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.

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%

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

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.

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

ReplyDeleteExcellent 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.

ReplyDeleteI've done a similar analysis myself, which is consistent with yours. Thanks for posting it in detail.

ReplyDeleteI 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.