Ironically, the better the system (like in sharpe terms) the deeper the aggregate drawdowns become because it is able to tolerate them and still recover to new equity highs. I wouldn't be surprised to see 90% drawdowns near the optimal (optimized only for returns) point.
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Risk (pain) vs Reward (gain)
- Thread starter nonlinear5
- Start date
Ironically, the better the system (like in sharpe terms) the deeper the aggregate drawdowns become because it is able to tolerate them and still recover to new equity highs. I wouldn't be surprised to see 90% drawdowns near the optimal (optimized only for returns) point.
Ironically, the better the system (like in sharpe terms) the deeper the aggregate drawdowns become because it is able to tolerate them and still recover to new equity highs. I wouldn't be surprised to see 90% drawdowns near the optimal (optimized only for returns) point.
This has been well studied. Indeed, for full Kelly leverage (the red point), there is 10% probability of a 90% drawdown. That's why I want to move to the left of the curve.
It still somehow feels like an artificial exercise to me, but haven't had use for leverage so don't know much about it.
If you trade (or invest), it means you use leverage. It may be less than 1, but it's still leverage. Leverage is simply the market value of your position divided by your account size. For example, if you have $10,000 account, and buy 10 shares of Apple at $100, then your leverage is
(10 * $100) / $10,000 = 0.1
2/0.2 reward:risk = 10. Good luck with buy and hold.
That was my initial reaction but it's become clear he is talking about an aggregate performance over some period of time. That is, the "reward" is net returns after a year (or whatever).
You need a better, more specific definition of "optimality". What you're possibly looking for is an inflection point, I guess. Until you hit that point, for every incremental increase in risk, your increase in reward is bigger than the previous iteration. That is "optimal" could be the point where you maximise your marginal return on risk. But it's you who has to define it...
This, like expectation, like risk of ruin or drawdown, like the expected growth optimal-quantity to risk itself, is a function of horizon (contrary to those who believe in the Kelly Criterion, which is asymptotic, and not directly applicable to capital markets to begin with). If you have a horizon as part of your criteria in trading, that inflection point's determination can be found here:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2230874
That was my initial reaction but it's become clear he is talking about an aggregate performance over some period of time. That is, the "reward" is net returns after a year (or whatever).
Yes.
More precisely, the reward (gain) is measured as log(R), where
log() is the natural logarithm,
R is the total return over the entire period.
The "optimal" point on that chart would be as far to the left as possible. As your slope turns you are getting less "bang for your buck" than simply leveraging the position.
True only on the first trade. After some t trades, that point beings to migrate "rightwards, and has, as its asymptote (as t->infinity) the expected growth optimal peak.
This, like expectation, like risk of ruin or drawdown, like the expected growth optimal-quantity to risk itself, is a function of horizon (contrary to those who believe in the Kelly Criterion, which is asymptotic, and not directly applicable to capital markets to begin with).
Correct. The Kelly properties (such as 10% chance of 90% drawdown, for example) are derived from the infinite horizon.
If you have a horizon as part of your criteria in trading, that inflection point's determination can be found here:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2230874
rvince99, are you Ralph Vince? Thanks for the reference, I'll take a look.
I see, so this is showing diminished aggregate return over a period of time for a large number of trades based on some leverage level proportional to your x?
You might then want to read Ralph Vince's books on optimal f. He is the guy that worked with Larry Williams when he was entering the futures world cup. They were looking at an approach to risk similar to Kelly betting. Their intent was to maximize the odds of winning (max return) in a short-term contest with a small account but the information can be useful in general.
Oly, the book that covers a lot of what is in this thread is the "Risk-Opportunity Analysis" book, which is also the least expensive, and covers this stuff in-depth without being a composite of academic papers. As I read this thread, I think too a point called the "zeta point" might be of interest to some on this thread too, (since one of the themes of this thread is optimal quantities where the criterion is not necessarily expected-growth optimality) it's the point where the ratio of reward-to-risk is maximized, and resides between the inflection point and the expected growth-optimal peak. I'm not trying to hustle the book (there is no money there for me, believe me) but rather put it together to bring the math of this stuff into one place. There are many very interesting applications of this stuff beyond trading - from population and pathogenic population growths, federal debt service reductions even a wider lens on Fisher's Fundamental Theorem on Natural Selection. So the book is presented in pretty fundamental terms and as a trailhead to these ideas if you're interested. If you're interested in some of the academic papers belying these ideas, those can be downloaded at my website www.ralphvince.com. I'm not trying to hustle you guys on anything here but some of these ideas.