cointegration

Stephen,

It depends what you mean by "logic".

If you mean statistical logic, I'll defer to Eric Zivot and Sarbo who are far wiser than I am. I will note, however, that you are testing for a p-value of 0.05, so I expect 5% of your test results to be misleading. In other words, for every 20 pairs tested by your batch job, I expect one will be suspect.

"Spurious cointegration" is a serious problem. I suggest Googling that topic. You may be suprised what you learn. (The irony, of course, is that cointegration was supposed to cure "spurious correlation." Oh well.)

If you mean financial logic, I strongly suggest not blindly risking money on your statistical test. Some filtering is required. Look for trades that make sense.

For example, my software reports that the stocks of MSFT and GOOG form a mean-reverting pair. But I would not trade that spread: too much idiosyncratic risk. My software also reports that Corn futures and Soybean Oil futures form a mean-reverting pair. But I would not trade that spread because the economic connection between corn and bean oil is too weak.

Hope that helps.

Paul

  _____  

From: r-sig-finance-bounces at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Stephen Choularton
Sent: Monday, October 18, 2010 9:46 PM
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] cointegration

Hi Folks

I'm using this to find cointegrated stocks on the AX.

library(xts)
library(quantmod)

# quickly re-source this file
s <- function() source('meanrev.R')

checkPairFromYahoo <- function(sym1, sym2, dateFilter='::')
{
  t.xts <- getCombined(sym1, sym2, dateFilter=dateFilter)

  cat("Date range is", format(start(t.xts)), "to", format(end(t.xts)), "\n")

  # Build linear model
  m <- buildLM(t.xts)

  # Note beta -- http://en.wikipedia.org/wiki/Beta_(finance)
  beta <- getBeta(m)
  cat("Assumed hedge ratio is", beta, "\n")

  # Build spread
  sprd <- buildSpread(t.xts, beta)

  # Test cointegration
  ht <- testCoint(sprd)
  cat("PP p-value is", as.double(ht$p.value), "\n")

  if (as.double(ht$p.value) < 0.05)
  {
    cat("###############################################################\n", sym1 ,":", sym2 ," is likely mean-reverting.\n", "###########################################################\n" )
  }
  else
  {
    #cat(sym1 ,":", sym2 ," is not mean-reverting.\n")
  }
}

getCombined <- function(sym1, sym2, dateFilter='::')
{
  # Grab historical data for both symbols
  one <- getSymbols(sym1, auto.assign=FALSE)
  two <- getSymbols(sym2, auto.assign=FALSE)

  # Give columns more usable names
  colnames(one) <- c('Open', 'High', 'Low', 'Close', 'Volume', 'Adjusted')
  colnames(two) <- c('Open', 'High', 'Low', 'Close', 'Volume', 'Adjusted')

  # Build combined object
  return(merge(one$Close, two$Close, all=FALSE)[dateFilter])
}

buildLM <- function(combined)
{
  return(lm(Close ~ Close.1 + 0, combined))
}

getBeta <- function(m)
{
  return(as.double(coef(m)[1]))
}

buildSpread <- function(combined, beta)
{
  return(combined$Close - beta*combined$Close.1)
}

testCoint <- function(sprd)
{
  return(PP.test(sprd, lshort = FALSE))
}

I run it on batches of stock-pairs and then have a look at those which are cointegrated.  Assuming my code is right (and anyone who thinks there is something wrong with it please let me know ;-)

Just wondered if anyone simply goes with the results, or if a test of logic is required.  I found, for example, that AGL ( a big gas company) was cointegrated with Bunnings Wharehouses (a hardware superstore chain).  Can't see the reason for that.  AMP (major insurer) cointegrates with AXA (another major insurer).  That makes sense and it cointegrates with  Westpac (major bank) still some logic but a bit thinner.  It also cointegrates with Fortescue Metals (big iron ore operation).  Not much logic there.  Anyway question is: do you get better results by using informed judgement on these things or just trust the figures?

Any comments most welcome.

Stephen Choularton Ph.D., FIoD

9999 2226
0413 545 182

for insurance go to www.netinsure.com.au
for markets go to www.organicfoodmarkets.com.au

cointegration

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