Pairs Trading - Copula Method vs Cointegration

Jingw, Thank you for your explanation. Regarding the quantity of each leg, I think it's understandable. But I still don't understand why trading from year 2017 (see backtest right above.) looks so disappointing. Compared to the backtest starting 2016, two results are not giving me any level of confidence. If I deployed this algo in Jan. 2017, I would've gotten so bad result. However, if I did in Jan. 2016, it would've been totally a different story. What do you think? Is there any other way to improve regarding this aspect? How will this algo go in live trading? Thanks :) 

HanByul, It is reasonable. As in algorithm, we just choose copula once and use this copula in the following days. The only thing that changes is the parameter of that copula. Your backtest starting from 2016 and starting from 2017 use the different history data to choose the copula, they might choose the different copula and the algorithm will use this copula for the following backtesting. You can control the copula you use by ignoring the copula selection process to reach the same result.

Jingw, Thanks for all the answers and explanation. I will dig into more about 'copula' method and see if we can implement for multi-pairs instead of picking one pair (If you've already done for multi-pairs, please let us know. I appreciate it.). Again, thank you for your great work and the opportunity to explore the 'copula' method.  :)

your universe is: tick_syl =  [["SPY","AGG","XME","TNA","FAS","XLF","EWC","QLD"],
                                         ["DIA","JNK","EWG","TLT","FAZ","XLU","EWA","QID"]]

as a non-programmer, I'm wondering if I can replace names here and run backtest with my names?  I've tried and gotten errors

If for a Gumbel copula we get a combination of (u,v) of (1,1) -> the pdf of your algorithm returns an infinity value.

Hi Dennis,

When (u, v) -> (1, 1), log(u) and log(v) are zero so the Gumbel pdf will be "inf". u and v are  constructed with the empirical distribution function from the log return series, there must be a 1 in u or v. Therefore, in the original algorithm I try to convert the infinity value to the finite number with

# Replace nan with zero and inf with finite numbers in lpdf list 
lpdf = np.nan_to_num(lpdf)

The finite numbers are still huge so the sum would be inf. A better solution would be converting the 1 in u or v to a number less than 1 for example 0.9999.

Hi,

I cloned the file and tried to run a backtest but its giving me an error

During the algorithm initialization, the following exception has occurred: TypeError : 'numpy.float64' object is not callable
at Initialize in main.py:line 61
at <listcomp> in main.py:line 61
at _lpdf_copula in main.py:line 180
TypeError : 'numpy.float64' object is not callable

Please let me know how to fix this error.

Here's the log

I recloned main.py and now its giving me divide by zero

Tweaked it to check for at least 3 days. The -2 position wasn't set yet.

Thanks Jared! worked like a charm

One more question, I am trying to use similar strategy for currencies, is it possible to change the ticker to use currency?

2 currency pairs: EUR/USD and NZD/USD

test for cointegration of prices between both assets

Two Questions:

1. How is the Quantity calculated? (i.e. where can I find the function CalculateOrderQuantity() )

2. 1200 days to determine which copula and 250 days to determine the parameters? So 1200 days are used to decide Frank/Gumbel/etc. and the parameter theta is optimized using the 250 days before each trade? Or how many times and when is this parameter updated?

Thanks in advance,

Dennis

Hi Jing Wu,

I have tried the pair selection as you did by selecting the highest Kendall’s tau of the pair log return. I ran though the data of entire NYSE stock list and pick the highest 30 stock pair of Kendall's tau each year from 2001 to 2017. Then I backtested the pair on the next year historical data. I find that the high Kendall's tau doesn't has a direct relationship with good performance. P.S. the backtesting is using the stratigy that you posted out.

Is there a better way to pick a good pair?

Hello,

How do I implement this strategy for forex pairs? Thank you

Hi All!

Sincere apologies for the above for some reason the page did not load for me.

I am really fasciantated with the above and would like to build on it.

I have a couple of quesions -

If i want to try another type of copula in a python package, how can i import the package

My first impression is that i could only do it locally.

So i would like to set up a local backetest enviroment preferably in jypyter notbeook.

What would be the best way to acheive this?

Many thanks all,

Best,

Andrew

For the request to add more python libraries, please submit an issue on Github 

We'll review the request and try to add new libraries to LEAN.

To use LEAN locally. the easiest is with a plugin we've made for Visual Studio. It automatically takes the code you've written and sends it to the cloud for backtesting.

You can see the plugin documentation here; we would love to have support for other IDE's but currently just support Visual Studio.

I am new to the platform, but can someone explain this to me and why is it 0.4?

Hi Ted Yap, you can look for the QCAlgorithm classes, method, and properties in the Algorithm Lab: 

what is the exit point?

I checked the copula code from the tutorial (one with 427 trades, 353% Net Profit). If you look at the trade log, it seems that it opens a long position in XLK on 2010-03-03 and the short QQQ gets rejected because of insufficient capital. Another pair trade is opened on 2010-03-26 in opposite direction and half the size. Then the two ~2k shares long positions in both instruments are held for 8+ years, producing most of the total net profit. Am I reading this right?