> 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. It can be, but again this is not an absolute rule. always remember that the model (and associated assumptions) are not the data, and model does include ways of projecting future risk and future profits. eg Even if OP strategy A and B were traded on the same security (which he doesn't say), AND both A and B had the same sets of model assumptions and thus risks but produced different return curves (eg say if one had it's parameters optimized but the other didn't), it could be true (that time and risk were correlated). However as mentioned above, there are many examples where this is not true. Of the possible universe of all strategies you will find many assumption profiles. iow This is a big mixed bag of strategy fruit, and assumming otherwise that we only have apples- no oranges- and thus all the apples and their profit and risk can be interchanged always in all cases... this type of thinking is what led to subprime meltdown.
Yes, both A and B trade the same instrument. I am surprised that you guys are not universally convinced that the shorter trade duration is preferable. Let's make the difference between A and B a little more pronounced. With everything else being the same as before, strategy A average holding time is now 1 minute, while strategy B average holding time is 1 year. To me, it's quite obvious that strategy A is superior to strategy B. Strategy A has less P&L variability while in an open trade, and it ties the capital to a given trade for much shorter periods of time.
============= Well short term congrats, on being a market maker , more or less. But for those who are not market makers; time frames longer than 1 minute captures more trends, less comissions. Wisdom is profitable to direct
All you have done is listed "reasons" YOU THINK strategy A is preferable. The OP asked how to quantify the strategies. Duration of hold by itself DOES NOT mean the strategy has less risk other than the form of exposure risk = exogenous event/news risk. I still think some form of "beta", maybe even a dynamic beta needs to be used for a normalized equation. This type of math is not my forte so have at it. Ummm, Duh. Less trading = less commissions. Imagine that. BUT, Commissions should NEVER be a consideration for taking what YOUR methodology/system deems a good trade, which can be ANY time frame your methodology/system uses. Trade On!
I am the OP, and yes, my motivation is scoring the trading strategies (I have literally tens of millions of them during the optimization) in such a way that takes average position holding time into consideration. Along with other factors, it would form a "cost function", or a strategy performance score. So, you think that holding time should not be a factor at all? Lacking the statistical foundation of how to evaluate risk as a function of position holding time, I've decided to let my intuition guide me. So, going back to the original strategies A and B (holding times are 4 and 16 minutes, respectively), I've figured that the factor improvement of sqrt(sqrt(time1)) / sqrt(sqrt(time2)) is just about right: sqrt(sqrt(16)) / sqrt(sqrt(4)) = 1.41 From this formula, strategy A would score 1.41 times better than strategy B, if everything else between A and B is the same.
In case anyone is interested, my entire strategy scoring function looks like this: score = 100 * (K * P) / D where K = pp - (1 - pp) / (averageProfitableTrade / abs(averageLosingTrade)) P = sqrt(trades) * (netProfit / trades) / stdev D = sqrt(sqrt(averageTradeDuration)) pp = numberOfProfitableTrades / trades trades = total number of trades stdev = standard deviation of all trades
Au contraire... I am an intraday index futures trader. Holds are from seconds to maybe a couple hours. I've not been able to quantify which trades are "better". I'd like too! But using time alone is misleading and inaccurate. Even with the same instrument. Let's use an instruments RTH range for a simple example. If the RTH range is say 100 pts (like YM), and strategy A (4m) nets 5 pts and strategy B (16m) net's 40 pts, time alone is not the correct measure of performance... In this case using time only, strategy B would be superior! Now what about days the rth range is narrow? All I'm saying there needs to be some sort of "beta" factored into the equation. Exactly what I don't know, I used the rth range only as a very simplistic example of what I think. Trade On!
Right. But I stated in the very first post, both A ad B have exactly the same performance stats, including average gain/loss, number of trades, max DD, net profit, etc. The only difference is the average holding time. So, going by your YM example, let's say both A and B capture 20 points. Strategy A does it in a 4 minute single trade, and strategy B does it in a 16 minute single trade. The question is, again, "by what factor is strategy A better than strategy B?" My answer is, "1.41 times better". I'd trade both, but I'd allocate 1.41 times more capital to strategy A.
I won't argue on a subject (quant math) I readily admit I'm challenged with. But to me, your usage is merely determining an optimal "hold time" (with all variables being equal, which is black swan in and of itself imo). The fact you are using it as a sizing calculator is your thing. Anyway, you know what they say ... whatever works works. Trade On!
You should think about your opportunity cost (what you be doing with your capital when you are out of the trade) and how many trades you get to take with each system. Maybe you could look at a day as your unit instead of a trade. For the time you are not in your trade assume you are in cash (or in your next best system if you want to get fancy), then calculate a return for the whole day. Then compare your string of daily returns for strategy A and B with your favorite performance metrics.