Volatility Stat-Arb Shenanigans

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This post deals with an impossible-to-implement statistical arbitrage strategy using VXX and XIV. The strategy is simple: if the average daily return of VXX and XIV was positive, short both of them at the close. This strategy makes two assumptions of varying dubiousness: that one can “observe the close and act on the close”, and that one can short VXX and XIV.

So, recently, I decided to play around with everyone’s two favorite instruments on this blog–VXX and XIV, with the idea that “hey, these two instruments are diametrically opposed, so shouldn’t there be a stat-arb trade here?”

So, in order to do a lick-finger-in-the-air visualization, I implemented Mike Harris’s momersion indicator.

momersion <- function(R, n, returnLag = 1) {
  momentum <- sign(R * lag(R, returnLag))
  momentum[momentum < 0] <- 0
  momersion <- runSum(momentum, n = n)/n * 100
  colnames(momersion) <- "momersion"
  return(momersion)
}

And then I ran the spread through it.

xiv <- xts(read.zoo("longXIV.txt", format="%Y-%m-%d", sep=",", header=TRUE))
vxx <- xts(read.zoo("longVXX.txt", format="%Y-%m-%d", sep=",", header=TRUE))

xivRets <- Return.calculate(Cl(xiv))
vxxRets <- Return.calculate(Cl(vxx))

volSpread <- xivRets + vxxRets
volSpreadMomersion <- momersion(volSpread, n = 252)
plot(volSpreadMomersion)

In other words, this spread is certainly mean-reverting at just about all times.

And here is the code for the results from 2011 onward, from when the XIV and VXX actually started trading.

#both sides
sig <- -lag(sign(volSpread))
longShort <- sig * volSpread
charts.PerformanceSummary(longShort['2011::'], main = 'long and short spread')

#long spread only
sig <- -lag(sign(volSpread))
sig[sig < 0] <- 0
longOnly <- sig * volSpread
charts.PerformanceSummary(longOnly['2011::'], main = 'long spread only')


#short spread only
sig <- -lag(sign(volSpread))
sig[sig > 0] <- 0
shortOnly <- sig * volSpread
charts.PerformanceSummary(shortOnly['2011::'], main = 'short spread only')

threeStrats <- na.omit(cbind(longShort, longOnly, shortOnly))["2011::"]
colnames(threeStrats) <- c("LongShort", "Long", "Short")
rbind(table.AnnualizedReturns(threeStrats), CalmarRatio(threeStrats))

Here are the equity curves:

Long-short:

Long-only:

Short-only:

With the following statistics:

                          LongShort      Long    Short
Annualized Return          0.115400 0.0015000 0.113600
Annualized Std Dev         0.049800 0.0412000 0.027900
Annualized Sharpe (Rf=0%)  2.317400 0.0374000 4.072100
Calmar Ratio               1.700522 0.0166862 7.430481

In other words, the short side is absolutely amazing as a trade–except for the one small fact of having it be impossible to actually execute, or at least as far as I’m aware. Anyhow, this was simply a for-fun post, but hopefully it served some purpose.

Thanks for reading.

NOTE: I am currently contracting and am looking to network in the Chicago area. You can find my LinkedIn here.

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