Italian Volatility Index

Somehow I missed the news, but about a month ago FTSE launched a series of new indexes, among them based on Italian MIB index link, bloomberg quote. The complete list of indexes is available here and is called FTSE Implied Volatility Index Series.

Volatility futures in the US declined as equity markets rallied, but VSTOXX and futures rose on European credit risk. SKEW index, and VVIX Index were pretty much unchanged, and I expect VIX to be around the current level over the next week.

Excel Big Data & Python in Finance

For readers in NYC area interested in augmenting their programming skills - there are two day-long workshops that I believe to be of excellent value for quants and traders. Learn a new skill and meet other finance professionals!

April 5, 2013, Python in Finance
The day-long conference in New York City brings together 300+ Python practitioners with a who’s who line-up of speakers from the world of Python and finance, including Claudia Perlich, Travis Oliphant, and Wes McKinney.
Details, and to register:, and use the code VOLATILITY for $100 off.

April 19th, 2013, Excel Big Data
Big Data is all the rage these days, but it's hardly accessible to the average person. However, few people seem to know that Excel is a great front-end for Big Data. This one day workshop and conference shows how Excel can be used effectively with Big Data.
Details, and to register:, and use the code VOLATILITY for $50 off.

I highly recommend the monthly HPC & GPU Meetup also organized by Andrew Sheppard of Fountainhead.

Disclaimer: onlyvix receives no compensation for this blog post; I publicize these courses because I think they will be helpful to my readers.

VHSI April 2013 Forecast

This afternoon was the expiration of March VHSI futures. It was an exciting action in the market as in the last half-hour of trading (which average to VHSI settlement value) index rose from 14.87 to 15.26 and tumbled down to close at 14.69.

The official settlement value from the exchange is available at day's lag, but according to my calculation should be 15.04, making it almost in between the market's futures level a month ago and my forecast, although I was correct on direction.

For the next expiration, my forecast is 14.82 vs futures value of 16.10 (mid). All forecasts are logged in volatility forecasts spreadsheet. Expiration dates for VHSI and other volatility indexes, as well as their settlement procedures are here.

Leveraged ETFs: How Biased Statistics Affect Your Portfolio

In this post I would like to introduce Alpay Kaya, author of Leveraged ETFs: How Biased Statistics Affect Your Portfolio

OnlyVIX: Before we get to the math, would you tell us about yourself?
Alpay Kaya: Like many others, I came to the world of finance from a technical educational background, Control Systems, which is an applied math field mostly populated by electrical & mechanical engineers. My research from those days has been published in academic journals and presented at conferences.

I was drawn to the investing sector of finance because of its connection to reality and the relation between human behavior & math. I joined Koch Capital, the prop trading unit of Koch Industries, where I developed systematic trading strategies (long/short equities, then FX options and rates futures). My output was a trading protocol implemented by the execution desk at notional values exceeding $100MM. Although the systematic approach appeals to me, the office politics between our unit and corporate became quite silly; to wit, a corporate director came to the office one day and announced that my FX trade would be doubled because it made the most money the previous year. Since portfolio allocation is not to be done by dictate, I left shortly thereafter to join a start-up fund, but whatever was lacking in office politics, the owner made up for with his outsized ego.

I was working on a general-interest investing book a little less than a year ago when I heard someone on CNBC mention that LETFs lost value because of 'compounding'...a term I find to be meaningless. There were no books on the topic, so figuring supply did not meet demand, I wrote one and found ample opportunity to cover important quantitative finance topics also. By defining negative drift in mathematical terms (not by example), my work expands even upon the current academic literature.

OnlyVIX: What can readers expect to gain from reading your book?
Alpay Kaya: Since fundamentals serve as the foundation for everything, a step-by-step review of all necessary math - from the definition of return to geometric Brownian motion (GBM) and Ito's lemma - is included. Readers can expect to understand GBM better than most because it is developed under both the arithmetic and logarithmic return models. The conventional derivation confuses many because it is statistically convoluted; that is to say, the parameters are not independent! Practitioners will also appreciate my use of a unified model (as opposed to long & short variants), which is justified by showing the equivalence of long- and short-leveraged portfolios backed by futures or the assets themselves (when applicable). For traders, my book explains why leveraged ETFs trade the way they do, which will help them avoid basic trading mistakes. The long-term value evolution differences between long- and short-leveraged (inverse) ETFs is derived. For the more mathematically inclined, my book is a compete resource on the quantitative aspects of leveraged ETFs, complete with formulas that can be easily implemented in Excel.

OnlyVIX: We have corresponded about leveraged ETFs and disagreed on some points; would you mind sharing them with the reader?
Alpay Kaya: The following take on distributions is directly from that text. For consistency of presentation, some points from Leveraged ETFs Decay And Symmetric vs Skewed Distributions are quoted below and addressed along the way.  

A Package Deal
It is important to view the log-normal distribution φL as a system of parts:
  1. a normally distributed INPUT: x ~ φN( μ, σ )
  2. a continuous growth PROCESS function: f(x) = exp( x )
  3. a growth factor (price ratio) OUTPUT: yi = pi / pi-1 = exp( xi )
for the purpose of correctly attributing any characteristics. For example, anyone faulting φL with nonzero skew should place blame with the exponential function. It is ‘guilty’ by virtue of transforming additive inverses to multiplicative inverses. Then again doing so has served all branches of the physical & life sciences very well. Besides, is it not logical that returns over any number of periods should sum to zero
x1 + … + xn = 0 <==> pn = p0

if and only if final price equals initial price? If the input driving the process is symmetrically distributed, do not necessarily expect the same of the output distribution.
This furcation is consistent with the notion that a price history is a discrete sampling of a continuously evolving reality. A standard result
E( yi ) = exp( μ + σ2/2 )

is that of the mean output being a function of mean input and volatility. To those who think of period return in terms of percent change, note that percent change is the first-order approximation of log return (i.e., the input x as defined above). Put another way, consider changing your perception of the price evolution process.
“…downward drift in leveraged ETFs is due to mean-median divergence…”
I disagree. A log-normal distribution’s mean output differs from the median yet φL exhibits no such drift. Given successive log returns x1, x2 such that x1 + x2 = 0, the two-period growth factor
p2 / p0 = y2 × y1 = exp( x1 ) × exp( x2 ) = 1

shows this to be the case. Since every symmetric input distribution is comprised of such pairs, this accurately reflects the general case for symmetric distributions. This applies to the discussion on LETF drift because it was first noticed in sideways markets (during which log returns sum to zero). Any choice of input leverage will not change this result.
“Many people have a mental model of ETF prices…some kind of symmetric price distribution.”
It is true that many subscribe to such a mental model, and, they are wrong. Considering equal-magnitude positive and negative moves ($1 up, $1 down) as symmetric is consistent with the percent change model. As one decreases the period of time over which percent change is calculated (or used to evolve prices), the results over multiple periods tend towards those consistent with the exponential growth process.
Serious study of financial mathematics should not be undertaken with a percent change model. I derive all the results in my book using both return models as a way of exposing all of the issues associated with doing so.
Don't Mess with Causality
I have one final point of contention with conventional presentations: distributions parametrized on volatility. Parametric graphs are a valuable visual tool; unfortunately, many are designed backwards. The future distribution of prices is a function of the input, and a parametric visualization should show how changing the input affects the output. Increasing σ (keeping μ constant) keeps the median output constant and increases the mean output.
It is unfortunate the designers of such graphs often decide that the mean output should be kept constant, thus changing both of the input's parameters. As they increase σ, they decrease μ just enough to keep the mean output constant. This convolutes the intent of parametric graphs. Both make clear the growing difference between mean and median price (and look pretty much the same), but the conventional presentation misleads many into thinking volatility is reducing the mean input.

This detail is no less important for its subtlety. LETF dynamics are mostly driven by the increased volatility that comes with leverage. As a related point, I would like to mention that a fair price is not one equal to the expectation of tomorrow’s price distribution. Today’s fair price (ignoring one day’s interest) is one such that tomorrow’s expected log return is zero.
Why Do LETFs Exhibit Negative Drift?
If neither the mean-median divergence nor the increased volatility driven by leverage leads to negative drift in φL , then why do LETFs exhibit it? Quite simply, LETFs leverage the percent change implied by the output ( yi - 1 ) not the distribution’s input ( xi ). LETFs are not log-normally distributed, but they can be pretty accurately represented by a log-nromal distribution with the correct parameters.

OnlyVIX: Any advice to someone who wants to start trading leveraged ETFs?
Alpay Kaya: All leveraged instruments help to increase alpha, but they do so in different ways. This necessarily means their risk profiles are different also. The most important thing is to know the fundamentals so you will not be surprised at how your portfolio responds.

Leveraged ETFs: How Biased Statistics Affect Your Portfolio is now available on

Cyprus Reaction: Asia vs Europe

I do not have to write about credit developments in Cyprus that came out over the last weekend. What followed over the next five days shows an interesting dichotomy between reaction from volatility indexes in Europe and Asia.

At the end of preceding week, Thursday 14th and Friday 15th volatility indexes around the world were relatively low. Over the weekend - Monday to Friday all volatility indexes rose, but there was no significant difference between the continents: Asian volatility indexes rose an average 2.1 volatility points, and average of 13%. European indexes rose an average 1.6 points, and average of 11%. Not surprisingly Russian Volatility Index rose the most in Europe.

However by the weeks end the situation changed, and implied volatility in Asia started to decline. Friday to Friday Asian volatility indexes rose an average 1.0 volatility points, and average of 5%. European indexes rose an average 3 points, and average of 22%. Surprisingly (to me at least) that Russian and Polish volatility rose less that other volatility indexes in Europe.

Data: For Asian volatility indexes I used VKOSPI , VNKY , VHSI, INVIXN (India), SPAVIX (Australia), and recently launched Taiwan Volatility Index. For Europe, I used RTSVX, VDAX, VSTOXX, VSMI, VAEX, VCAC, VFTSE, and my own Poland Volatility Index based on WIG20 options.



VIX,VSTOXX Expiration and Forecasts

Yesterday all CBOE volatility products expired, and also VSTOXX on Eurex. My forecasts did will on Sim PL metric, but statistical error was worse than the market. The most challenging was VSTOXX that rose over the weekend in reaction to credit developments in Europe. I have updated volatility forecasts spreadsheet with the new values. 

For the next expiration, April 17 2013 my forecasts are:

VIX 13.18 vs 14.50 in the futures market
VSTOXX 19.40 vs 19.80
GVZ 13.92 vs 15.45
VXEEM 17.56 vs 19.50
VXEWZ 19.07 vs 21.65
OVX 20.11 vs 22.30
VXN 13.96 vs 15.65

You can find all forecasts and performance analysis in the volatility forecasts spreadsheet; expiration dates for world volatility futures and summary of settlement procedures can be found here.

VIX / VVIX Divergence

Last week Matt at Distressed Volatility posted a chart showing recent divergence between VIX and VVIX index (volatility index based on VIX options). It looks from the chart that for VIX and VVIX followed similar trajectory but in the recent 3 weeks have gone in starkly different directions - with VIX declining while its implied volatility rising. Looking at the chart the spread seems significant.


However looking at longer history of VIX and VVIX different picture emerges: the levels of indexes are not really related. Here is the same plot for the past 6 years -  there is some similarity (timing of the peaks) but the levels are not really related.  I also fitted a more complicated model to quantify relationship between levels of VIX and levels of VVIX but without success.

Scatterplot also does not show a simple relationship.

However a simple relationship exists between changes in VIX (daily difference) vs changes in VVIX, and returns in VIX vs returns in VVIX - on daily, weekly, and even monthly time scales. The chart on the side is the scatterplot of daily returns on two indexes, a consistent relationship with correlation over 0.6. This is not much different from SPX & VIX - little correlation in levels but high correlation in returns. 

Using weekly data I estimate that VVIX returns are ~ 0.41 * VIX returns sigma=0.066, which makes last weeks move (VIX lost 10% VVIX gained 11%) to be significant. However this is not to conclude that indexes will mean-revert; rather they will continue their paths from these new levels.

Nikkei Volatility Index April 2013 Forecast

Nikkei Volatility Index has been in the uptrend over the last few months while the rest of the world volatility indexes have been in the decline. As I hear the increased volatility worked well for quant-funds trading Japanese equities, but it is a risky currency environment given the rise of USDJPY volatility (although USDJPY skew has declined from its highs.

This is my first forecast for VNKY - to expire at 25.07 vs futures price 24.40 . Currently this is the only forecast for a volatility index to rise - if you look at the chart there is significant upside potential for the index. With VNKY closing at 25.13 I calculate there is 14% chance that it will expire higher that 30.00 .As always, all forecasts are logged at forecasts tracker spreasheet.

Week In Volatility

Volatility News:

Equity markets up, volatility indexes down -  no need to regurgitate old news, just summarize the stats: VIX fell 2.77 , VSTOXX  lost 4.39, VNKY is the only index that has gained 0.13 - I am planning a post analyzing the complete divergence of VNKY from other vol indexes... Speaking of  Technical glitch created bad price for Nikkei Volatility Index on Mar 4th

Two books coming out in the second edition: Volatility Trading by Euan Sinclair and Inside the Black Box by Rishi Narang. I wrote before about Volatility Trading; Rishi Narang's book is not volatility focused but covers quantitative strategies in detail, and specifically explains how strategies interact, and under which circumstances they succeed or fail, what quantitative strategies can accomplish and what they cannot. It is a straight-forward non quantitative book that is meant to provide an overview of quant trading ecosystem without technical jargon.

RTSVX April 2013 Forecast

RTSVX - Russian Volatility Index closed on Thursday at 20.31. The value was significantly closer to my forecast of 18.97 than to 25.85 - the futures value at the time of forecast, and also my forecast was correct on the direction capturing a healthy difference of 5.54. However my recent analysis shows that RTSVX is one of the more volatile indexes and one of least predictable, and I am curious how accurate the forecasts will turn out for the rest of the year.

My forecast for the April expiration for RTSVX to close at 20.00 vs futures value of 25.60. The model is still bearish on volatility throughout the world, but I certainly advise against outright trades. As usual all forecasts are tracked monthly at forecasts tracker spreasheet.

VIX is to SPX as VVIX is to ?

The answers seems obvious - VIX is the 30-day volatility of SPX, VVIX is the 30-day volatility of VIX, but in reality it is a little more complicated than that, as least when it comes to the difference between historical and implied volatility, or volatility risk premium. After discussing this with one of the readers I decided to make this a short post.

VIX measures 30-day implied volatility of SPX options, and is a (granted, biased) predictor of future 30-day historical volatility of SPX index. However this same is not true for VVIX, that is VVIX is not a predictor of future 30-day historical volatility of VIX. It is however a predictor of future 30-day historical volatility of 30-day VIX forward. Such instrument does not exist, but the next best thing is VXX - ETF that holds front and second month futures to approximate returns on 30-day forward.

Something to note that theoretically term structure of implied volatility of VIX is decreasing with time to expiration, but VXX has a flat term structure, corresponding (approximately) to 30-day VIX implied volatility.

Forecast Volatility with Skew

I came across a research paper "Corridor Volatility Risk and Expected Returns" the other day. To summarize in one sentence researchers construct volatility indexes using a subsets of SPX options, e.g. call VIX or put VIX, and find that equity risk premium is correlated to call VIX, not put VIX.

That gave me an idea to check the same on volatility risk premium - or alternatively figure out a better way to forecast future realized volatility using skew information. I regressed VIX on following 22-day realized volatility ( beta ~ 0.75 ) and tried to correlate residuals to CBOE SKEW Index (and couple of different transformations of SKEW Index).

Result: nothing; I did not find any way to improve volatility forecasts using SKEW. I don't know if there is really no relationship - I suspect that there is one, and I just failed to figure it out. If you have more success that me, please send an email.

Poland's Volatility Index

Index options based on Polish WIG 20 Index started trading in September 2003, and since then the market has matured to the point that one can develop a volatility index. The Warsaw Stock Exchange does not publish an ‘official’ volatility index, so I decided to create one and publish the data.

POLAND_VOLATILITY_INDEX.csv in US format (02/28/2013,2452.01,16.36)
POLAND_VOLATILITY_INDEX_EUR.csv in European format (28/02/2013;2452,01;16,36)
Everyone is permitted to copy and distribute this file as long as you cite the original source.


There is one academic work, ‘Emerging versus Developed Volatility Indexes’ by Slepaczuk and Zakrzewski, which does address a WIG20 volatilty index, however the authors do not provide data for their index and differ substantially in methodology from my own.

I teamed up with Grant Shannon – personal friend and one of the creators of South-African Volatility Index to crunch the numbers. We followed the original VIX Whaley (1993) methodology – basing the index on most liquid ATM options, instead of the Derman et al (1999) methodology because the skew information is not particularly informative: 2012 is the sole year that the exchange listed more than 30 strikes per expiration, and option volumes actually declined from the year before.

Most of the OTM options don’t trade, or trade very little – so a volatility index based on OTM options would not be robust. This is in contrast to Slepaczuk’s paper that used the Derman methodology, but had to create significant modifications to make it work for the Polish market. Using Whaley’s methodology also allowed us to create a 30-day index, just like the VIX. We believe this is also an important advantage over Slepaczuk’s 91-day index since liquidity is concentrated in near term options. Also 30-day index allows for direct comparison with other international volatility indexes like VIX, VSTOXX and others.

Grand Shannon specifically noted that emerging market volatility indices typically do not trade, i.e. they are built more for information and risk management purposes than for trading. This is a critical point because it means that there is no need to build an index that has skew built into it; a simpler model would work for emerging markets such as Poland - at the money volatility is transparent and sufficient as a starting point for risk management. The index also would be accurate as ATM implied volatility data is much more readily available in most emerging markets. In addition, an ATM implied volatility index is much more understandable too - as opposed to one that includes skew.

We calculated the index from inception on September 22, 2003 to present. By the end of the week I plan to start updating the spreadsheet daily with most recent index values.


My efforts to create this new series are aimed at assisting empirical researchers and interested market participants in gaining new insights into the emerging volatility space. One interesting application of the new index includes an analysis of the recent world-wide volatility spike of August 2011. On August 4th Jose Manuel Barroso, the head of the European Commission warned that the eurozone debt crisis was spreading from the smaller debt-laden nations to Italy and Spain. Italian and Spanish yields rose sharply while German yields fell. On the evening of August 5th after close of trading, S&P downgraded credit rating on USA.

During the first week of August WIG20 fell from 2726.31 to 2447.21 and the WIG20 Volatility Index more than doubled from 13.36 to 35.27. On Monday August 8th most of the indexes experienced a free-fall: Euro Stoxx 50 declined 3.7%, S&P 500 declined 6.7%. ECB launched a massive buying program of Italian and Spanish debt. Volatility rose across Europe; the VIX jumped from 32 on Friday to 48 on Monday’s close where it topped out. Wednesday 10th seems to be the worst day – WIG20 fell 5% - it’s 8th consecutive down day while the WIG20 Volatility Index reached 57.74.

Weekly market report

Wall st delivered a mixed bag of news with VIX, VNKY, and VSTOXX and their underlying markets almost unchanged. VXD - volatility index based...