Jan 30, 2011

Week in Volatility

Market rose from Monday to Thursday, and fell hard on Friday. This created a very interesting movement in the VIX term-structure: first - VIX index closed above the front month futures, second - front month futures rose, as back months fell (week to week). For me that means that market is still expecting VIX to go lower, while risk premiums fell across the months. This should put less of a negative bias on VXX returns as term structure is now much flatter than week ago.

Such particular term structure help explain something about VIX futures: there are two factors that control shape - expectation of the VIX movement, which can be positive or negative, and risk premium, which is always positive. This allows for much flexibility in term structure, such as the one we saw on Friday.

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.

Jan 20, 2011

VIX Expiration

Yesterday VIX expired at 16.38, down 2.49 from previous expiration. My prediction made on Dec-26 was for 17.66, when the front-month futures traded at 19.80.


For the next month I forecast a higher VIX, at 18.42 vs 18.80 in the Feb futures, and somewhat flatter term structure.

Jan 12, 2011

VIX vs Implied volatility in other asset classes

Everyone wants to know what will happen to the VIX in 2011. Goldman Sachs analysts are forecasting the index to be in the 16-20 range (link), and AlphaShares analyst is concerned that investors have become "too comfortable," and is surprised at the current low levels of implied volatility (link).

I wrote about month ago that as VIX was making multi-month low other volatility indexes tied to other asset classes were not at corresponding levels. Yesterday I finally got around to crunch some numbers. What I did is robust linear regression (in log-levels) with VIX as dependent variable vs MOVE index which measures implied volatility in US treasury market, JPMVXYG7 which tracks implied volatility of G7 currencies, and GVZ index that measures implied volatility of GLD ETF. With each regression I get a theoretical level for the VIX that is statistically consistent with other indexes.



All the indexes seem to point out to a higher level for the VIX. Will VIX move higher, or will other indexes come down? I honestly cannot predict that. The analysis that I constructed above is not something I would use for trading, because although volatility usually spills over from one asset class to another, connections between them are weak, and most importantly not directly tradable. And while my trading model is also bullish on VIX, I want to remind everyone (especially myself) about prolonged bear volatility markets in 2004-2006, when every day someone would complain that VIX is too low, statistically, historically, by this measure or that, and it took years for VIX to get above 20!

Jan 6, 2011

Case solved: no arbitrage

Apology to the readers - I got too excited and did not read prospectus carefully enough. The fair value of XXV should be calculated as $20 * (1-return on VXX). I used Aug 4, 2010 as a reference price, since it is the first trading day for XXV, however prospectus says that the reference price should be the one from "inception date" of July 16th. On that date VXX closed at 109.48 (adjusted for split) , creating the following formula:

simulated XXV = $20 * (1 - (VXX-109.48)/109.48 )

which results in values that are fairly close to actual XXV values. See prospectus on page PS-7 for the proper formula.


For more exact calculation I reverse-engineered a better reference price of 108.03, which is probably close to the VWAP price of VXX on that day, making the formula

simulated XXV = $20 * (1 - (VXX-108.03)/108.03 )

This answered my previous question of why XXV return was lower than VXX - it was not, I just was using the wrong reference price. The second question was regarding volatility - XXV has about half of daily volatility of VXX. Here again the explanation is fairly simple - as VXX goes lower its dollar volatility decreases, and dollar volatility of XXV decreases, but in % terms XXV volatility decreases because XXV is now at a higher price.

In fact I can make a prediction that at some point as VXX goes lower, XXV will approach its maximum value of $40 slowly, penny by penny.

I want to thank all the readers who emailed me with their comments, especially William W. for his helpful explanations!

Jan 3, 2011

VXX - XXV Arbitrage ?

Happy New Year, traders! Hope that 2011 will be a healthy and prosperous for you and your loved ones!

I don't watch XXV on a daily basis, but few days ago noticed an interesting pattern: since XXV started trading few months ago it did not rise as much as VXX fell, in other words, XXV did not exactly replicate "short VXX" I don't know why it has happened - was it because of transaction costs, or some other reason - I don't have an explanation, but looking at some basic stats I think it maybe an idea for a trade. Before I proceed I must disclose that I don't intend to put this trade on myself as I am busy with my main trading activities, but I do believe this can be an actual trading opportunity for someone else. Ok, here's the numbers: since 8/4/2010 VXX had an average daily return of -0.75%, and XXV +0.31%, total of 0.44%. That means that if an investor were to enter a portfolio of short VXX and short XXV without any costs, they could capture a daily return of 0.44%. The pattern persist across the time - in Dec it is 0.89%, Nov 0.12%, Oct 0.76%, Sep 0.44%. In August the number is -0.09%, but I think that is because of the excess volatility in the first few days of XXV trading. A trader with ability to borrow these two instruments can short both VXX and XXV, pay short interest (very reasonable compared with ETN gains) and walk away with a profit. Daily rebalancing is not required for this to work, since XXV is not a daily inverse VXX, but rather simple short VXX.

What is the reason for XXV relative under-performance? Bid-ask and financing charges seem to have only a minute effect on profitability, certainly not the ~20% difference in less that half of a year. What is more puzzling is that volatility of XXV is about half of that of VXX. I thought that perhaps XXV is under-leveraged compared with VXX, possibly because of higher margin requirements on short futures, however I could not find it in the prospectus. Ideas, explanations, criticism? Good luck traders, and watch your deltas!