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Thursday, March 25, 2010

VIX: Coincident or Leading Indicator ?...Or Is It a Lagging Indicator ?


The current large decline in the VIX (5yr chart at left), the CBOE volatility index, to the lowest levels since 2008. has sparked a good deal of writing (quotations from articles below) about what this means about what the market will be doing going forward in terms of both direction and volatility.

I think the short answer is not much in terms of the future direction of the market  Some of the misunderstanding stems from what exactly it is that the VIX is and what it isn't.  In my view the frequently cited "fear index" moniker is not really useful.

In reality the VIX can be considered "a derivative of a derivative of a derivative". The index is a calculated value of the implied volatility based on a mix of near term options on the s+p 500 futures. So the vix, the implied volatility is calculated by using the prices of options  a derivative of the s+p futures. And the s+p futures of course is a derivative of the cash value of the stocks in the s+p 500. And the options used have from one week to 37 days to expiration and are close to the money. A complete explanation of how the index is calculated is here.

Some knowledge of option pricing and option trading will help one to understand that the VIX is much more than a "fear index". A good explanation of the "greeks" of option pricing is here. Remember that the VIX is a volatility index, not a measure of any directional view (calls and puts are used in the calculation which means pure plays on volatility, which do not incorporate a directional view = straddles and strangles are affected as well . 

Buyers of options need volatility to stay high to make their options profitable. sellers make money in stable (low volatility) markets. In fact a market with very high daily or even intraday moves are good for option holders even if the market makes no significant medium term price movements. Under such conditions one would expect no declines and probably increases in implied volatility (vix).

A market that is moving slowly up or down will be bad for option holders and lead to a decline in implied volatility. A sharp move up or down in prices will lead to a move up in implied volatility although experience has taught traders that markets are more volatile on the downside than on the upside (meltdowns are more frequent than "meltups"), so the volatility of volatility is much higher when markets sell off sharply.

One more piece of the puzzle: The VIX is based off the implied volatility of very short dated options. Dead markets are the mortal enemy of option holders particularly when the options are short dated. Every day that the market doesn't move their option declines in value (time decay or theta (greek). And this theta is not linea,r the shorter the maturity of the option the greater the theta (loss per day in value), theta for options increases sharply during the last 6 weeks prior to expiry. So the very options used to calculate the VIX are those with high time decay.

When the markets are stable for a period of time option holders get uncomfortable. In the current market for example those holding long positions are experiencing  slow grind upwards with small but steady gains. The option owners on the other hand are being killed by the steady tick of time decay as their long options positions decrease in value. Gradually the option holders start to sell and some traders reacting to the stable market anticipate that to continue and become active sellers looking to collect that steady but small gain from being short options that are decaying in value each day. As option prices go down so does the implied volatility (vix) calculated off the index.

In the terminology of the option "greeks" short maturity options like those used to calculate the VIX,have high vega (change in volatility as option prices move) The short dated also have high theta (time decay) and the high gamma ("delta" sensitivity to change in the underlying and thus sensitivity of the option price to price changes in the underlying index. All this creates alot of "volatility" for the volatility index the VIX. and makes it verty  sensitive to the actual volatility in the s+p 500. A quick increase in actual volatility will leak to spike up in the vix and narrow range markets will take the vix down (as we are seeing now).

I would argue that the VIX tends to overshoot in both directions due to its extreme sensitivity to short term actual volatility in SP 500.

So is the VIX a "fear" index ? I think that is a very imprecise term for a couple reason:

1. Although it is true that the VIX goes up more during a sharp down move than a sharp upmove in the markets, a market volatile on the upside could lead to an increase in the VIX.So changes in the VIX don't necessarily give any information on market direction.

2. A market that swings with broad price ranges on a daily basis could keep the vix high even if the day to day price swings are neglible. Again not a market situation most investors fear.

3. A market that ground down at a steady rate for months on end would produce a lower vix .But that doesn't give any information of when and by how much volatility might start to increase and cetainly no information about market direction when volatility picks up.

 Right now the extremely low levels of the vix (notwithstanding the move up today - March 24) it is very close to a 2 year low. That low level is a response to the low level of actual volatility not an indication of "compacency" among traders about a possible selloff. In my view the vix is as likely to lag the market as it is to act as a leading indicator. If the market sellsoff sharply demand for options will go up  and the implied volatility and vix will go up.In the meantime there is little interest in buying short dated options that quickly give up time decay each day the market is stable, And this translates to a low VIX

Is the VIX a leading or coincident indicator ?

It seems pretty clear to me the VIX might be a coincident fear indicator or more likely a lagging indicator. In response the sharp and volatile moves to the downside demand for puts (downside protection goes) up pulling up the implied volatility of the options which translates into a higher vix. At that point one would hardly need to look at the level of the vix to know that fear is rampant in the markets.


The fall of 2008 when the VIX jumped to record levels illustrates my point. On Oct 22 the s+p 500 had a range between high and low of a bit over 9%. (5 yr s+p500 chart is pictured directly above.  The same day the VIX jumped from 53 to close to its all time high of 80. Did anyone need to look at the VIX to conclude the market was fearful ? And the 50% intraday jump in the vix from 53 to 80 hardly showed that the options market anticipated either the direction or the severity of future market moves.

In fact there is a useful calculation that can tell you what kind of move in the underlying is implied by the implied volatility

courtesy of option pundit:

Volatility is usually expressed in annual terms, and represents a one standard deviation move in the stock. Dip into any statistics book, and it’ll explain that one standard deviation, up and down, encompasses about two-thirds of all occurrences. So, two-thirds of the time, the stock with an implied volatility will theoretically be between up 35% and down 35% in one year. But how do you convert that to a more useful time frame, when most of the options you trade expire in the next couple of months?
If you assume that a stock has an annualized volatility of 35%, how much might it move in 1 day, 1 week, or 1 month? Well, open that statistics book again and see that the standard deviation increases proportionately to the square root of time. So, if there are 252 days in a year, you want to multiply 35% by the square root of 1/252 to get the 1 standard deviation for 1 day. That comes out to about 2.2%. So, in one day, two-thirds of the time the stock will be between up and down 2.2%.
To get that number for any number of trading days from today, multiply 35% by the square root of the number of days/252. That is, for the range 5 days from now, multiply 35% by the square root of 5/252. For 20 days from now, multiply 35% by the square root of 20/252. So, in 5 days, theoretically two-thirds of the time the stock will between up and down 4.93%, and in 20 days, between up and down 9.86%.
So let's plug that formula into the VIX when it hit the all time high. At the 53% implied volatility that implied that two thirds of the time the s+p 500 would  a have a daily move +/-  3.3%. At 80% volatility number would move to +/- volatility implied a move in the sp 500 of 5%. Given the extreme range (9% high to low) in the s+p 500 Oct 22 and the daily move from oct 21 to oct 22 of 5.8% the move in the vix = implied volatility would certainly be justified.

In fact in this case in Oct 2008  at the most extreme high levels for the VIX one could argue that not only wasn't it a leading indicator, it wasn't even a coincident indicator. It was more of a lagging indicator. The traders in the options market clearly were caught running (literally ) cover to buy implied volatility in reaction to the actual volatitlity.

 So that brings me to comment on two recent articles onthe vix

 Here's what recent articles on the vix have said on the message of the market in the vix's decline. My bolds my comments in blue

 From the FT

Analysts scramble to read the signs of a calmer Vix

By Aline van Duyn in New York

Published: March 20 2010 02:00 |

One of the most closely watched measures of volatility in the stock markets, the Vix index, has dropped to its lowest level since May 2008.
....The Vix was regularly on the front pages of newspapers during the financial crisis, as it rose to record levels. The fact that it is often dubbed a "fear gauge" by many market participants implies that ups and downs in this measure may say something about the future direction of stocks.
Since hitting a high in November 2008 of 80.86, the Vix has steadily declined. This week it reached 17.19, a level last registered nearly two years ago.
The question is what the 80 per cent plunge in the Vix index from its peak signals about the state of the equity markets, or their future direction. Does a drop in volatility mean all is well in the equity markets? It is a question a growing number of analysts have scrutinised, and in most cases the conclusion has been that the Vix has limited predictive powers.
"The Vix really tends to track the day-to-day movements in the S&P 500," says Dean Curnutt, president of Macro Risk Advisors. "The folks that are setting the Vix are trading equity volatility and they're just responding to how much volatility the market is experiencing now. We found that the Vix does not do a good job of looking forward." 

An analysis of the Vix and moves in the S&P 500 by Birinyi Associates, published this month, reached the same conclusion.
"The Vix is alleged to be an indicator and has become a staple of analysts and journalists alike," the report says. "We respectfully disagree and ultimately conclude it is a measure of current volatility with little or no predictive or indicative value regarding the course of the market.".....

Mr Curnutt says that the benefit of the fall in the Vix is that investors can buy insurance against a decline in shares much more cheaply, a strategy which many investors continue to pursue. Indeed, there has been some pick-up in hedging activities, as some investors see a sharp fall of the Vix as a potential sign of turbulence ahead a type of contrarian indicator.
As I noted it seems to me to be a coincident or even a lagging indicator
Not necessarily, they could be people like me with no directional view simply looking for a hedge against possible large selloffs. The low VIX levels to me are certainly a buying opportunity for a hedge that would have been done anyway, perhaps a chance to grab a bargain or average in to a long term position. I sincerely doubt that I am alone particularly with the volatility etns available (and those of course are priced off the vix futures)....

From the WSJ an attempt to read a directional forecast into the VIX which imo is wrongheaded.

A Key Volatility Index That Says 'Buy' May Mean 'Bail'

imo not only is it not the "be- all and end-all it is pretty much irrelevant.

The index, launched in 1993 with data stretching back to 1990, moves up and down depending on the price that investors are paying for options on the Standard & Poor's 500-stock index. When investors buy bearish options on the S&P, known as puts, the options become more expensive and the VIX moves higher. Conversely, when investors sell those put options on the S&P, the options become less expensive and the VIX moves lower...

(well that is just half right the vix is composed of the volatilty of both put and call options )...

If anything, the VIX is most useful as a contrarian indicator. When the index remains unusually high or low for an extended period of time, it can mean a major market change is in the offing. For instance, the VIX had trended downward, and stocks upward, for several years leading up to the Dow Jones Industrial Average's record close on Oct. 9, 2007. Then the subprime meltdown sent stocks plummeting as a historic bear market took hold.

One year later, during the diciest moments of the financial crisis, the VIX spiked to a record high of 80, capping a yearlong rise. Then it reversed course and fell sharply as stock markets enjoyed their most dramatic rally in decades.

During the fall  2008 market collapse  the s+p 500 dropped 30% in six weeks with many heart stopping days of interday moves close to 5% and wide intraday ranges. During the recovery the same magnitude upmove in the market took six months and along the way the inter and intraday volatility was far less extreme. In other words the vix is a coincident indicator. So the difference in levels of the vix during those  the markets rapid drop and its more steady accounts for the difference in the levels of the VIX>

Right now the VIX isn't pointing to a major market move, since it is just now settling into its historical range. Under normal circumstances, the index moves in a fairly narrow band, mostly between 10 and 20. Having drifted gently downward for months, the index now sits at 17....

It's not the rally that is causing the decline in the vix its the fact that the rise of the market is during a low volatility market. Low actual volatility = low implied volatility (vix)
So how can traders best make use of this oft-misunderstood index? By studying what is happening in the futures market. Professional investors have traded futures contracts on the VIX since 2004. When the futures are significantly different from the VIX itself, it is a signal that the index—and possibly the stock market—could soon reverse course. When the futures are significantly lower, it could be a bullish signal. When they are markedly higher, it could be bearish.

This seems to be a misreading. The vix futures always move more slowly than the index because they are sensitive to longer term changes of actual volatility,
The vix futures may indicate an expectation of higher implied volatility but I don't think they tell much about future direction of the s+p 500

So VIX as fear index ? not necessarily ? and it's certainly not a directional indicator ?

VIX as a leading indicator ? not a leading indicator or market direction and not an indicator contrary or otherwise of future volatility .

In my view the VIX is simply an indicator of actual volatility in the market but one that is very sensitive to changes in actual volatility particularly if it is on the downside.

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