) when the returns are leveraged. If you make 70% gain in one period, followed by the 70% loss in the next period, the arithmetic mean is 0%, while the geometric mean is -28.6%. This...

Correct. Yes, what we are looking for is the max distance between the thick blue curve and the straight red identity line. That would be: Max[CR(L) - (L * slope)] with respect to L.

Okay, here is the quantification. I'll try to be very precise and detailed, to avoid any ambiguities, so that the results can be reproduced by anyone who wishes to try. Let R be a series of trade returns: R: {r(1), r(2), r(3), ..., r(N)}, where N is the number of trades, r(i) is the return on...

I am thinking perhaps this revised version makes more sense (see below). The "spirit" is still the same, which is to maximize the distance between the red identity line and the risk/reward curve. The change is that instead of the maximum North-West distance, this version uses the maximum...

Okay, I understand now. Those perpendiculars are no longer perpendiculars when you change the scale. That's a good point. You are right, it has to be scale-invariant.

Ralph and I have a different definition of the "optimal point", so I am not sure which one you are questioning.

Understood. The novelty of your determination of the optimal leverage is that it's a function of the time horizon (and not just the function of the returns distribution). Your optimal leverage is equal to full Kelly when time horizon is infinite, and is less than full Kelly when time horizon is...

Stepan, can we please discuss this in some other thread? I really hope that we can stay on topic.

It looks like the convergence is very fast. After some 20 periods, it would be almost indistinguishable from the infinite horizon, correct? I am including the figure from one of your papers below (hope you don't mind). In my case, the number of periods is around 300.