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Expectancy and SQN
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Expectancy and SQN

  #1 (permalink)
Fortitudo et Honor
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Expectancy and SQN

Can someone please walk me through the calculation for SQN.

I can calculate my expectancy, but I have no idea what a "decent" expectancy happens to be.

The SQN is the root of the trade number (N) multiplied by the expectancy in R multiples? divided by the standard deviation of (net profit/trade) in R multiples? R is your initial risk on a trade (what exactly is that? The position size? The margin requirement? The initial stoploss?

Is that correct? I don't understand the convention that's used in the formulas I've seen. What the hell is trade P/L? Is that net profit/trade?

Also, here is the metric/grading chart I've seen for Expectancy to Standard Dev R:
1.6 to 1.9 (poor but tradeable)
2.0 to 2.4 (average)
2.5 to 2.9 (good)
3 to 5 (excellent)
5 to 6.9 (superb)
7 and above (holy grail).

Apparently, the more important number removes the square of trade number, as that's easy to increase by expanding your portfolio.

Also, here is the metric/grading chart I've seen for Expectancy to Standard Dev R:
.16 to .19 (poor but tradeable)
.20 to .24 (average)
.25 to .29 (good)
.3 to .5 (excellent)
.5 to .69 (superb)
.7 above (holy grail).

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."
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  #3 (permalink)
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I can't help you with the R-multiples - not sure what that is. I also haven't read van Tharp.

Below is the definition of SQN I have seen:

SQN = sqrt(N)*E/sigma

where N is the number of trades, E is the expected (average) gain from each trade (the expectancy), and sigma is the sample sandard deviation of the P/L set (of length N).

SQN is really a fairly straightforward metric. The E/sigma part is simply a normalization by the standard deviation. The classical Gaussian z-test or Student's t-test does the same thing. All this part is saying is "How many sigmas away from breakeven is the expectancy?" The root of N term is a weak condition saying you prefer more trades than less trades. This term is simply for robustness.

If I were defining SQN, I would prefer this:

SQN' = 1.96*sqrt(N)*E/sqrt(sigma)

This formulation normalizes by the standard error, sqrt(sigma/N), rather than the standard deviation, and the 1.96 gives you a 90% confidence (or something). To each his own.

Keep in mind that SQN is a normalization by a parametric statistical parameter. All that lingo means that you're assuming a distribution to the expectancy, E. In this case, you're assumming E is Gaussian or at least normal in shape.

A far more robust method of measuring performance is to not assume Normality. Run a Monte-Carlo, make a CDF (cumulative distribution function - NT does this, although it plots it sideways) and pick off the 10-th and 90th percentile points for expectancy for whatever you like.

Any distribution converges to the S-curve of a Gaussian CDF given enough sample points. This method: a) is more robust because there are fewer statistical assumptions, b) gives you the mean (50th percentile) as well as the tails, and thus (c) lets you quantify both mean/expected performance as well as the fatness of the tails of your system.

Sorry. Maybe that was more info than you wanted?


RM99 View Post
Can someone please walk me through the calculation for SQN.

I can calculate my expectancy, but I have no idea what a "decent" expectancy happens to be.

The SQN is the root of the trade number (N) multiplied by the expectancy in R multiples? divided by the standard deviation of (net profit/trade) in R multiples? R is your initial risk on a trade (what exactly is that? The position size? The margin requirement? The initial stoploss?

Is that correct? I don't understand the convention that's used in the formulas I've seen. What the hell is trade P/L? Is that net profit/trade?

Also, here is the metric/grading chart I've seen for Expectancy to Standard Dev R:
1.6 to 1.9 (poor but tradeable)
2.0 to 2.4 (average)
2.5 to 2.9 (good)
3 to 5 (excellent)
5 to 6.9 (superb)
7 and above (holy grail).

Apparently, the more important number removes the square of trade number, as that's easy to increase by expanding your portfolio.

Also, here is the metric/grading chart I've seen for Expectancy to Standard Dev R:
.16 to .19 (poor but tradeable)
.20 to .24 (average)
.25 to .29 (good)
.3 to .5 (excellent)
.5 to .69 (superb)
.7 above (holy grail).


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  #4 (permalink)
Fortitudo et Honor
Austin, TX
 
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serac View Post
I can't help you with the R-multiples - not sure what that is. I also haven't read van Tharp.

Below is the definition of SQN I have seen:

SQN = sqrt(N)*E/sigma

where N is the number of trades, E is the expected (average) gain from each trade (the expectancy), and sigma is the sample sandard deviation of the P/L set (of length N).

SQN is really a fairly straightforward metric. The E/sigma part is simply a normalization by the standard deviation. The classical Gaussian z-test or Student's t-test does the same thing. All this part is saying is "How many sigmas away from breakeven is the expectancy?" The root of N term is a weak condition saying you prefer more trades than less trades. This term is simply for robustness.

If I were defining SQN, I would prefer this:

SQN' = 1.96*sqrt(N)*E/sqrt(sigma)

This formulation normalizes by the standard error, sqrt(sigma/N), rather than the standard deviation, and the 1.96 gives you a 90% confidence (or something). To each his own.

Keep in mind that SQN is a normalization by a parametric statistical parameter. All that lingo means that you're assuming a distribution to the expectancy, E. In this case, you're assumming E is Gaussian or at least normal in shape.

A far more robust method of measuring performance is to not assume Normality. Run a Monte-Carlo, make a CDF (cumulative distribution function - NT does this, although it plots it sideways) and pick off the 10-th and 90th percentile points for expectancy for whatever you like.

Any distribution converges to the S-curve of a Gaussian CDF given enough sample points. This method: a) is more robust because there are fewer statistical assumptions, b) gives you the mean (50th percentile) as well as the tails, and thus (c) lets you quantify both mean/expected performance as well as the fatness of the tails of your system.

Sorry. Maybe that was more info than you wanted?

Thanks,

So expectancy is simply the net profit/trade? Also, the sigma applies to the standard deviation of that number (of sample set N)?

I'm following your ideas about using different distributions. I'll dig into it.

Part of the allure of performance metrics is the ability to come up with a quick, down/dirty comparative method to evaluate a strategy compared to other strategies (either your own or other traders).

Obviously there's a ton of metrics that one could use and you have to look at a lot of different aspects. I focus mainly on drawdown (monte carlo), net profit/trade, avg win/avg loss, etc (in that order).

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."
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  #5 (permalink)
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RM99 View Post
So expectancy is simply the net profit/trade? Also, the sigma applies to the standard deviation of that number (of sample set N)?

Sort-of. More or less the statistical articulation of the P/L. Because winning and losing trades may have different probabilities, just can't find the average of the whole set. Just to we are talking about the same thing, expectancy is:

E = Pwin*Xwin + Plose*Xlose

if Pwin is the probability of a trade making more than zero (number of trades making more than zero divided by total number of trades), Plose is 1- Pwin, and Xwin and Xlose are the average values of the winning and losing trades (note that since Xlose is a mean of negative numbers because it only averages the trades that lose money, Xlose is negative).

Yes, the sigma is applied the the whole set. So, if TradesPnL = {x1, x2, x3, x4, ..., xi}, you'll find sigma by computing the stantard deviation of all of the set of TradesPnL.


RM99 View Post
I'm following your ideas about using different distributions. I'll dig into it.

I have found it fruitful. Your mean may be great. But, if you have a fat tail in the wrong direction, 5% of your trades by wreck your mean. Note that SQN attempts to articulate this. If you are maximizing your SQN, you are saying "I want a high expectancy, and a very small standard deviation." A small standard deviation means that the S-curve of teh CDF will by steep. In theory. In real life, and in nonlinear systems such as this, the nice, clean classical statistical metric can lie. In these cases, the non-parametric method I mentioned above is more robust.

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  #6 (permalink)
Fortitudo et Honor
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serac View Post
Sort-of. More or less the statistical articulation of the P/L. Because winning and losing trades may have different probabilities, just can't find the average of the whole set. Just to we are talking about the same thing, expectancy is:

E = Pwin*Xwin + Plose*Xlose

if Pwin is the probability of a trade making more than zero (number of trades making more than zero divided by total number of trades), Plose is 1- Pwin, and Xwin and Xlose are the average values of the winning and losing trades (note that since Xlose is a mean of negative numbers because it only averages the trades that lose money, Xlose is negative).

Yes, the sigma is applied the the whole set. So, if TradesPnL = {x1, x2, x3, x4, ..., xi}, you'll find sigma by computing the stantard deviation of all of the set of TradesPnL.



I have found it fruitful. Your mean may be great. But, if you have a fat tail in the wrong direction, 5% of your trades by wreck your mean. Note that SQN attempts to articulate this. If you are maximizing your SQN, you are saying "I want a high expectancy, and a very small standard deviation." A small standard deviation means that the S-curve of teh CDF will by steep. In theory. In real life, and in nonlinear systems such as this, the nice, clean classical statistical metric can lie. In these cases, the non-parametric method I mentioned above is more robust.

I'm getting the same value by calculating (Pwin*Xwin - Plose*Xlose) as the average net profit per trade. Am I doing something wrong?

Secondly, if that's true, then the standard deviation of the average net profit/trade should be sufficient?

The root of the trade number is definitely throwing the values off. I'm getting a higher SQN for a system that's very profitable, but has a rather large drawdown period.

I guess drawdown has more to do with the order of the trades, rather than the variance away from the mean for profits and losses.

"A dumb man never learns. A smart man learns from his own failure and success. But a wise man learns from the failure and success of others."
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  #7 (permalink)
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Van Tharp admits to some issues with SQN in Super Trader.

He points out that if you have a system with a SQN of .4, and you add say a huge winner to the mix, it would actually lower the SQN score. This is because it effects the deviation more than it does the average size of winners. I find this unacceptable. Is there a way to fix it?

Also, I like Modigliani's modification of Sharpe, which created an easier to understand metric. I feel something similar could be done with the SQN.

Lastly, Van Tharp admits his metric does not account for trade opportunity. For example, if you have what Van Tharp terms a 'Holy Grail System' (SQN >.75), but you get very few signals over the course of your trading period, your opportunity to profit from the system is simply absent. Consider a very strong system, with an expectancy of 2, and a more average system with an expectancy of .5. If the first system trades just once per week, your monthly return is about 8R. But lets say the second system trades twice per day. That would be about 20R per month, more than twice the return.

I would be very interested in a way of incorporating opportunity into the SQN.

forker


Last edited by forker; August 18th, 2011 at 09:25 AM.
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