Comments on: Seasonal pair trading

By: Dzidorius Martinaitis

Dzidorius Martinaitis — Sun, 16 Jan 2011 22:22:59 +0000

Craig,
I found the comment, check the 4th one:
http://epchan.blogspot.com/2009/08/using-r-to-test-for-cointegration.html

I saw more examples where the returns were used instead of the prices in finance. Good summary can be find here: http://www.portfolioprobe.com/2011/01/12/the-number-1-novice-quant-mistake/

By: Craig

Craig — Sat, 15 Jan 2011 05:56:11 +0000

To say it doesn’t matter, I would say is somewhat incorrect as each option results in a different model.
Logically, one must be more optimal that the other.

In answer to your other question, you need to regress the prices, check a papers database for stat. arb. stuff, there is plenty around if you do a bit of digging.

By: Dzidorius Martinaitis

Dzidorius Martinaitis — Fri, 14 Jan 2011 21:51:14 +0000

Craig,
I remember reading his answer somewhere on this blog: epchan.blogspot.com. Shortly, it doesn’t matter, if you regress prices, but you have take into account, when you regress the returns.

Mark,
yes, I know this method, it is linear regression or OLS. R has many ways to to it (the result is the same) lm(), lsfit(). As I mentioned before, the first question is – what should I regress: the prices, the returns (simple or log)? I tried all of them, but couldn’t get the same hedge ratio.
I have to do further test, but I think, that the hedge ratio was derived by using minimum variance ratio. This ratio takes into account correlation and variation of two assets.

By: Craig

Craig — Fri, 14 Jan 2011 20:54:01 +0000

I wonder why he forces the intercept to zero with x ~ y + 0 as opposed to x ~ y?

By: Mark

Mark — Fri, 14 Jan 2011 20:32:18 +0000

In one of the other docs of Teetor, he calculates the hedge ratio as:

beta <- coef(lm(x ~ y + 0))[1]
spread <- x – beta*y

beta would be your hedge ratio here.
I'm not saying this is the best way, just thought to let you know…

Regards,

-Mark-

By: Dzidorius Martinaitis

Dzidorius Martinaitis — Fri, 14 Jan 2011 15:16:33 +0000

Talking about returns, we can have either arithmetic return or logarithmic return. I use Delt() function and by default it provides arithmetic return (P1/P0)-1. Teetor derived dollar’s spread, I opted for arithmetic return.
I will try to extend this post, but at the moment I stuck with hedge ratio. Hedge ration can be based on: price, arithmetic return or logarithmic return. I’m trying to find with best way.
Let you know, when (if) I figure it out!

By: Mark

Mark — Fri, 14 Jan 2011 12:39:47 +0000

In the code i noticed that you used Delta() to calculate the daily difference in the spread. This calculates a simple return.
I think Teetor, although he does not provide any code. is using diff() as a spread can have negative values as opposed to plain price data.

Using Delta() or diff() will give completly different results…

-Mark-

By: Dzidorius Martinaitis

Dzidorius Martinaitis — Tue, 11 Jan 2011 16:25:33 +0000

Greg,
the data can be find here: http://www.eia.gov/dnav/pet/pet_pri_fut_s1_d.htm
You have to download Contract1 for Crude oil (easy).
For RB, I merged two data series into one – Reformulated Regular Gasoline Contract1 and RBOB Regular Gasoline Contract1.
If you find difficulties in doing this – let me know where can I upload 2 csv files.

By: Greg

Greg — Tue, 11 Jan 2011 16:13:53 +0000

Nice work. Thanks. Can you please also post the data (csv files). Thanks.

By: Dzidorius Martinaitis

Dzidorius Martinaitis — Tue, 11 Jan 2011 09:05:46 +0000

Craig,
yes, it is true, that for the spread construction I didn’t use a hedge ratio. The idea behind – the investment is done for short time period (1 month) and it is much simple to understand and manage such investment.
However, I have a plan to write similar post, where I will introduce a hedge ratio.