Let's say you have trading strategy A and trading strategy B. The performance stats (such as net profit, max DD, profit factor, number of trades) are exactly the same. The only difference is that strategy A holds a position for an average of 4 minutes, while strategy B holds a position for an average of 16 minutes. Intuitively, strategy A is preferable to strategy B, because it's less exposed to the market. But what if you wanted to quantify this? Namely, by which factor strategy A is better than strategy B? 4 times better (16 / 4 = 4)? 2 times better (sqrt(16) / sqrt(4) = 2)?

It's a good question. I'm not a math guy so I won't even attempt to give you a formula, but it seems some sort of "market beta" (or something denoting market time exposure risk) should be included to normalize the equation. Just my 2c Trade On!

The performance stats you mention are not valid. They are, however, accepted by the entire finncial industry. The basic reason is that the FI is sales oriented and not really performance oriented. If you wish to actually use a standard of performance, you can use the market's offer and make a comparison to what you are achieving in that manner. Presently, some books and experts consider a business's annual performance successful if it makes about 3 hours (about 1/2 a day) of the market's offer in a year. You mention market exposure. In the two limits, 100% and 0%, more exposure seems inherently better if you are always taking the market's offer. I design my systems with that in mind. I go in on the open and stay in all the time that day margin is available. My trading segments are arranged to anticipate the market sentiment.

tiddlywinks is right, the length of holding is not frequently the best proxy for risk unless A and B. eg if B is trading something 10x more volatile than A then the length of holding doesn't factor much. even if A and B are trading the same instrument, the actual risk (in terms of loss of capital) is more factor of vol. eg if you trade something that only moves a few cents a day, holding for 4 vs 16 minutes isn't going to be much different. likewise for high vol securities, the risk comes from vol more than the time. still there are many different formulas to approximate prob of loss in something... VaR is designed exactly for this purpose and monte carlo simulations can also be used. if you're looking for a quick approximation, you can use beta as tiddly winks suggests or the std deviation of up/down movements of the security or portfolio in question. idea is to use a vol measure that tracks risk perceived by your strategy class without being tied a particular timing method... sometimes trading platforms will report these as stats. you can lookup the formulas for beta, stddev and var in google. all of them rely on parametric analysis meaning they're subject to statistical sampling errors and fat tail risk. you can find non parametric techniques/formulas by adding that term to your queries.

The Volatility term scales with SQRT(time) in some price models. So in one sense at least, the 16 minute system is exposed to twice as much potential stochastic change as the 4 min system. Which is what you're saying, i.e. that it's exposed longer to the risk of the market ... so the other is better in that sense ...

abattia wrote : > Volatility scales with SQRT(time). not correct, see my post above. believe abattia confusing modeling with data... in certain data models (eg ones based on CLT and normal-like distributions), vol scales can scale with time but that is a function of the model NOT any fundamental rule about volatility. see here for more info : http://www.wilmott.com/messageview.cfm?catid=8&threadid=80317

Ha ha! Yes ... I had edited my original (incorrect) post from the one you quoted ...but, yes, the original was wrong ... and the modification is perhaps only marginally less erroneous ... and thanks for clarifying ... and I stand corrected ... and all that ... But if we ignore terminolgy for a moment ... at an intuitive level, the longer I am in the market the more oportunity there is for the unexpected to occur ... so, all other things being equal, getting the job done quickly ought to be better than getting it done more slowly, no?

It's not the time exposed it's the risk exposure. Let's say strat A trades 1 minute before non-farm payrolls and BoJ rate announcements, and strat B grinds out ticks on globex after hours by fading stop-loss spikes. Strat B is about 10+ times less risky than strat A. It is trivial to have a strategy which holds assets for months and is far less risky than one that holds for seconds. Timeframe is NOTHING to do with risk.

It's the ratio of 'unexpected risk' to profit potential. If being in the market 10 years increases your profits 10 fold and your risk 5 fold, then per unit risked it is half as risky as something that holds for 1 second.

no worries, the wilmott thread above also touches on why there is a misconception about this. "so, all other things being equal, getting the job done quickly ought to be better than getting it done more slowly, no?" Yes this is true for a given strategy and profit targets, but it's independent from the risk of the actual security. Eg if your goal is to make X dollars and you can do it in with strategy A in Y time or B in Y/D time (where d is natural number), choosing the second option will maximize your profits over time and also minimize your assumption risk (assumption risk = the "known unknowns" associated with your particular data model and "unknown unknowns" inherent to any business activity, like probability of an asteroid hit). These choices introduce additional optionality that has nothing to do with the choice of security. I think another reason people get confused about this is because they hear that avoiding overnight positions limits risk. This isn't mathemetically true though because you can construct long term portfolios that have less risk than portfolios which are held for seconds or minutes. I think it's a case of reading more from daytrader materials than portfolio finance (or knowing that a rule of thumb isn't absolute/precise like a proof). eg rules of thumb like Market risk from having overnight positions comes not from the extra time of being in the securities but from news can come out after market that you can't react to. This isn't a function of time, but on the rules of trading a particular market. If you're trading something that is 24x7 or close to it (like FX), or you're trading futures with fixed price movements... these all affect the maximum risk (and upside) for a particular security that are independent of time.