[R-SIG-Finance] Real-world Pairs Trading?

[G See]

Michael,

This is not related to R.  I'm sure the good folks at NuclearPhynance
and Wilmott will be able to help.

crossposted:
http://www.nuclearphynance.com/Show%20Post.aspx?PostIDKey=159781
http://www.wilmott.com/messageview.cfm?catid=3&threadid=90072

Just to clear it up, crossposting is *discouraged*

Thanks,
Garrett

On Sat, Apr 7, 2012 at 9:41 AM, Michael <comtech.usa at gmail.com> wrote:
> Real-world Pairs Trading?
>
> Hi all,
>
> Happy holidays!
>
> I just had a question on pairs trading in real-world. How are pairs trading
> done in real-world?
>
> My understanding of the procedure:
>
> 1. Test stock A using ADF to decide whether A is I(0) or I(1).
> 2. Test stock B using ADF to decide whether B is I(0) or I(1).
> 3. Using Johansen or Granger-2-stage methods to decide if A and B are
> cointegrated.
> 4. Trade the pair if they are decided to be cointegrated.
>
> My questions are:
>
> 1. Are steps 1 and 2 neccessary?
>
> In real-world, most prices series are either I(0) or I(1). And if two stock
> prices series are I(0) and I(0), we can still do
>
> pairs trading on them, no?
>
> Do we really need both series to be I(1) to do the pairs trading?
>
> 2. In steps 1 and 2, there are different versions of the ADF tests: for
> example, in R, the function ur.df
>
> has "none", "const", "trend", "both" options.
>
> How can we select the best ADF options programatically and automatically,
> both cross-sectionally and along the time axis?
>
> For example, if we have a large universe of stocks and if we need to do
> rolling-window ADF tests, choosing the ADF options "automatically"
>
> and "programatically" become tricky...
>
> 3. In steps 1 and 2, does the option of "none", "const", "trend" and "both"
> matter?
>
> For example, if setting "trend" leads to the conclusion of stationary while
> setting to "const" leads to the conclusion of non-stationary,
>
> should this series be declared as "stationary" or "non-stationary" for
> trading purposes?
>
> 4. I read that cointegration is more or less a long term concept. How
> "long" is long term here?
>
> Suppose I am doing these tests on 15minute bars, how many data points shall
> I use in my rolling-window tests along the time axis? I am thinking of 500
> data points. But maybe that's too much, remember the markets are changing
> and we have to be a bit adaptive... Any thoughts on this?
>
>
> 5. Johansen has the advantage of being symmetical in A and B. But Johansen
> is not stable at all if we look at the rolling-window cointegrated
> vectors(the eigenvectors).
>
> It seems that to get the hedge ratio, still one needs to use linear
> regression since it's more stable.
>
> But then would you regress A onto B and regress B onto A? They do make a
> difference, from my experiment...
>
> Or does that matter?
>
>
> 6. Some literature also mentioned using returns to do all these.
>
> My understanding is that returns are used to find the hedge-ratios
> approximately.
>
> Ultimately we are still trading prices, those are the tradables. We arenot
> trading the returns.
>
> So after we do all the tests and obtained hedge ratios using returns or
> other series, we still come back to prices to form a pair and pairs-trade
> the price levels...
>
> The hedge-ratio obtained from regressing returns of A onto returns of B is
> an approximation to the hedge-ratio obtained from regressing prices of A
> onto prices of B.
>
> When the prices of A and B are I(1), regressing prices onto prices will
> lead to spurious regression, but the estimate of Beta (the hedge-ratio)
> itself shouldn't be a problem.
>
> It's the inference that is messed up.
>
> Am I understanding this correctly?
>
> Thanks a lot!
>
> [CPed on Willmot etal]
>
>        [[alternative HTML version deleted]]
>
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