Jan 24, 2011

De-constructing XVIX

XVIX is a new ETN from UBS that is designed to take advantage of term structure of VIX futures, and provide excess returns by holding daily rebalanced portfolio of short and long-term VIX futures.

UBS' XVIX page here, including factsheet, and prospectus. XVIX is designed to track S&P 500 VIX Futures Term-Structure Index Excess Return, available on Bloomberg as SPVXTSER. The underlying is a daily rebalanced index of :
  • short 50% of Short-term VIX futures index, based on which VXX trades,
  • long 100% of Mid-term VIX futures index, based on which VXZ trades.
Again, note the part about daily rebalancing: you cannot create XVIX by holding a static portfolio; you would need to rebalance the portfolio daily if you wish to replicate the index. The plot on the website and in the factsheet display a relatively smooth equity curve, generating 24% annualized return with very small drawdowns, even during volatility skipes in the fall of 2008, and May 2010.

I took the data for the last 5 years (19-Jan-2006 to 19-Jan-2010) and reproduced the underlying indexes, labeled as their corresponding ETFs, in the same colors as UBS' website. According to my calculations in the past 5 years index rose 193%, or 24% annualized, with the maximum drawdown of 15% in the fall of 2008 (the drawdown lasted only two months) . Performance by the year is as follows:
  • 2006 Return 11%, MDD 12%
  • 2007 Return 18%, MDD 15%
  • 2008 Return 14%, MDD 15%
  • 2009 Return 24%, MDD 10%
  • 2010 Return 55%, MDD 5%
You can see that 2010 has been an excellent year for the index, but even taking the entire history of the index performance is quite good. These results are of course only historical simulation; the big question is will this historical performance hold in the future.

Why did the analysts at UBS chose this particular set of parameters -0.5/+1 for the ETF? I have compared other possible allocation ratios from -2/+1 to 0/+1, and calculated sharpe ratio (return / standard deviation) and calmar ratio (return / maximum drawdown). So in my simulation I am always short VXX, and long VXZ, starting from short twice VXX on the left, to short no VXX and just long VXZ on the right. Before I calculate the ratios I adjust portfolio weights to have the same notional (1.5) as XVIX.



Allocating -0.54/+0.96 results in the highest sharpe ratio, and -0.48/1.02 in the highest calmar ratio.One can plainly see that in hindsight the best allocation is very close to -0.5/+1 XVIX allocation.

Are these parameters stable? Using calmar ratio the best allocations for different years are
  • 2006 -0.66/0.84
  • 2007 -0.40/1.10
  • 2008 0.00/1.50
  • 2009 -0.62/0.88
  • 2010 -0.54/0.96
Looking at the parameter changes it is clear that 2008 was a very different year from other ones. Ignoring that year the allocations range from -0.4 to -0.66 for VXX, and from 0.84 to 1.1 for VXZ. That puts XVIX performance from 24% to 32% annualized with MDD from 14% to 29%. If we ignore 2010 (because of its exceptional performance), the simulated returns are about 21%, with MDD from 14% to 29%.

Using sharpe ratio the best allocations for different years are
  • 2006 -0.75/0.75
  • 2007 -0.37/1.13
  • 2008 -0.29/1.21
  • 2009 -0.62/0.88
  • 2010 -0.53/0.97
Although range of parameters seems to be wider, 2008 is not an anomaly in this optimization. The total performance now ranges from 20% to 35% with MDD from 21% to 41%. Ignoring 2010 performance now ranges from 21% to 22% with MDD from 22% to 41%.

It seems to me that UBS' choice of parameters was clearly the result of optimization, however the parameters are relatively stable over different periods, and performance is adequate for a reasonable range of parameters. In other words, I think that there is a reasonable expectation that XVIX can take advantage of VIX futures term structure to produce positive returns. Under the range of parameters analyzed above the worst case expectation for XVIX to return 20% per year with MDD up to 41%. 

Full disclaimer: there is some mathematical research on quantifying different biases of backtesting results. I am not familiar with such research, and I think that it would come very helpful in evaluating XVIX, as opposed to simple analysis that I did above. If any of the readers is familiar with such research, please email me a note or a link.

3 comments:

  1. Very interesting/helpful analysis. Aside from historical backtesting, is there a theoretical expected return based on the slope of the futures curve?

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  2. Excellent question coleman! If we're to derive a model, the expected pl would be dependent on assumptions that go into the model. To get any sensible result the model would have to be robust and parsimonious, probably time-homogeneous process that has stochastic vol of vol and jump components. That's all I can say for now.

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  3. I've done a similar analysis myself, which is consistent with yours. Thanks for posting it in detail.
    I have also found that correlation between VIX and VXX/VXZ pair is almost zero for -2:1 ratio. For other ratios the combo is not market-neutral.

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