Breaking Down Volatility of the VIX

I had never heard of the VVIX index (the volatility of the stock market's volatility "volatility of VIX") until a week back when Bill Luby from the always insightful 'VIX and More Blog' posted about the recent gap seen between the historical volatility "HV" of the VIX (i.e. the trailing volatility of the VIX index) and the implied volatility "IV" (i.e. what was currently priced in as the forward expected volatility of the VIX index).

To Bill:

Much to my surprise the current 20-day HV is 144, while the current IV is only 98. In other words, the markets expect the VIX to be considerably less volatile in the month ahead than it has been over the course of the last month.

But as we'll see, based on the historical relationship between the VIX and VVIX, the pricing wasn't all that unexpected. Over the previous month, the VIX index had fluctuated between roughly 17 and 26, so (ignoring any opinion of the market for a moment) the reading of 98 was actually right in the heart of where one would expect it based on historical data since the VVIX index 2007 inception.

And this is where things get interesting.

The historical chart shown above makes the assumption that the volatility of the VIX index is lower when the VIX index is lower, which would have been my first guess had I not really thought about it. When I did think about it, that actually makes no sense whatsoever.

Why?

• Volatility is a measure of change in percent terms
• A change from a low starting value is a much higher percentage change than an equivalent unit change from a high starting value (i.e. a 2 point change from 10 is a 20% move... a 2 point change from 80 is a 2.5% move)

With that understanding, the chart below showing the realized one month change from various VIX starting points shouldn't be too surprising because a 15 point move higher in the VIX from a starting value of 15 is much more likely than a 40 point move higher in the VIX from a starting point of 40.

The interesting thing is that this conflicts with how the VVIX (vol of VIX) has been priced. At low levels of VIX, the VIX is MORE likely to have wide outcomes (in percentage movement) while at high levels the mean reverting characteristic of the VIX has made a move down from high levels much more likely.

A chart attempting to summarize the first two charts is shown below. It shows the realized one-month forward volatility of VIX resulting from various starting VIX and VVIX index values. Interestingly enough, it shows that realized volatility of VIX spikes when the VIX index is low, but only when the market isn't pricing it in.

Potential thoughts from the above to consider further...

• When the VIX and the implied volatility of the VIX are low, buy options on the VIX (i.e. calls / puts)
• When the VIX is high and implied vol on the VIX is high, sell calls on the VIX

Source: CBOE

VIX as a Predictor of Equity Returns

Marketwatch has a post Cash is still king, at least for now, which points to a model that goes to cash when the VIX is above 20:

Consider a hypothetical portfolio that switched in and out of the Wilshire 5000 index according to whether the VIX was above or below 20 — investing in the market on a given day if the VIX closed the previous session below that level, and otherwise staying in cash. This portfolio would have produced an 8.9% annualized return since 1990, when the CBOE’s data for the VIX commence, in contrast to 8.5% for buying and holding. (I chose 20 as the threshold level for illustration purposes only; it is not far from VIX’s median level over the last two decades.

I thought I'd take a look at the results using daily VIX levels and SPY data for daily equity performance. As SPY didn't launch until January 1993, the comparison isn't apples to apples in terms of equity index or timing, so I can't vouch for the accuracy of the returns in the paragraph above, but I can state the model didn't work as anticipated for the data I pulled. More important, it did show some interesting results that I will share.

The chart below shows the different "buckets" of VIX levels I utilized, which were selected based on getting a close to even distribution across these buckets (as can be seen each grouping had between 500 and 700 days of returns to analyze).

Then I simply took the daily 1-day forward returns (including dividend) associated with each bucket and calculated annualized returns and standard deviation based on a 252 day trading year.

The result?

While volatility was significantly less when VIX was lower (showing volatility is sticky), returns appear to have been better at extreme readings, perhaps when securities were selling at a huge discount. Also of note, performance appears to have been worst when VIX levels read between 17.5 - 20 and 22.5 - 25, while performance was best (in sharpe ratio terms) when the VIX read between 15 and 17.5.

A further breakout of bucket '30+' is shown below (note these buckets are not even, as most data points fall within '30-35').

My thoughts based on data from 1993 - present... when the VIX creeps higher from teens to low 20's, be cautious. When it flashes red, if you can stomach EXTREME volatility (and EXTREME drawdowns) it may be a good time to buy.

Source: Yahoo Finance

Here We Go Again

As I've detailed over the last month, market volatility appeared suppressed due to all the liquidity thrown at the problems:

• Buying Options
• Suppressed Volatility

Volatility is finally picking up and I want NO part of it. So today, I closed out most of my long volatility positions (with the exception of those tied to commodities and Treasuries... I think we're going one way or the other here) and happy to sit on cash until dislocations become wider or markets calm down a bit. We seem to be are treading in awfully familiar territory, which brings to mind a great Operation Ivy song.

Here We Go Again

Buying Options

The U.S. may or may not default on its debt (I am going with the not), may or may not be downgraded (I think it is likely within the next 12 months), and may or may not be a completely dysfunctional mess in Washington (okay, this is a definite). In times like this, I would like optionality (calls and puts) even if it were expensive.

But, lo and behold... the VIX is currently priced below its 5, 10 and 20 year average.



Which is why I am buying options....

Source: Yahoo Finance

Suppressed Volatility

FT Alphaville has a post Crouching Vix, Hidden Volatility claiming that:

Volatility is out there. You just have to look for it — and not by glancing at industry-standard, the CBOE Vix index.

The blog then points to a post by ConvergEX that states:

If you only focused on the CBOE VIX Index, you’d be tempted to think that the recent market volatility was pretty modest.

The problem is that it wouldn't only be a temptation, it would be a fact.

Looking at implied volatility, as defined by the VIX, relative to actual realized three month volatility of the S&P 500, the VIX has (much like most of history) been consistently overstating volatility (the VIX recently closed at 19 vs. three month realized volatility of 12, a difference of 7 relative to the average difference of 4 over the previous 20 years).

This isn't to say that I believe the VIX accurately reflects the economic environment and risks associated with investing in the current environment (I absolutely don't). It just isn't some conspiracy theory that the VIX is being artificially suppressed relative to the underlying market or that volatility is more accurately reflected in other sectors.

It is simply (in my view) that volatility across ALL sectors and asset classes has been suppressed by the liquidity that has successfully (to date) been finding its way into riskier and riskier asset classes following the combination of unprecedented fiscal / monetary stimulus and a lack of "real" investments (i.e. investments that feed into economic growth and create jobs) for this liquidity to go.

So tread carefully my investment friends. The part of the investment cycle where an investor can generate positive returns by simply providing liquidity to the market is likely over.

Source: Yahoo Finance

Realized 20-Day Vol at 39 Year Low

Vix and More details:

Since I haven’t seen it mentioned anywhere else, I thought I should note that 20-day historically volatility in the S&P 500 index hit its lowest level since April 1971, the same month that the Rolling Stones released Sticky Fingers and Charles Manson was sentenced to death.

Source: Yahoo Finance

When ETN's Attack: VXX

A lot of growing chatter around the VXX ETN (exchange traded note) to play volatility, but heed this warning.

First, what is it? Per Yahoo Finance:

The investment seeks to replicate, net of expenses, the S&P 500 VIX Short-Term Futures Total Return Index. The index offers exposure to a daily rolling long position in the first and second month VIX futures contracts and reflects the implied volatility of the S&P 500 index at various points along the volatility forward curve. The index futures roll continuously throughout each month from the first month VIX futures contract into the second month VIX futures contract.

As VIX and More has detailed on multiple occasions:

VXX may be even less effective as a long-term holding. As previously discussed in VXX Calculations, VIX Futures and Time Decay, VXX suffers from negative roll yield when the VIX is in contango (when the front month VIX futures are less expensive than the second month futures), with the result that VXX loses a few cents each day due to rebalancing, just like a tire with a slow leak.

The current contango in the VIX is striking. This morning, when the spot VIX was 24, the one month forward contract was almost 27. If you buy this one month out contract (i.e. what the ETN does) and nothing changes in one month, the contract loses more than 10% (24/27-1 = 11%) of its value.

As long as contango remains steep, you better be damn sure volatility is going higher if you do anything, but short this security.

Source: Bloomberg

The Certainty of Uncertainty

Abnormal Returns has a great post about uncertainty and investing; a topic that has been on my mind of late due to the bomb scare, oil spill, natural disaster, and of course sovereign crisis (for anyone interested, I asked for / received help in understanding the potential for a Eurozone breakup back in January '09). To the post:

Alexander Ineichen writes directly to the issue of time diversification and uncertainty:

We believe time amplifies risk. It is true that the annual average rate of return has a smaller standard deviation for a longer time horizon. However, it is also true that the uncertainty compounds over a greater number of years. Unfortunately, this latter effect dominates in the sense that the total return becomes more uncertain the longer the investment horizon.

The logic here is that over the longer term, more bad things can happen and the probability of failure (i.e., non-survival) is higher. The probability, for example, of San Francisco being wiped out by a large earthquake over the next 100 years is much larger than over the next 100 days. If accidents happen in the short term, one might not live long enough to experience the long term. After all, the long term is nothing else than many short term periods adjoined together.

Ineichen uses the recent example of Japan showing that sometimes a market, even a developed one, can go down and stay down. The issue isn’t one of better estimating the equity risk premium or volatility of returns. It stems more from the fact that we really don’t know what the future holds. Recognizing the limitations of our statistical knowledge is a necessary step in facing uncertainty.

And here it is... the chart shows the Nikkei 225 index and the change from its previous peak (note that the chart does not include reinvestment of dividends). 20+ years and the index is still 70% below its peak.



An outlier right?

Well, it took the U.S. Equity market* from 1929 - 1954 (i.e. ~35 years) to re-reach its prior peak post Great Depression.



These "outliers" are important to keep in mind as the global economy has never been more inter-connected or had less "cushion" if an event were to occur (sovereign balance sheets were sucked dry during the crisis making any large bailouts [sovereign or banking] much more difficult going forward).

The result is that any little hiccup (in any part of the world) may have a far greater impact on the entire system than the market is currently pricing in. While it may not happen over the next day, week, month, or even year(s)... it is coming.

* the S&P 500 recreated by Professor Shiller to pre-date its 1957 inception

Is Volatility Cheap?

Daily Options Report reports (hat tip Abnormal Returns) on the relative cheapness of volatility (as currently priced in options):

Bottom line is options have gotten cheap enough to where net selling them looks very risky as you have little cushion for a sudden move. But by the same token, it doesn't mean you go back up the truck and cross your fingers that volatility starts ticking up right........now.

It is true that the VIX (which tracks the daily implied volatility on S&P 500 options) has come down MASSIVELY from Fall highs. In the actual marketplace, realized daily volatility has also snapped back in recent months as seen below.

Daily Options Reports continues...

But cheap does not always mean a buy. At the end of the day, you will need realized volatility in GOOG (or anything) between now and expiration to exceed the implied volatility you paid for the option. In other words, you could catch the absolute low tick in GOOG options volatility and still lose money if GOOG volatility itself remains lower.

True, you could. BUT, you can also catch a higher level of volatility and still make money even if volatility decreases. One recent example, I am fortunate enough to say, happened to me. I purchased a boatload of Out of the Money "OTM" calls on QQQQ (to be more specific September 43's) a few weeks back for a few cents each, which I delta hedged by shorting QQQQ's and later by buying QQQQ puts when QQQQ became difficult to short.

What has happened since then? Well, QQQQ's have run up significantly in price and I've continued to delta hedge, BUT the implied volatility on QQQQ's has actually fallen slightly since that time. Importantly, even with that drop in volatility, the combined positions have done quite well. Why? Because daily volatility does not always reflect exactly what is being captured.

According to Wikipedia, volatility is:

More broadly, volatility refers to the degree of (typically short-term) unpredictable change over time of a certain variable.

Thus, volatility only measure the predictability of short term changes. When you buy an option, you don't care how volatile the underlying security performs around the mean (i.e. lots of small movements unless you want to be abused by transaction fees), but rather you care about short-term, yet significant, moves in absolute terms. As an extreme example, if a security returns 0.5% EVERY day for a month, the volatility over that month is... ZERO. Yet, the security would have moved by more than 10% over a 20 trading day period, which is very volatile for the broader market. Thus, while volatility has declined, the option position has likely paid out BIG time.

This can be seen in the chart below. Rather than the previously shown monthly volatility (as calculated on a daily price change), we show the six month change on a monthly basis. Here, we see that volatility over longer times frames has actually not moved down much at all, but has actually remained at a historically high levels.

And this is the reason why I feel that options (and volatility) continue to be cheap.

Source: Yahoo Finance

Don't Read too Much into the VIX

Bespoke details:

Even though the market is barely up on the day at the moment, the VIX volatility index is down more than a point and has broken below 40. As shown in the long-term chart of the VIX below, prior to the current bear market, the VIX seldomly moved above 40. However, since last September, the VIX has remained solidly above 40. Since the VIX is widely considered a "fear" gauge that rises along with investor nervousness, the bulls would like to see the index break solidly below 40 for a longer period of time.

Rather than a measure of fear, the VIX has been closer to a reflection of actual volatility of the market. As the chart below details, the VIX has moved almost one-for-one with the actual volatility of the S&P 500, as measured by the rolling one-month standard deviation of daily price movements of the S&P 500 annualized (assuming 252 trading days in a year).



Source: Yahoo

Why Are Markets Still Volatile?

Amusing rant over at 1-2-Knockout in response to Floyd Norris' reporting of this CFA member survey (three links in one sentence... I am the man.)

Click for insanely large chart.

VIX: It Has Been a Heck of a Week

Per Bloomberg:

The VIX, as the Chicago Board Options Exchange Volatility Index is known, increased 17 percent to 81.13 at 11:14 a.m. in New York after earlier rising to 81.17. The index measures the cost of using options as insurance against declines in the Standard & Poor's 500 Index, which lost 4.5 percent. The S&P 500 tumbled 9 percent yesterday. Today's VIX record eclipsed the peak of 76.94 on Oct. 10, when U.S. stocks completed their worst week since the 1930s.

Source: Yahoo Finance