Week in Volatility

S&P and Eurostoxx fell about 2% this week, however Friday's action really pushed VIX futures higher. VSTOXX futures ended the week only slightly higher - mostly because of the time difference having closed on Friday while VIX continued to rise, and I fully expect VSTOXX futures to open lower on Monday (by about a point) to make up the difference.

Overall this week's action surprised me. I was positioning my portfolio to profit from further fall in the VIX, where my max profit zone is from about 18 to 20 in the front month, however given Friday action (VIX high at > 21) with just 2 full trading days to go before expiration seems like a very uncertain proposition.

While I thought that the market decided that it is the time for low volatility regime, we're still probably in the mid vol levels - and can easily see VIX push higher given a catalyst.

Canadian VIX - VIXC

Few weeks ago Montreal Exchange changed the methodology of its volatility index. The old index, MVX was constructed in the same way as the VXO - using implied volatility of ATM options, while the new index VIXC (Bloomberg symbol VIXC:IND) uses the same methodology as the VIX. Here is a presentation on the index construction. Unfortunately the old index was completely discontinued, while the new index has only one year of history. For my research purposes I combined the two, averaging closing values on the overlapping period. Exchange data here, and you can download the combined data here.

Below is the chart of the combined history MVX-VIXC vs VIX.

Confused by VIX / SPX correlation? You are not the only one!

This morning I came across this gem on FT blog. Based on her statistical and technical analysis (see the chart attached to the post) the author writes that recently correlation between SPX and VIX has been positive, and predicts that it needs to return to the norm. The problem is that the author has got it all wrong, confusing price correlation and return correlation.

If we look at some short time periods, it is not unusual to observe VIX prices to look like a mirror image of SPX prices, just like in the chart on FT website. This pattern however is not robust - if we look at a scatterplot of SPX prices vs VIX prices over the last 20 years, it is clear that there is no correlation. It is also intuitive - S&P moves around all over the place, while VIX stays most of the time in a range.


Where correlation is robust is in returns - percent changes (daily, weekly, etc.) The scatterplot of daily returns for the last 20 years clearly shows strong negative correlation (-0.69) in the data.

The same pattern exists for weekly and monthly returns (I created the plots using non-overlapping returns)

From what I see in the data any correlation between SPX and VIX price levels is mostly spurious and coincidental.

What is equally puzzling is the authors' claim that correlation turned positive since October 22nd of this year. There's been only 8 trading days, and hardly any statistic should be calculated on only 8 observations, especially such a "noisy" one as correlation. Even if I were to agree with Ms Brooks methodology, the correlation observed is 0.35 +/- 0.37 (MSE using 10K bootstrap simulations) i.e. the real correlation cannot be reliably estimated based on such a short sample. The last plot is the histogram of correlation coefficient.

Two points in conclusion:

1 - there is no stable correlation between SPX and VIX price levels, but there is a stable robust correlation between SPX returns and VIX returns on different time horizons.

2 - need more than 8 days of data to create reliable statistics.

MOVE Index, Part 2

My last post was about predicting VIX index using MOVE index where I posted a basic model for VIX fair value. MOVE closed last week at 99.80 (Bloomberg) , implying VIX price of 20.98. Of course to use the model one needs to investigate the average error. To do that I used 10K bootstrap regressions to figure out mean absolute error of 4.72(histogram below). While not amazingly accurate, VIX fair value model is good enough as a basic cheap/expensive indicator. Since the current VIX value is well within the error of the forecast, it is clear that equity implied volatility is in line with the Treasury markets.

MOVE Index and VIX Index

MOVE index was developed by Merrill Lynch to measure implied volatility of US Treasury markets. It is a yield-curve weighted average of normalized implied volatility of 30-day options. The index has been in existence for several years now, however it is seldom discussed, either in itself, or in relationship to the VIX. What I am interested in is if volatility in the treasury market can forecast volatility in the equities.





The images above show the MOVE and VIX indexes for the last 5 years, and ratio=VIX/MOVE. While it appears from the plot that MOVE started increasing much earlier in apparent anticipation of 2008, corresponding to low points in the ratio plot, subsequent rise in the VIX was much more severe than that of the MOVE.

To get a better view of the relationship between the two indexes I conducted a number of regression-based tests. The results all indicate that indeed MOVE index can help predict future level VIX. The simplest model for the VIX level based on the MOVE is
VIX = EXP(-1.84+1.06*LN(MOVE))
You can type the formula directly into Excel. MOVE index closed yesterday at 98.70, implying VIX price of 20.65, compared to the last VIX price of 20.88.

Week in volatility, VIX forecast analysis

Equity indexes traded in a range this week, ending almost unchanged / slightly up over week. However VIX futures fell strongly across the board, declining an average 1.76 points, which VSTOXX futures fell 1.05 points. The sharpest decline was in Nov VIX futures (current front month, following October expiration 5 days ago) that feel almost 3 points from 24.05 to 21.10.







Despite this sharp decline I continue making bearish bets. It is true that we are in a low volatility regime, but my own research indicates that such low-volatility regimes are usually persistent, and provide a good opportunities for selling volatility. I plan to write more about this when I have more time.

October futures and options expired last Wednesday, settling at 21.41 . My forecast made last month for October expiration was 22.62 (error=1.21) vs market forecast 25.55 (error=4.14). I do not have yet forecast for Nov expiration, because of some software issues, however I plan to update the blog as soon as I have them.

Good luck traders, and hedge your deltas!

STLFSI and VIX

First off, let me apologize to all my readers for infrequent posting. I was very busy moving to NYC and just did not have the time to follow up on all the news in the volatility universe or questions that you emailed me. Also, I would like to thank my friend Ethan for all his help.

Last week vixandmore wrote two excellent posts about stress indexes, namely St. Louis Fed Financial Stress Index and Kansas City Financial Stress Index, here and here. I previously mentioned STLFSI and its relationship with VIX here.

I don't have any criticism for the indexes, however I think that practically they are useless - STLFSI is published weekly with at least one week lag (right now the latest release is dated 9/24/2010), and KCFSI is published once per month. If you're trading, such delays are simply impractical, and reconstructing indexes from raw data to create daily values seems like a lot of work.

Good luck traders, and hedge your deltas!