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Synthetic hedges, cointegration, mean reversion and similar stuff

  • #281
  • Mar 4, 2011 1:36pm Mar 4, 2011 1:36pm
Quoting 7bit
By setting diff=false there is no trend by definition. I am always long below 0 and always short above 0. USDCAD vs. NZDUSD seems to have very stable coefficients, its one of the nicest two-pair hedges in my opinion.

I have started trading it last week at level 2 and now its at level 4 so at the moment I am in drawdown. I made some quick&dirty visual backtests (after observing how stable the coefficients are even during longer periods) and this seems to be quite profitable.

Very nice "simple" Basket indeed!
It has been in this range since july 2007, that's the longest ranging basket i've seen so far.
Looking at this period, it seems like it is now due for retrace...
Going long very soon!

Attached is my "Basket Profit 2 Pairs" indicator that i have developped to probe 2-pairs hedging baskets.
I have also put a template that will plot it with your NU/AC basket.
Use D1 chart.
The "grid" levels are profit levels in $;
Lot sizes are set to 0.894/0.8 lots, so that's not even 1 lot each.
And at this rate, each 0.5 SD step is roughly $1000...

Switching to H1, we can clearly see that there is room for the Grid to make money on smaller moves.

Well done!

Attached Image (click to enlarge)
Click to Enlarge Name: basket-nu&uc.gif Size: 32 KB


SQ
Attached File(s)
File Type: mq4 Basket Profit 2 Pairs sq.mq4   17 KB | 1,092 downloads
  • #282
  • Edited 5:39pm Mar 4, 2011 5:10pm | Edited 5:39pm
Correlations (NZDUSD, USDCAD) for different intervals (view in HD)
http://forum.mql4.com/c/forum/2011/0...USD_USDCAD.png
  • #283
  • Mar 5, 2011 9:46am Mar 5, 2011 9:46am
Hi Squalou,
Thanks for your indy. Could you also please post your template? Thanks.
  • #284
  • Mar 5, 2011 10:51am Mar 5, 2011 10:51am
Quoting squalou
....
The "grid" levels are profit levels in $;
Lot sizes are set to 0.894/0.8 lots, so that's not even 1 lot each.
And at this rate, each 0.5 SD step is roughly $1000...

SQ

Hi SQ

Please can you help me out here. I am just working through the calculation to try to get your result of ~$1000 per 0.5SD for the NZDUSD/USDCAD basket.

I don't usually have to worry about all this TICKSIZE/TICKVALUE mularchy as I trade through a Spread Bet broker where £1/pip is just what is says, irrespective of whether it is Forex, Oil or SP500 etc.

But I am setting this up for a friend who trades thru FXCM so I am just making sure I understand the calc for a "real" broker. LOL!

I am not getting the same result as you, almost certainly due to my brain failing due to my advancing years!! Please can you tell me what I am doing wrong?

These are my calculations based on US dollars:

NZDUSD : 100,000 * 0.0001 = $10/pip for 1 lot.
(I think this is right as my TICKVALUE for a GBP account is £6.146 = $10)

USDCAD : 100,000 * 0.0001 / USDCAD = 10/0.9715 = $10.29/pip for 1 lot.
(I think this is right as my TICKVALUE for a GBP account is £6.236 = $10.29)

When I construct the basket as (0.89 * NZDUSD) + (0.8 * USDCAD) I get a standard deviation of around 192 pips.

So 0.5 SD = 96 pips times $20.29 doesn't give me $1000.

Is it possible your TICKVALUE is based on Euros since you are in France? Or have I clearly screwed this up somewhere!!

Many thanks and best regards,

OD
  • #285
  • Mar 5, 2011 11:02am Mar 5, 2011 11:02am
Quoting Old_Dog
So 0.5 SD = 96 pips times $20.29 doesn't give me $1000.
96 pips is the move of one pair against the other (for example NZDUSD not moving at all and USDCAD going up 96 pips), so it is roughly 10$/pip * 100pip.

edit: sorry, it should be 0.8 * 10$/pip * 96pip, so its only around 800$

edit2: and when running a grid it would only trade only 0.2 lot at each level, making it less than 200$ profit per level.
  • #286
  • Mar 6, 2011 2:31am Mar 6, 2011 2:31am
thanks getch,

apparently there is not much difference between the 2 methods (^2 and ||)


Quoting getch
Condition Sum (Coef ^ 2) = 1 is Recycle2 Method1:
Condition Sum (|Coef|) = 1 is Recycle2 Method4:
Comparison:

I propose to compare Recycle2 with your method. Source data (AUDUSD_EURUSD_GBPUSD_USDCHF_USDJPY_USDCAD_NZDUSD) are here.

P.S. Changing factors in the dynamics can be found here.
  • #287
  • Mar 6, 2011 2:35am Mar 6, 2011 2:35am
Quoting 7bit
This one looks interesting (the lines are 0.5 stddev, I just started running a grid strategy on it (buy on each level when it goes down, sell on each level when it goes up), wish me luck):
Attachment
good luck 7bit, looks good.

If it doesnt revert soon, what is the worse negative std you can tolerate? or will you keep adjusting the weights till it reverts and taking mini losses in the process?
  • #288
  • Mar 6, 2011 5:27am Mar 6, 2011 5:27am
Quoting Old_Dog
Hi SQ

Please can you help me out here....

Hi OD & 7bit,

you had it almost right.

If you take 2011.02.10 as an example, which is when the basket line crossed 0SD, (this is "profit 0.00" level on my picture):

until "today" (2011.03.04), which is -2SD currently, NZDUSD moved -258p and USDCAD moved -219p (approx).

NZDUSD is $10/pip for 1 lot (that is always exact for any xxxUSD pair) ==> 258 * 10 * 0.89 = $2296
USDCAD is $10.29/pip for 1 lot ==> 219 * 10.29 * 0.8 = $1802

total is about $4100, so that's about $1000 per 0.5 SD.

As you can see from my pix, it shows a profit of about $4000.
With the indicator loaded (use the attached template -- i gorgot to attach it on my last post) you can use the ruler to display the difference between those 2 dates, which also displays aruond $4100.

My account is in USD, so this is $$ not €.

Sq
Attached File(s)
File Type: tpl basket-nzdusd-usdcad.tpl   43 KB | 745 downloads
  • #289
  • Mar 6, 2011 6:30am Mar 6, 2011 6:30am
Quoting challenger78
If it doesnt revert soon
Don't ask such heretical questions...

With my current lot sizing everything below 4 SD won't make me nervous.

I have not decided about an exact level yet but once I start feeling uncomfortable about a trade (which means I can't find any reasons to justify the position (or its size) anymore) I usually interpret this as an exit signal.

And with a grid I can also at any moment decide to switch the trading mechanism off and instead put a break-even TP for the entire position at ~50% of the total move and hope for a partial retracement.
  • #290
  • Mar 6, 2011 12:21pm Mar 6, 2011 12:21pm
Sorry for the naive question. Is the "recycle2" code freely available somehwere, and if so, where? At a minimum I saw that the video had some automatic data downloader, just that alone would be useful.

Regarding the normalization, it only changes scale, i.e. where you would consider placing a trade on the synthetic instrument and not the composition itself.

If I understand things correctly the only difference is multiplying the initial coefficients which come out of the analysis by

1/sum(abs|g_i|) vs

1/sum(g_i^2)
  • #291
  • Mar 6, 2011 3:17pm Mar 6, 2011 3:17pm
Vector1 is solution to the optimization problem with the condition Sum(Coeff^2) = 1.
Vector2 is solution to the optimization problem with the condition Sum(|Coeff|) = 1.

Then Vector1 and Vector2 are not proportional: Vector1 !~ Vector2 (Vector1 != K * Vector2)

These two optimization problems are quite different. This is not a question of scale.
  • #292
  • Mar 6, 2011 6:35pm Mar 6, 2011 6:35pm
Thank you 7bit for your continued contributions! I'm still working with the software and trying to put together a strategy for trading this. A grid strategy would work beautifully if you knew how many pips were between each standard deviation and could place an account percentage on each trade.

ex. between each deviation is 1,000 pips. Place a trade that equals 3% of your account for those 1,000 pips for the given basket (lot size would need adjusting). That way one could adjust for volatility depending on what basket you were trading and you could mitigate risk.

Below is a basket I've got my eye on that seems well behaved (between 2std dev) yet volatile enough over the past 6 years to profit well off of while not eating your margin level like a basket of 7 does. A grid system would probably work well.

Please let me know what your thoughts are on the above example. Thank you!

Placed on GBP/USD Daily

http://i67.photobucket.com/albums/h2...2/untitled.jpg
Attached Image (click to enlarge)
Click to Enlarge Name: untitled.JPG Size: 69 KB
  • #293
  • Edited Mar 7, 2011 2:19am Mar 6, 2011 8:54pm | Edited Mar 7, 2011 2:19am
Quoting getch
Vector1 is solution to the optimization problem with the condition Sum(Coeff^2) = 1.
Vector2 is solution to the optimization problem with the condition Sum(|Coeff|) = 1.

Then Vector1 and Vector2 are not proportional: Vector1 !~ Vector2 (Vector1 != K * Vector2)

These two optimization problems are quite different. This is not a question of scale.
Yes if that is the case, then yes they are different. What exactly are the optimzation problems? What are the inputs and what is being optimized.

In traditional linear regression they are definitely different

minimize sum_j (y_j-z_j)^2 with y_j = a + b_i*x_ij, subject to sum(b_i^2) = C
is known as "ridge regression", and

minimize (y_j-z_j)^2 subject to sum(abs(b_i)) = C
is known as "lasso regression". There is no single-pass deterministic algorithm for lasso regression as far as I know. (z_j is target, can be zero).

I think I found the code in question: http://codebase.mql4.com/ru/source/25578

Is this correct?

I do not understand the mathematics of the algorithms being used; there are no comments. In particular GetOptimalVector3() and GetOptimalVector4().

Are they doing some kind of lasso regression method that I've never heard of?



What precisely are the optimization problems?
  • #294
  • Edited 1:49am Mar 7, 2011 1:36am | Edited 1:49am
http://forum.mql4.com/c/forum/2011/0...2_Problem4.png
More information can be found here.
P.S. Matrix - matrix of ln(prices).
P.P.S. GetOptimalVector3() is quick solution, but is not complete. GetOptimalVector4() is complete solution to the problem.
  • #295
  • Mar 7, 2011 2:16am Mar 7, 2011 2:16am
Thanks. It appears to be what close to what I thought. I want to know more about the algorithm of #4. It's not something I've ever seen before---seems quite intriguing. Do you know of any more references (e.g. mathematical papers/web sites?)

In the above equation, is it necessary to subtract first the empirical mean of ln(price) before insterting values into Matrix?

I believe that looking for cointegration on ln(price) and sum(abs(coeff)) normalization is the correct way to do things. I made a small demonstration that this gives the expected coefficients when you go to the limit of a known problem, i.e. determinstic arbitrage (of course this is not profitable for retail clients).
  • #296
  • Mar 7, 2011 2:40am Mar 7, 2011 2:40am
Quoting mbkennel
Thanks. It appears to be what close to what I thought. I want to know more about the algorithm of #4. It's not something I've ever seen before---seems quite intriguing. Do you know of any more references (e.g. mathematical papers/web sites?)
Never able to find the formulation and solution of this problem
This is my own algorithm, developed specifically for Recycle2.

Quote
In the above equation, is it necessary to subtract first the empirical mean of ln(price) before insterting values into Matrix?
var(R) = Sum((R_i - mean(R))^2). Notice the subtraction in the formula.

Quote
I believe that looking for cointegration on ln(price) and sum(abs(coeff)) normalization is the correct way to do things. I made a small demonstration that this gives the expected coefficients when you go to the limit of a known problem, i.e. determinstic arbitrage (of course this is not profitable for retail clients).
Statistical arbitrage is more suitable for the stock market.
Comparison of all Recycle methods (View in HD)
  • #297
  • Mar 7, 2011 9:42am Mar 7, 2011 9:42am
An interesting article:

http://codebase.mql4.com/6185
  • #298
  • Mar 7, 2011 9:46am Mar 7, 2011 9:46am
Money management still apply for this method/way etc, you just have to find out whats your comfortable DD before closing if it didnt go your way...put the odds to your favor...

Big tf, diversification ,hedging > another step for success

The lower the risk,the better

Credits for 7bit for giving us these tools,if not we would have to use MATLAB...which is expensive
Trend-o-mat is something new for me, godsend maybe?
Once again 7bit, i appreciate your efforts,Thank You
  • #299
  • Edited 3:58am Mar 10, 2011 2:58am | Edited 3:58am
Quoting squalou
Hi OD & 7bit,

you had it almost right.....
Hello Sq

Many thanks indeed for the clear explanation - I see it all now!

And apologies for not getting back to you sooner - no disrespect intended. Mrs. OD been back in hospital so mind on other things (she's fine now).

I have been running several baskets in parallel on my live account for a number of months now. Interesting how you get hedging within the baskets and between the baskets. Looks like a very safe strategy.

The margin is pretty low as my broker is very good at netting margin on opposing positions, and as the baskets move, the margin stays pretty much rock steady.

I currently have:

5-basket

GBPUSD -1.0
AUDUSD +0.4
EURUSD +0.4
USDCAD +0.9
USDCHF -0.3

3-basket (Yen)

GBPJPY -1.0
USDJPY +1.0
EURJPY +0.5

2-basket

NZDUSD +1.0
USDCAD +0.9

The ADF test statistic for the 5-basket and the 3-basket rejects the unit root hypothesis at the 99% level for lags up to 10, so I am pretty confident we have tight cointegration here and a stationary basket.

The 2-basket only rejects at the 90% level but this may be "...near enough for Government work..." as they say!

Best regards

OD

EDIT

Note - the weights given above are RAW lot sizes for my Spread Bet broker. If you trade thru a real FX broker, you will need to make the adjustments for TICK_VALUE etc that, thanks to Squalou, I think we now all understand.
  • #300
  • Mar 10, 2011 9:22am Mar 10, 2011 9:22am
Quoting Old_Dog

The ADF test statistic for the 5-basket and the 3-basket rejects the unit root hypothesis at the 99% level for lags up to 10, so I am pretty confident we have tight cointegration here and a stationary basket.


.
Hi

Did you modified the 7 bit's code to run the ADF test? Would you mind sharing how you do it.

Thanks

Kim
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