Pairs trading strategy on bond futures

Hello everyone,

I am new here. Here is a simple pairs trading formula for calculating the spread between two assets
(equation 1).

So, I have backtested a simple pairs trading strategy on the german bond market, especially on the
pair Euro-bund/Bobl (Euro-bund = 10 year treasury note futures and Bobl = 5 year treasury note
futures for the german bonds). I don't test the correlation between the two assets, but in general it is
pretty high (over .90 or 90%).

So, here is the backtest I have done on the past five years (1/12/2009 – 17/10/2014). In the datas
that I used, some gaps are there (no data between 28/2/2013 and 29/4/2013 excluded and between
30/8/2013 and 2/10/2013 excluded). The prices used are the close prise on the Euro-Bund and
BOBL futures (EUREX) from 1 december 2009 to 17 october 2014.

Here is the formula to measure the discrepancies between the two assets:



Here are the trading rules:

• No stoploss because we assume that the capital and the margin call are not a limit,
• A position is opend each time the threshold of 1 is crossed upward for +1 and downward for
-1, just one cross (for example is the signal passed from -0.9 to +1.1 a position is opened),
• The position(s) opened is closed once the mean (0) is crossed downward for a +1 cross and
upward for a -1 cross
• The parameters are i = 1, A is the Bobl futures and B is the Euro-Bund futures,
• The trading period is the beginning of the month from the futures contrat ending the same
month and the end is the last trading day of the month previous the futures contract ending
the month after (for example for the setpember 2014 Bobl futures, the trading period would
be the June 2nd 2014 to August 29 2014),
• In order to calculte the signal, 20 previous datas are taken from the same futures contrat of
the trading period.

It is possible to backtest more periods from the equation 1, but if I chose the return of 1 period and
the standard deviation from the last 20 periods the reason is 1 for the mispricing on a daily basis
and the 20 for a averaged volatility of the return on the last trading month numbered in days.

The results are as follows:

• Sharpe ratio = 0,25
• first drawdown from 29/11/10 to 30/7/12 about 10,6%
• second drawdown from 24/6/13 to 9/6/14 about 3,3%
• 27 trades in total
• Winning rate of 74,07%

Here are the descriptive statistics:












Conclusion:

The results are very interesting and without parameters optimization because of the lack of datas (two
gaps) and the data-mining or data snooping bias (which means the overoptimization of the
parameters of the model based on transient noise in the historical data).

The histogram of profits and losses shows a positive skewness, so this pairs trading strategy seems
profitable. Bootstrapping method or Monte Carlo simulations could confirm that, but with only 27
occurencies in a sample is borderline. Besides, the two gaps in the data put the trading results at
stake, because big losses could happen.

More than 66% of the trades are closed after 1 day duration or 2 consecutive trading days. The
winning rate is 74,07% and the losses are largely overwhelmed by profits. This short time exposure
on the german bond futures market is interesting because it is possible to add some identical pairs
trading strategies on the same futures account. In doing so, the profits could be larger and the losses
as well.

great test ...i think it would be great to implement it on a pair of currency cross, or better on a currency ring ....

I have already done a backtest on the 28 major currency pairs, and for now it seems fine.

I have to test it in real time in order to compare the resultas with the backtests, but with the formula you have th idea. A profitable pair trading strategy is 95% in research and 5% in analysis.

you enter same quantity on the both side ?

No, 1 eurobund contract for two bobl contract because the eurobund futures is more volatile.

Okay but how you calculate the quantity ? if i want test on another instrument.

You could three options to do that:

1. Money neutrality or money neutral = same amount of money on each leg
2. Beta neutrality or beta neutral = OLS on the returns of the two assets (or another method to estimate the beta)
3. Volatility neutrality or volitility neutral = I don't know what it is

The options that I chose was the beta neutral by rounding up to 2.

Finally, it is up to you. Your backtest results can help to choose from the 3 options, with the money neutral and beta neutral been the most used in pairs trading.

Thanks. I want test on EUROSTOXX50 vs CAC40 CFD.

My pairs trading strategy based on arbitrage between the indices CAC40 and DAX30. Proper selection size of positions is a very important element of this strategy. It is important that the same percentage change in each index change caused equally expressed in money.
e.g.
http://s17.postimg.org/6w55uq7xb/2014_10_31_131547.jpg

This script calculates the sizes of positions according to my conception.
https://www.dropbox.com/s/veq9t343be...tails.ex4?dl=0

http://s28.postimg.org/6eljcm7p9/2014_10_31_140133.jpg

Sound good Kasia, you trade only on Daily time frame ?

Sometimes when I have time and I'm at the computer play on H1. In such cases hunt for occasions and play manually. In addition on H1, also I trade with crude. For D1 robot trades automatically. Both strategies D1 and H1 are currently tested on demo accounts.

D1 http://www.myfxbook.com/members/Trej...ax-555/1026725
http://s30.postimg.org/5osqhg6rl/2014_11_01_194909.jpg

Very nice perf Kasia !! it' s ready for start in real mode ?

It's based only on correlation ?

I think there are more divergence of correlation on Crude vs WTI... You haven't test EURSTOXX vs CAC ?

So I tested different pairs. I think that Eurostoxx is "too heavy and too slow" to this trading system. By trading on Brent and WTI also can have a good result. It is important that the broker did not receive swap points. It worsens the result when the positions are open for a few days.
For small real accounts system works with similar results for several months. Just to verify brokers.

With some delayy, here is a signal long 1 euro-bund futuress CFD contract and 2 short BOBL futures CFD contract with CFD at Actvtrades

 

1. long 1 euro-bund futuress CFD contract at 151.07
2. 2 short BOBL futures CFD contract at 128.11 (not 128.13 my mistake)

We have a 66% chance to close the trade Monday night before 10 p.m. Paris time.

@surfeur
Give some data for CAC40 and EUROSTOXX 50. I will backtest quickly in order to see raw results.

hey TheArrbitrage, are you any good at Matlab? My only reason is there is a toolbox called Neural Network in Matlab which can be used to correlate data clusters or pattern regcoginition between datasets, so figured this could be of use to you?

hello arb, how do you do with currencies? thanks

same here

I don't use matlab since a long time ago. I get to used R, it is free and easy to implemente some basic statistical functions, but my preference goes to Excel (easy to write code and for pairs trading the code is not so difficult to write anyway). I am learning R little by little.

I have worked on global models for forex, but it is more simpler to find one by one good currency pairs trading strategy.

In Algorithmic trading by Ernest Chan, he talks about the AUDUSD/CADUSD pairs trading.

Yep, I have found a winning model on currencies and I am going to test it. I would post a trader explorer.

You read a lot of scholar articles and you test the models until finding some winning models!

Pairs trading is finding, backtesting and forward testing. The models with time have to change unfortunately.

Hi Kasia,

I pm'd you but probably you did not notice, where can we get the correlation indi you are using?

Thanks
4x