### Volatility and Sentiment Tidbits…and Today Doesn’t Matter

Some semi-random thoughts inspired by today’s market action:

- The VIX:VXV ratio spiked up to 1.12 at 1:12 p.m. EDT (I’m not superstitious, but that’s an interesting bullish signal)
- The underappreciated VXN (volatility index for the NDX or NASDAQ-100) spiked over 34 on Friday and made it as high as 33.76 earlier today. That’s not enough to satisfy the “VIX must spike over 30!” purists, but it is an interesting data point, particularly because the VXN and NDX excludes financials
- My VIX algebra says that two medium to large VIX spikes on Friday and today do not equal one large capitulation-friendly VIX spike
- The CBOE equity put to call ratio – an excellent market timing indicator – is looking bullish

When all is said and done, I don’t think we can have a serious market rally until the tone of the news flow changes, regardless of market technicals and sentiment data. There must be several bullish macroeconomic and/or fundamental data points which collectively give the bulls a reason not to be so skittish. At a minimum, the markets need to navigate the PPI, CPI, industrial production and capacity utilization data due out tomorrow and Wednesday, then weather the flood of earnings reports (with strong representation from some key financial institutions) on Thursday. Even then, there is the Citigroup (C) earnings story on Friday morning.

Whatever happens to the rest of today’s session, the balance of the week will tell the story.

## 18 comments:

Seems close enough to make a directional play here. I think it is dangerous to expect to pick the exact bottom, or top, in any market. The risk/reward seems good at this point for going long the market.

Yeah, been watching the VIX/VXV indicator - but so far so bottom or bottoming-type action. Today was another classic example. I agree with the former poster that it makes sense to start getting long.....

VXO is not over 35.Only if VXO is going over 35, we will have uptreand

The Vix cash index spiked to levels of 37.57 and above 35 at the January and March 2008 stock market lows. A spike in oil prices and/or some additional weak economic data may cause the Vix cash index to spike above 30 and/or for the DJIA to close near its next support level of about 10700. The major stock market indexes have not completed a significant rally since the DJIA high of about 13140 on May nineteenth.

You know the old joke, "Just because you're paranoid doesn't mean they're NOT out to get you?" The current market corollary might be, "Just because everybody is pessimistic doesn't mean things can't get worse." It will be interesting to see how the data plays out.

The DJIA future is down 134 points and the S&P future is down fourteen points in pre-trading. Also, oil is trading near $146 per barrel, gold is up ten dollars to $984 dollars per ounce and the U.S. dollar index is down more than one half cent. The DJIA closed about 175 points from its 2008 low. It should be interesting to see if the VIX spikes to new lows and/or if the DJIA reaches new 2008 lows.

Recently stumbled upon your blog; very neat stuff.

Might I suggest that there is an implied volatility index that might be a much better bet that either the VIX or the VXV?

That index is the IV Index on SPX Calls.

Read the following article for a more in-depth look into the topic.

http://blog.themarketmessenger.com/blog/2008/7/14/a-more-accurate-contrary-indicator-than-the-vix.html

The DJIA and S&P 500 index did trade to new 2008 lows earlier today and the VIX cash index spiked to 30.81 earlier today. The VIX cash index has not reached this level since mid-March. The possibility of a bullish turnaround is increasing, although it has not yet transpired on price charts for the major indexes.

Panic selling happens only when the market is oversold.

The VIX cash index sharply decreased from a level of about 30.8 to todays closing level of 25.1, a 18.5% decrease in less than two trading days. The VIX level of 30.8 that corresponded to the DJIA 2008 trading low of 10828 may be the turnaround levels for a short-term bullish rally. Crude oil decreasing almost eleven dollars in two days also had a bullish impact on the U.S. stock markets. The DJIA, S&P 500 index and QQQQ indexes all increased by about 2.5% today and the XLF, XBD and XAL indexes skyrocked by 12.4%, 13.1% and 18.1% today. These are the largest percentage increases in these indexes since the major U.S. stock markets started their bearish leg down on May nineteenth.

seems like VIX/VXV may not be mean reverting to me... of course VIX/VXV aren't independent, but it seems like the more volatility you get the more you are likely to have and since VIX has less time to maturity it will alway be larger when volatility is increasing... the faster volatility is increasing, the larger it should be relative to VXV and VIX should be smaller... as volatility wanes. VIX/VXV -> VIX as volaility -> "We won't be alive in 93 days!" aka (al gore was right.)

seems exponential... maybe the geometric mean of the derivative would give the expected rate of increase and the second derivative the inflection points you're looking for...

- Contrary

Properties

The Cauchy distribution is an example of a distribution which has no mean, variance or higher moments defined. Its mode and median are well defined and are both equal to x0.

When U and V are two independent normally distributed random variables with expected value 0 and variance 1, then the ratio U/V has the standard Cauchy distribution.

If X1, …, Xn are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean (X1 + … + Xn)/n has the same standard Cauchy distribution (the sample median, which is not affected by extreme values, can be used as a measure of central tendency). To see that this is true, compute the characteristic function of the sample mean:

\phi_{\overline{X}}(t) = \mathrm{E}\left(e^{i\,\overline{X}\,t}\right) \,\!

where \overline{X} is the sample mean. This example serves to show that the hypothesis of finite variance in the central limit theorem cannot be dropped. It is also an example of a more generalized version of the central limit theorem that is characteristic of all Lévy skew alpha-stable distributions, of which the Cauchy distribution is a special case.

The Cauchy distribution is an infinitely divisible probability distribution. It is also a strictly stable distribution.

The standard Cauchy distribution coincides with the Student's t-distribution with one degree of freedom.

The location-scale family to which the Cauchy distribution belongs is closed under linear fractional transformations with real coefficients. In this connection, see also McCullagh's parametrization of the Cauchy distributions.

Hi Contrary,

Thanks for the primer on a Cauchy distribution.

With respect to the VIX:VXV, I think there are aspects of it that are mean reverting and others that are not, depending upon the time period one focuses on. In the short term, volatility has a tendency to trend, over longer periods, it will mean revert, and over the long term, it has a tendency to move in cycles. All of this makes it difficult to model, but good for mental gymnastics.

Cheers,

-Bill

No no you miss the point, there's no such thing as "mean" and period functions are actually easy to model.... winter comes in December every year! The problem here is the function is recursive, volatility begets more volatility. it would be like if the days just kept getting longer and each longer day increased the chance the next day would be longer still. eventually we may get back to winter when the pattern is disrupted but be won't know when. But as for the "circleness" the cauchey is the tangent function for a randomly generated angle, vix/time would then be sine of that angle and vxv/time would be cosine

Perhaps we do have a disconnect, but I don't think so.

Volatility begets more volatility in the short-term, but is mean-reverting over longer periods. These ebbs and flows are somewhat predictable in terms of the shape they take, but the more difficult part is determining their period. Some volatility events stretch and twist time severely, while others cause much less distortion.

Of course, when we travel at the speed of light, this entire analysis of the VIX:VXV ratio breaks down...

Thanks for jump starting some new thinking on my part.

yes, there is a disconnect. There is no "mean" to revert to, you may get back to the ratio vix/vxv = 1 or volatility and this may occur at say ~ 45% over some period, and then at ~ 25% another time, but the volatility is not reverting to the "mean" we are moving the scale (by setting volatility equal to a %) if we look at VaR instead of volatility you can easily see that company with assets $100 and VaR $30 if the company grows to have $1000 Var will not revert to its previous mean of $30. the %VaR may have increased or decreased depending of the size of the firm relative to the market for its assets and other factors. Volatility is "scale invariant" but since we're already dealing in %'s here we are the ones moving the scale, to the nominal value of volatility, volatility is not reverting back to anything. Of course this happens at the incremental level for each option contract (they will be scaled by larger dollar increments)

The result is the same, but the

causalityis completely different. Because of this, you will not be able to determine the period. (Of course if the period were predictable, then everyone would just wait until the volatility was lower to raise capital, and then when every one came back at the same time to raise capital, volatility would be shifted and amplified by the very action of predicting it. http://en.wikipedia.org/wiki/Lucas_critique)http://www.amazon.com/o/ASIN/0387983635/105-3865035-0214811?SubscriptionId=0AM07842GGE1QVDN6KR2

This is one of the reasons CAPM works so poorly, it assumes, normal distribution which is based on predictable central moments. Such problems are only amplified when dealing with derivatives, where prices are more often discontinuous.

Gotcha.

Thanks for the clarification.

Cheers,

-Bill

This is a very interesting case, made particularly so due to the nature of the vix as an index of volatility. (quite interestingly I recently read a paper suggesting that Beta in CAPM should be replaced with: Beta* = (sign of r) ((std individual stock) / (std market))) Don't let my assertiveness fool you, I have been trying to describe this probability density function for sometime subconsciously but only stumbled up on the Levy and Cauchy distributions recently. The Aforementioned paper "INVESTMENT VOLATILITY: A CRITIQUE OF STANDARD BETA ESTIMATION AND A SIMPLE WAY FORWARD" therefore projects that stock returns will vary based on a cauchy distribution. and if the market return is the aggregate of the individual stock returns....

It seems like finance theory, maybe about to make a step forward.

I will also work on modeling this to try to improve my understanding. Though, i'm sure i will have recruit someone with far better math skills that I, to assist me. Though I may use this "IV Index" put forward in the comments. The problem with the VIX, is it skews toward responding to the negative market moves. I assume this is due to the volatility smile in put prices but since when is volatility only associate with negative price moves? (since 1987, i would guess) Large up market days continue to reduce the vix, when really its the amplitude of the swings that I care most about in a bear market... in any market really since you don't know its a Bear market until its too late.

P.S. I misspoke earlier, I believe you will be able to represent the period of VIX/VXV but it will not be constant...

This "little" project should be interesting.

anonymous,

Damn. nice work.

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