Yes, this is a problem we are all wrestling with. Everyone pretty much agrees that thr ground is really moving under our feet -- things are changing and rapidly, seemingly accelerating. The reasons are many from the geopolitics of the world to the mechanics of the markets with the nascent 24 hour trading day and electronic markets and new, conglomerate products, uptick rules, etc. My own take was that around '92 things started to shake and change, and it has gotten evermore tricky in that regard (I think everyone would have a different start date on that). I really had to develop a solution that would allow me to weather the worst conceivable case (provided I lived through it!) With that, I am clearly sub-optimal from a growth-maximization standpoint.
rvince99, IMO you are mixing up two different things: portofolio diversification through allocation and trading risk (of ruin) management. Portoffolio diversification deals with unsystemic risk. A well-diversified portofolio in inversely correlated assets protects capital from risk related to particular market sectors or asset classes. Trading risk management is a method for minimizing the probability of ruin or maximizing equity growth, or both (unlikely). Systematic risk cannot be diversified and portfolio managers can only hedge it (futures, options, etc.) The method you claim as new is the oldest one futures traders have been using for a long time to calculate position size based on maximum expected drawdown: Position size = Equity/(maximum expected drawdown*+ margin") * per contract This minimizes the risk of ruin from drawdown. Edit: This minimizes the risk of ruin from drawdown provided risk percent per position is kept low. Most experts suggest 1% or 2% maximum value.
I think readers of the thread should really go out and get a copy of "The handbook of Portfolio Mathematics," or at least find some papers on LSP by Ralph Vince, before commented on the seemingly obvious. http://www.amazon.com/Handbook-Port...=sr_1_1?ie=UTF8&s=books&qid=1242835009&sr=8-1 Try to be a little more open and just you might learn something from one of the more knowledgeable authors in this business. P.S. To RV and others, an example of a paper that you might want to look at to get a better feel on some alternative viewpoints to simple kelly sizing under continuous outcome distributions is the following: "The kelly Criterion for spread bets," by S. Chapman. In it he describes how the probability distribution of a positive bankroll varies with time and fractional kelly sizing. It is a more mathematical explanation of something I think a lot of experienced traders have come to realize about kelly. I also think it is related to RVs realization; although it is a bit more targeted to long run probabilities. Time is the major killer in harvesting profits while guaranteeing avoiding stepping on poisonous thorns, thought needs to be given on how to reasonably reduce that time factor.
http://eprints.maths.ox.ac.uk/594/1/43.pdf Anyone that wants to skip through the math should just focus on fig 2. cheers, dt
I'm not sure why this is particularly applicable - especially if it's for position sizing a strategy. The basics of kelly and all of its derivatives is that it's optimized for gambling, where randomness is iid (independently and identically distributed). This assumptions is false in general in asset returns and ESPECIALLY false in strategy returns. There are many instances of strategies where kelly's and its derivatives are the exact opposite of an optimal sizing strategy.
There may be some degree of serial correlation is some financial or strategy based return series (I assume that is what you are referring to?), but that doesn't preclude kelly concepts from being applicable. Again, I think that kind of goes back to your earlier observation on what the particular goal or notion of what an 'optimal' objective is. Rather than think of it as one 'optimal' point, some people like to view it as a 'cliff of death' (i.e. looking at the rolloff of the curve rather than focusing on the optimal point). There are good and bad arguments for kelly and much controversy; but, I think we have to evaluate the pros and cons (which both exist) and apply them towards our own goals. It is not an objective, 'one size' fits all solution. One of the benefits that appeals to me personally, is the idea of wealth preservation, not so much maximized gain.
Why not? Kelly is only optimal if returns are iid. iid isn't a fairly harmless conceptual assumption for kelly[*]. It's the a core concept without which it is no longer optimal or valid. [*] Try a simple AR1 model of returns. There are very wide ranges for the autocorrelation that would show that Kelly's has a negative expectation.
I think I get your reasoning. Would it be possible for you to post an AR1 series with a thousand or so data points using some real financial object (I'd prefer to see that rather than a modeled one) along with a plot of the terminal wealth (assuming geometric growth) vs. fractional bet size curve? I'm curious to see what the curve looks like. Forget the theoretical assumptions, we can simply look at a brute force sweep of the response. I can certainly see that an infinite series of negative returns compounded would produce a negative expectation, but I'm not so sure that reflects reality. Nor does it really reflect a 'general' model of typical return processes; it is a specific hypothetical case.