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Attachments: Nonparametric Association Measures in Systematic Trading
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Nonparametric Association Measures in Systematic Trading

  • Post #1
  • Quote
  • First Post: Edited 8:58am Dec 26, 2017 5:17am | Edited 8:58am
Dear Fellow Traders,

I am collecting links and other resources that contain examples of using nonparametric association measures in strategy development and risk management. Two main examples of nonparametric association measures are Kendall’s tau and Spearman’s rho. The two measures are based on ranks. As such, they are naturally suitable for trading, where we care more about the asset going up/down and less about the actual magnitude of the movement.

The measures are robust in the sense that they are not sensitive to big infrequent spikes in the data. For that reason they are more stable than correlation… The robustness may be a blessing in some situations (where “smoothing” is necessary) and it may be a curse in others. I use nonparametric dependence measures in a few places in my strategies but their usefulness is certainly much wider. So I would like to improve my scope and, perhaps, write a nice systematic web-resource one day... Any information would be appreciated.

Thank you.
To get the ball rolling, here’s the first block of links.

1] Rebalancing a portfolio of ETFs using “mean-variance” principles. Instead of employing the regular covariance matrix of ETFs, the authors employ its modification based on Spearman's rho.

https://cssanalytics.wordpress.com/2...-optimization/


2] Pairs trading of US goldmine stocks, with Kendall’s tau and Spearman’s rho used to select the pairs. Several trading strategies are considered, including cointegration-based trading and copula-based trading.

https://thesis.eur.nl/pub/34694/Landgraf.pdf


3] Pairs trading of ETFs, with Kendall’s tau used to select the pairs. Copula-based strategy is considered.

https://www.quantconnect.com/tutoria...ding-strategy/
Attached File(s)
File Type: pdf Landgraf.pdf   1.4 MB | 603 downloads
how do you apply these stuff to Forex?
Quoting staassis
we care more about the asset going up/down and less about the actual magnitude of the movement.
I remember a post by the redlion (I can't find it) where he showed an up trend containing more down bars than up bars. The trend was created by a minority of big up moves.
No greed. No fear. Just maths.
Quoting PipMeUp
{quote} I remember a post by the redlion (I can't find it) where he showed an up trend containing more down bars than up bars. The trend was created by a minority of big up moves.
Thank you for this example, PipMeUp. Yes, such situations happen all the time (when one big player has to work a big notional, for example). However, seeing more down bars than up bars in your example is just a matter of setting the bar frequency. If you had chosen a time step large enough you would have seen just one up bar, would you not?... At the end of the day/week/month, first and foremost, we care whether we are any good as prop traders. We care whether our signals are strong, whether our call was correct and we have made money on the trade... And then we care how much.

Sorry if I was not very clear in my first post. I was just trying to express an idea that, overall, the direction is more important. But there are situations on all levels where magnitudes are very important as well... And "non-parametric smoothing" is just one possible application (suitable only in some corners of prop research). As I also mentioned, oftentimes ignoring magnitudes is a curse.
Quoting alphadude
how do you apply these stuff to Forex?
Applications of nonparametric dependence measures in pair selection was just the first block of links that I posted. This is not the only area with potential (and not the most promising one). However, even here they may be connections with the macro world. In particular, we all are interested in finding pairs where the k-th lag of indicator (cross) A leads indicator (cross) B. Some of the aforementioned statistical methods may serve as a building block in a more complex analytical framework.
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If you had chosen a time step large enough you would have seen just one up bar, would you not?
Obviously. So what?

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first and foremost, we care whether we are any good as prop traders
Why should I do that?

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We care whether our signals are strong
There is no such thing as a A+ setup. If such a thing existed you could filter out the non-A+. This post-filtering of your strategy would simply generate a new strategy emitting normal signals.

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whether our call was correct and we have made money on the trade...
I disagree. This is a whim of willing to be right. The illusion of control. The outcome of the next trade is irrelevant. What is important is the expectation (will the strategy make money in the long run) and the variance (to estimate the risk of ruin) of the next 1000 trades.

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we all are interested in finding pairs where the k-th lag of indicator (cross) A leads indicator (cross) B.
I don't think I do that but I don't really understand what you mean.



I will try to use Spearman's correlation to see how it compares with Pearson's for the risk allocation problem I discribed here https://www.forexfactory.com/showthr...63#post6910163
No greed. No fear. Just maths.
Quoting PipMeUp
{quote} I remember a post by the redlion (I can't find it) where he showed an up trend containing more down bars than up bars. The trend was created by a minority of big up moves.
There is also data out there that maybe 10% of market days make up 90% of market movement.
If you are good at something, never do it for free--Joker
  • Post #9
  • Quote
  • Edited 6:20pm Jan 3, 2018 8:48am | Edited 6:20pm
PipMeUp, you are missing the point that this thread is not about well-documented asymmetry of returns (interplay between magnitude and direction) but about interesting prop ideas based on Spearman's rho, Kendall's tau and such.

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There is no such thing as a A+ setup.

Sure, but there is a difference between being right 50.5% of the time (precarious) and 75% of the time (better). Also, unfortunately I cannot agree with this

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The outcome of the next trade is irrelevant. What is important is the expectation

Expectation is just another performance metric of the next random trade. And how do you estimate the expectation anyway, in this constantly changing environment?... Any trade is relevant, especially an unsuccessful one, because it may signal structural changes in the market. Now, having that said, structural changes are somewhat difficult to detect with nonparametric association measures. Better tools exist. So let us return this discussion into the following area: where are nonparametric association measures useful and where do they have suboptimal properties?... Any examples of strategies or risk management tools would be appreciated. Thanks.
Interestingly enough, here is an example of Spearman's rho in trend detection. The paper is somewhat technical. So a regular FF member may skip most mathematical parts to get an idea of the proposed methods.

My opinion: the proposed tests may serve as one input in a more complex detection system. They are not sufficient on their own.
Attached File(s)
File Type: pdf Yueetal2002.pdf   728 KB | 527 downloads
Quoting staassis
Interestingly enough, here is an example of Spearman's rho in trend detection. The paper is somewhat technical. So a regular FF member may skip most mathematical parts to get an idea of the proposed methods. My opinion: the proposed tests may serve as one input in a more complex detection system. They are not sufficient on their own. {image}
This academic paper is full of formulas that may or may not have any relevance to trading.

Complexity in trading does not work; simplicity does work. I have spent heaps of time in research in the past; including artificial intelligence; and nothing seems to be solid for long term trading.

I have two bookshelves at home; one for things that works; and one for intellectual master*****n stuff.

take my advice; and for for KISS
Quoting alphadude
{quote} This academic paper is full of formulas that may or may not have any relevance to trading. Complexity in trading does not work; simplicity does work. I have spent heaps of time in research in the past; including artificial intelligence; and nothing seems to be solid for long term trading. I have two bookshelves at home; one for things that works; and one for intellectual master*****n stuff. take my advice; and for for KISS
Alphadude, If you are so easily scared by formulas, I told you to skip the mathematical parts and focus on the idea of the tests. You sound lazy enough not be willing to read rigorous text and just chat, chat, chat on this forum. Any method can be phrased in formulas (even if it's unnecessary). So by your logic, any method is wrong... I use higher mathematics to generate profits every week, by running non-trivial classification algorithms.
Quoting staassis
{quote} Alphadude, If you are so easily scared by formulas, I told you to skip the mathematical parts and focus on the idea of the tests. You sound lazy enough not be willing to read rigorous text and just chat, chat, chat on this forum. Any method can be phrased in formulas (even if it's unnecessary). So by your logic, any method is wrong... I use higher mathematics to generate profits every week, by running non-trivial classification algorithms.
my bad. I will have a look at time this weekend.
did a quick search in youtube; and got to understand the formulas bit better:

Inserted Video

Inserted Video


I can see a potential use for these correlations; and the paper above.
Thank you, Alphadude.
staassis, have you tried to formulate a spread series between correlated pairs?

basically you trade the spread the same way you trade the cross pair (i.e. trade EUR/USD and USD/JPY, instead of EUR/JPY)
Alphadude, I believe trading the spread between A and B is a particular case of pairs trading (if I have understood you correctly). In greater generality, pairs trading allows one to choose optimal weights for A and B. I'm also not sure that A and B should be chosen based on correlation only. Some time ago I did pairs trading where the choice of pairs and determination of weights was based on cointegration. This was in a macro asset class but not FX. I did have encouraging results but, sadly, for institutional reasons I never ended up making millions on my strategy. In my opinion, that strategy worked because there were fundamental reasons for the assets to co-move. Time series analysis alone is insufficient, unless one trades very big portfolios for a short period of time..... Having that said,

_______ Kendall's tau or Spearman's rho + cointegration based trading + fundamental reasons for the assets to exhibit similar dynamics

sounds interesting. Please note that all those ingredients are present in the paper by Landgraf et al... I am cautiously curious about copula-based trading but have not backtested / traded anything like that yet. Purely intuitively, the choice of pairs must be more important than deciding between copula based execution and cointegration based execution.
Nice sharing.
Quoting staassis
Alphadude, I believe trading the spread between A and B is a particular case of pairs trading (if I have understood you correctly). In greater generality, pairs trading allows one to choose optimal weights for A and B. I'm also not sure that A and B should be chosen based on correlation only. Some time ago I did pairs trading where the choice of pairs and determination of weights was based on cointegration. This was in a macro asset class but not FX. I did have encouraging results but, sadly, for institutional reasons I never ended up making millions...
Another way to trade the spread (aka pairs trading); is to create stationary timeseries. an example is to detrend the price series.

the next problem that appears is mean drift of the stationary timeseries.

I think it is possible to create a portfolio of FX instruments with varying weights; to create a stationary timeseries; and trade that portfolio.
Quoting alphadude
{quote} Another way to trade the spread (aka pairs trading); is to create stationary timeseries. an example is to detrend the price series. the next problem that appears is mean drift of the stationary timeseries. I think it is possible to create a portfolio of FX instruments with varying weights; to create a stationary timeseries; and trade that portfolio.
Alphadude, I think there is potential in this direction. There are at least two ways of using stationary combinations of financial indicators:

1) The combination is tradable and corresponds to the price of some portfolio, perhaps with constantly rebalanced weights,
2) the combination is not tradable, e.g. RSI(asset 1) - RSI(asset 2) (just a silly example).

Various posts and books have concentrated on case 1. However, in the FX world case 2 may have better prospects. The stationary combination may serve as a signal generating tool for trading closely related assets. Backtesting several ideas in that direction is on my list.
Quoting staassis
{quote} Alphadude, I think there is potential in this direction. There are at least two ways of using stationary combinations of financial indicators: 1) The combination is tradable and corresponds to the price of some portfolio, perhaps with constantly rebalanced weights, 2) the combination is not tradable, e.g. RSI(asset 1) - RSI(asset 2) (just a silly example). Various posts and books have concentrated on case 1. However, in the FX world case 2 may have better prospects. The stationary combination may serve as a signal generating tool for trading...
Option (1) does have potential. Think about it from fundamental perspective; holding a basket of currencies; if weighted properly; should holds its value stationary (small up and downs will be white noise, and averaged to 0 over time).

Pretty much what China is doing with its currency; they value it using a *secret* basket of currencies.

The challenge of course is to find those weights; and update them periodically (at end of day); and balance the portfolio accordingly.

The signals generated can be netted using various currencies; so that we reduce the number of required transactions. Those signals should be traded intraday on 1h, 15m, 5m, or even 1m timeframe.

Option (2) is doable for sure; and the moving average is perhaps the best option I can think off.
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