XXV is up in its first week, moving in what seems like a perfect inverse of VXX. The daily volume is still light, topping at about quarter million shares. Will the volume pick up? Probably. Will XXV continue to mirror VXX? I think so, although professional bloggers continue to debate the issue, e.g. here.

Data from Bloomberg. Barclays webpage on the XXV, fact sheet, pricing supplement.

## Jul 28, 2010

## Jul 27, 2010

### Russian Volatility Index

[EDIT: Updated info on Russian vol index here]

My interest in IVO volatility index is not purely theoretical - understanding similarities and differences of other volatility indexes helps me develop better models for VIX trading. As you can see from the chart the behavior of VIX and IVO is overall similar. Average level of IVO is 46, about twice that of the VIX (23). Maximum of IVO is 195, compared with 80 for VIX. The distribution of extreme points fit to a power-law with similar exponents. Interestingly enough both indexes were at around the same value in late 07 - early 08 before spiking during the credit crisis.

## Jul 25, 2010

### Modeling VIX For Trading

Here is my VIX forecast for the next expiration: 24.80 +/- 5.40 (See my previous posts 1, 2 on the methodology)

But how accurate is it? The model that I developed can predict "local" probabilistic behavior. Sometimes market undergoes a dramatic regime change, like in the autumn of 2008, or this year when VIX went from under 20 in April to 35 and 40 in May. On a side-note news wires reported of sizable losses Goldman Sachs sustained in the 2nd quarter due to short vol exposure.

These kind of events that the model will fail to anticipate. Recently I've been researching economic indicators that could help forecast such extreme shifts. One of indicators that I came across is St Louis Fed Financial Stress Index. STLFSI is a "portmanteau" index that consists of 18 interest, yield, and volatility related indexes. Below is the plot of VIX and rescaled STLSFI weekly data from Dec-1993 to Jul-2010. Unfortunately, Fed publishes the index once a week, with 1 week delay, making it useless as a leading indicator. Still, perhaps it is something to keep an eye on.

## Jul 24, 2010

### New Volatility Indexes

The stock indexes around the world were up this week, while international volatility indexes feel on average 5%, or 1 point. As I mentioned in the previous post VSTOXX was inexplicably up 1 point for the week; I really don't have an explanation why would a major index buck the overall trend like it did.

There are several additions to my list of volatility indexes:

VKOSPI - based on Korean KOSPI200 options markets. The details on index calculation are here, but the algorithm is no different from the one used for VIX.

CHIX - AlphaShares China Volatility Index, which measures the implied volatility on FTSE Xinhua China 25 and Hang Seng (HSI) indices, and is also calculated like VIX. I could not find the technical details on the index, but the press release from the firm is available from their website here.

Six Asian volatility indexed from Citigroup, on which I could not find any information. There is some overlap with other volatility indexes, but the values are different - maybe because the method of calculation is different, or maybe because they're based on different indexes.

CITJAVIX - Australia Volatility Index

CITJHVIX - Hong-Kong Volatility Index

CITJIVIX - India Volatility Index

CITJJVIX - Japan Volatility Index

CITJKVIX - Korea Volatility Index

CITJTVIX - Taiwan Volatility Index

Also, I removed the VXJ - Japanese volatility index. The reason is that Osaka University which disseminates the index has up to 2 weeks delay, which creates problems in tracking week to week changes. I will continue to monitor the index - maybe in the future it will become more prompt.

There are few volatility indexes that I am missing:

SAVI - South Africa Volatility Index, there is some information on the exchange website, but no time series, and don't know the Bloomberg symbol for it.

VOI ? - Brazil Volatility Index. Bovespa website seem to indicate that the index exists somewhere, but no further information.

AVIX - Australia VIX, based on ASX 200 Index options.

IVO - Russian Volatility Index based on options in RTS / FORTS index. At the end of May Interfax reported that RTS is planning to launch the volatility index sometime this fall.

### VSTOXX Futures, VIX Futures

Another mixed week in volatility - VIX Index fell almost 3 points, while VSTOXX rose 1 point. Both stock indexes rose - S&P up 3.5%, and Euro Stoxx up 2.7%.

VIX futures fell uniformly about 2.5 points. Since Jan-11 options were listed after expiration I was trying to place an option spread to against the Jan kink in the curve, but could not get a good price.

## Jul 21, 2010

### VIX Expiration

About a month ago I made a prediction - VIX will expire at 26.58 +/- 5.86 vs market's forecast (derived from futures and options prices) of 28.50 +/- 7.56. I'm still waiting for the official $VRO print, but last night VIX closed at 23.93, and opened this morning at 23.61, making my forecast closer.

It was interesting to note that even short-tern VIX options command exorbitant premiums. For example, 26-strike calls that had only overnight risk closed at 0.05-0.1. That was not a misprint - 2 points OTM calls were nickel bid and I sold one contract (just to test the market, not as a strategy) Implied volatility bid was 130% .

EDIT: VRO @ 23.79

## Jul 18, 2010

### Volatility and Expected Range

Despite what you read on many blogs, volatility and expected range are not the same, not even close. This fallacy is common among internet pundits who do not know any better, but to traders like me who have real money on the line such mistakes can be dangerous. This is not a post to correct some abstract mathematical technicality, or merely a semantic point. Rather I hope to shed some light on widespread mis-estimation of important risk metric.

"So, why is the VIX important? For one, it provides you with a reasonable projection of the expected range within which the S&P 500 is likely to trade within the next month. To use the current environment as an example, the S&P 500 closed on June 19 at 1240.14. The June 19 closing VIX reading of 17.83 suggests that options traders and investors anticipate that between now and July 19, the S&P 500 is likely to trade roughly within 1.49% range (17.83 divided by 12) of 1240.14 — or between 1221.71 and 1258.57."

First of, VIX is not the expected range. Second, VIX is not a measure of where the index is likely to trade. Third, none of these risk measures scale linearly with time, so dividing VIX by 12 months is rubbish. Fourth, simply from intuition, does is make sense that S&P will trade in a 1.49% range in a given month? To me as a trader, that number seems ridiculously low, even in low volatility market.

Ok, so what does VIX mean, and what does it imply? Technical definition of VIX (available from CBOE here) is the annualized square root of 30-day variance swap rate calculated from option prices. This is different from volatility swap rate, but for the purpose of this discussion I will use the terms interchangeably. The volatility that VIX references is not the volatility of prices, but of returns - another difference that I will ignore for today. We will treat VIX as simply market's expected annualized volatility.

Traders, pay attention to numbers and formulas you use in your trading. Mistakes can costs you money!

For example, certain Mark Bail provides us with the following gem of ignorance here

To convert VIX from annual to monthly volatility, one needs to divide not by 12, but by square root of 12. Likewise, if you want to find daily volatility, don't divide by 252, but by √252 ≈ 16. So in Mr Bail's example above, expected monthly return volatility of S&P 17.83 / √12 = 5.14%, and monthly price volatility 5.14% * 1240.14 = $63. Daily volatility is 1.12%, or $13.92.

As I wrote here, expected range of a random walk is 2 * √(2/π) ≈ 1.6 times the volatility. Therefore expected range for S&P for the month is 1.6 * 5.14% = 8.21%, or $101.85. Expected daily range is 1.79%, or $22.22. Expected monthly high, and low come out to $1291.06, and $1189.21. Please note the magnitude of difference between Mark Bail's forecast and mine - his expected range for the month is smaller than my daily range!!!

Now let's compare these predictions using historical data... After I wrote the previous sentence I tried to figure out when the article was written. There is no date on the article, the date that is referenced in the paragraph above is "June 19", however I could not any such date on which S&P and VIX closed at the levels reported in the article. I really do not know if the author just made a mistake or simply confabulated the numbers.

What I did find is that VIX happened to close at 17.83 on May 30th, 2008, so for comparison purposes I will use that date, dealing only with percent forecasts, since S&P level on that day differs significantly from the one in the article.

During the calendar month from 5/30/2008 to 6/30/2008 S&P index had a daily return volatility of 20.44% (annualized), which is a bit higher than the VIX, but not radically so. That month S&P had an open of 1400.38, high 1404.46, low 1272, closing at 1280. The range (1404.46-1272)/1400.38 = 9.4%, is much higher than 1.49% reported in the article, and much closer to my calculation expected range of 8.21%. Make your own conclusions from here.

## Jul 17, 2010

### Week in Volatility

Mixed movement in volatility - VIX is up, VSTOXX down. S&P lost 1% for the week - rose 2% to an intraweek high on Tuesday, stayed flat, and declined sharply 3% on Friday, which also was an options expiration day. EURO STOXX 50 lost 1% for the week - is rose steadily for four days, but declined 2% on Friday. World volatility indexes on average rose 1.5 points, or 7%.

This week I have added a graph of VSTOXX futures. It is the first time that I've seen the dynamics of two tradable volatility indexes side by side. The scale on both plots is the same - as you can plainly see that VIX rose pretty much in parallel across all months, VSTOXX index actually declined, while VSTOXX futures rose only moderately. What is interesting is that both contracts have a relatively cheap December volatility. Meanwhile FT Alphaville is predicting the end of the world in October.

## Jul 14, 2010

### 8 Simple Rules For Measuring Risk

Below I describe fast and easy heuristics that relate the price of ATM straddle to expected volatility, range, high, low, and maximum drawdown. These formulas may be useful to traders to quickly reassess their trading positions after a jump in price/volatility, or provide alternative view for a fair value of an option based on traders’ opinion on expected range, for example calculated from support / resistance levels.

To derive the formulas I assume the price follows arithmetic Brownian motion with no drift, and zero interest rate. These assumptions or course are not realistic, but quite workable for short-dated options, or for small volatility. The advantage of making such assumptions is great simplification of formulas. Heuristics work well for stocks and currencies, where there is no mean reversion in price, but would not work for interest rates, or VIX index.

1. Expected price volatility ≈ 1.25 * ATM straddle

2. Expected price range = 2 * ATM straddle

3. Expected high = current underlying price + ATM straddle

4. Expected low = current underlying price - ATM straddle

5. Expected maximum draw-down ≈ 1.6 * ATM straddle

6. All the formulas are linear in underlying price

7. All the formulas are linear in return volatility

8. All the formulas are linear in √T

Example: IWM closed today at 63.98. Strike-64 straddle expiring on 21-Aug-2010 closed at 5.21 using mid-market prices. The expiration is in 27 trading days.

1. Expected volatility (until expiration) is $6.5. This can be translated into implied by 6.5 / 64 * √252/27 = 31% ( which is about 0.5 points away from implied that I see in my software ) . Daily volatility is of course 6.5 / 64 / √27 = 2%.

2. Expected price range, that is expected high - low is $10.42. Daily expected range is 10.42 / √27 = $2

3. Expected high (resistance) is 63.98 + 5.21 = $69.19

4. Expected low (support) is 63.98 - 5.21 = $58.77

5. Expected MDD is 1.6 * 5.21 = $8.34

Over the next month I'll keep an eye on how these implied measures compare to realized, and will write an update after Aug expiration. Hedge your deltas!

## Jul 10, 2010

### Volatility Around The World

After a short trading week, S&P was up every day, gaining over 5%. Volatility indexes around the world lost 18%, or 5 volatility points. The biggest loser was VFTSE down 7.7 points, while FTSE was up 6%.

VIX index lost 5 points, distant month VIX futures losing 2.6 points. My forecasting model predicts further decline in the VIX over the next few months, however I'm still surprised as to how volatile the back-month futures can be.

There was a technical problem with VXJ update, so the value is the same as last week.

## Jul 8, 2010

### Shorting VXX riskier than appears

VXX has been going down since the day it listed, losing on average 8% per month (using data since inception until friday close), so it's not really a very original idea to short it. I did not short the ETF outright, but put on a few small bearish option positions. However the other day I got around to do some digging and found out a few things that I did not know.

EDIT: earlier I wrote that VXX lost about 10% per month. That figure was based on calculations I did few months ago - in the first year of trading VXX declined from 104.58 to 31.64 at a rate of 9.9628%, which I rounded to 10%.

Why did VXX decline so much? As Bill Luby and many others explain there are two reasons: the term structure of VIX futures, and trading costs. Most of the time VIX chain is sloped upwards (contango), that is front month futures are cheaper than the second month, making the roll costly. I collected data from the beginning of VIX futures trading until the end of last year. While I did not simulate the exact rolling algorithm used by VXX, I used rolling just once a month, on the expiration day. What I found is that the average difference between the front and second month futures to be 0.8 VIX points (t=2.47), or 6.7% of VIX value (t=6.03), and second month future is more expensive than the front in 82% of cases (53 out of 64). These costs do not include the bid-ask spread; they are statistically and economically significant.

However this is not a complete picture. Since VXX has about year and half worth of data, I needed to look for more. VXX is based on SPVIXSTR - S&P 500 VIX Short-Term Futures™ Index (overview here). I was able to find historical data for the index, and reproduced the chart below. It is clear from the chart that while the index has been in a steady decline since volatility peak in late 2008 (VXX was launched shortly thereafter in January 2009) going short the index would not have been without significant risk.

In four and a half years (54 months) since the index inception it declined on average by 1.65% per month, much less than 8.3% for VXX. While 1.65% is still significant, it pales in comparison to the maximum drawup (maximum drawdown for short-seller) of 523% from the low of 37,098 in Feb 2007 to the high of 231,276 in Nov 2008. For the life of the index the average drawup is 94%! I used simple returns for drawup calculations.

Now to put things into perspective, during the last 17 months for which VXX existed, VIX declined from 44.84 to 24.98, at a rate of 3.4% per month vs, 8.3% for VXX, and 8.0% for the SPVIXSTR. In the past 54 months VIX rose from 11.19 to 24.98, at a rate of 1.5% per month, while SPVIXSTR declined at 1.6% per month.

To measure the risks I conducted two studies - Monte-Carlo on index returns, and a parametric model like the ones I described last month. I used the two methods to generate forecasts for VXX and VXX options, and while I won't share the details, I realized that what I saw as a relatively low-risk opportunity in VXX, was rather moderate risk, low-edge trade.

## Jul 7, 2010

### Volatility Arbitrage (?)

I don't know how big the bid-ask spread is in VSTOXX futures, but this chart based on Jul 6, 2010 prices from the two markets should make you think about putting on some trades. Coming soon - vol skew comparison between the options markets.

## Jul 4, 2010

### Week in Volatility

VIX futures are up this week, and in an interesting pattern - distant months rose more that the near months. This is an unusual pattern since most of the time the volatility and sensitivity to spot index declines as one goes out further in expiration.

I have not researched the historical patterns of term structure, but I recall seeing a similar pattern in the spring - summer of 2008. After a spike in May, front months declined, but back-month futures stayed relatively expensive, or rose. I wonder if this is a sign of upcoming vol spike.

Elsewhere on the web SurlyTrader notes a bump in the term structure of VIX futures as opportunity for a calendar spread between October and December. See follow-up comments to the post.

## Jul 3, 2010

### Volatility Around The World

Markets fell again, S&P declining 5%, with gap on Tuesday morning and another large decline Wednesday afternoon. Volatility indexes around the world rose by almost 2 points, or 7.5%.

While compiling different volatility indexes I noticed some surprising extremes - India VIX, and Mexican volatility index in low 20s while VIX is at 30. Why is that volatility in emerging/developing markets is lower than US? Is it because of USD exchange rate risk, or something else? I really don't know.

In addition - US-traded ETFs do have higher ATM volatility (all numbers approximate b/c of large bid-ask spread)

INP (India) - 30%

EPI (India) - 30%

PIN (India) - 33%

EWW (Mexico) - 33%

It is possible to arb between domestic and US volatility? I don't have access to foreign markets, but other traders possibly could.

## Jul 2, 2010

### Cornucopia of volatility indexes

I have been slowly adding to my database of volatility indexes. Here's the list I have assembled so far:

VIX - S&P 500

VXD - DJIA

VXN - Nasdaq 100

RVX - Russell 2000

VDAX - DAX, Germany

MVX - S&P/TSX 60, Canada

VSMI - SMI, Switzerland

VFTSE - FTSE 100, UK

VSTOXX - EURO STOXX 50, Europe

VAEX - AEX, Netherlands

VBEL - BEL 20, Belgium

VCAC - CAC, France

VXJ - Nikkei 225, Japan

India VIX - Nifty 50, India

VIMEX - IPC, Mexico ( unlike other indexes it targets 3 month volatility )

And also commodity volatility indexes based on ETFs:

EVZ - FXE, Euro

GVZ - GLD, Gold

OVX - USO, Crude Oil

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