## Smile Modeling; What Is SKEW?

I am sending this out, but will not be able to respond to questions till Monday as I am on an annual “family” business trip this weekend.

This post will be a bit dry, but hopefully interesting to those who trade options.  This may sound educational, but hopefully it encourages some deep thought. To be blunt- all of this- is so I can say I have a vega of 3 today and a vega of 4.5 in two weeks. 99% of traders cannot do that (or they think they can but their math is wrong). Yet the guy on the other end of the trade (market maker) clearly knows about smiles, convexity, or stochastic volatility. This is why call rape (patent pending), skew rape (patent pending), and retail IV crushes (patent pending) all occur. If you believe it or not, as tricky as the SPX is concerning IV’s inverse correlation to price and skew’s positive correlation to price, I have seen more blowups in Corn futures when novice traders do not fully evaluate IV and IV smiles.

First off, what is an IV smile? Smiles are the shape of the IV for a particular contract at 1 point in time. Each option has its own IV. I use a simple polynomial regression (eg beta means smile width, skew means direction, IV means the smile intercept). Its a “quadratic” equation, but also a simple “right click, add trendline, click polynomial, order 3″ in excel. Or  {=linest(YY,XX^{1,2}) }if you prefer.

Why does this matter? Well first off, it is hard to value options without modeling the smile- let alone evaluate risks in the form of using greeks. If you think you have a -50 delta, and the market moves south, you may or may not have a -1 delta at a lower price. That depends on how much theta or vega you have on your book. In any case, you have to understand what is moving your P&L- otherwise you might wake up one morning being completely correct on market direction but wrong on vol.  Corn futures do this often.

Without EVIL ado let’s dig in to the data.

Here is what a corn IV smile looks like (recently).

Here is the SPX (a while back if I remember).

Clearly the Emini looks completely opposite of Corn. Ignore the corn prices on the bottom of this chart, I applied the SPX smile to corn prices to compare the smile “apples to apples.”

What does this mean?

Well, in general, the IV smile tends to reflect market distribution. Distribution meaning probability of up versus down (averages mean little if you have read any of my previous posts). BSM (Black Scholes Merton) option pricing is based on lognormal (gaussian, normal etal) distribution. Normal meaning the up deviation and down deviation are equal. However, we know that the S&P has a bias to grind higher and flush lower; therefore, it tends to have a negative skew. Or the deviation from average has a negative tenancy (bias). To adjust for this real world problem, option pricing models “charge” a higher IV for OTM puts to compensate for real distribution. Many claim it is due to lack of liquidity- I do not really agree as options are priced at both the BID and the ASK and there no way the EMINI puts are illiquid and Corn puts are not inasmuch, relatively speaking. So it is more likely the smile reflects market distribution and not low liquidity  IMO.

Here is where this gets complicated. If  smile reflects historical distribution, then historical data should Jive with option smiles.

Here is SPX/EMINI historical distribution (since 1990 i believe).

You can see it clearly does have a negative skew. So I presume this makes sense with the smile – which is negative (above).

However, corn is different.

Here is CORN since 1957:

It has a negative skew, yet the smile is currently (+)???

Now here is Corn over the past few years- just to confirm that there is no positive skew.

The skew here is 0, but yet not positive like the smile suggests? What is going on? Is theory fubar or is something else going on?

Well let’s look at historical IV skews for corn (past 3 years daily).

This tells me it generally has a positive skew.. which does not jive with historical real price distribution. Clearly it stays well above 0 until about 25 days till expiration.

Ok so what then? WTF is going on? SPX makes sense according to historic data but corn does not? If one just blindly traded on theory they (1) would have sold risk reversals on corn to arbitrage the skew and (2) probably lost money.

I think there are a few explanations.

(1) perception of a bullish bias for corn outweighs historical reality. I believe this, but I would also say China sells puts on grains since 2008 as well- which will in turn changes the smile. Both are “fundamental shifts” to the price of grain that I believe should be considered. I would like to believe this simple answer, but my mathematically inclined head says something else is different.

(2) The SABR (stochastic alpha beta rho) volatility model should be considered.

The SABR model was a concept originally published in Wilmott finance to adjust smiles for skews, correlation of skew to price, and vol of vol. It models fixed income very well, but I do think the “theory” does help to explain option IV skews and IV “contangos.”

Ok I know that sounds complicated, but lets discuss the “basic” concept.

Information is abundant at Wilmott or if you want the code you can go here.

The “basic” concept is that option prices should price in the RISK of future price movements (eg distributions). However, options truly must price in future OPTION valuation distributions- this includes IV curves. Remember an option’s value before expiration is dependent upon more than the price of the underlying asset. Consequently, if price (SPX speaking here) is to rise one must mathematically compensate for IV to drop and the SKEW to rise. So one cannot just model something linear as up moves decrease IV and increase skew, while down moves increase IV but decrease skew. So the present value of price paths for an option is not the same for up and down due to inherent smile correlations.

I am sure that sounds over complicated, bear with me…

We know from many posts here that SKEW moves with price and IV (eg VIX) is inversely correlated to SPX movements. Many claim this to be the black swan index (including myself). This is mostly likely the case- however- I do believe there is more to this story. Otherwise live cattle futures would not have a negative skew, corn a positive, and SPX negative when the underlying distributions are rather similar. Go look at JUL corn options versus DEC corn options. Notice from a fundamental standpoint DEC has MORE upside risk than JUL given the former \$105 new crop old crop spread. Furthermore, old crop is planted- so theoretically there is no weather risk like DEC (new crop, just being planted). YET JUL has a larger (+) skew than DEC….

Here is SPX versus a skew. Skew moves with price for the most part.

In practicality, what does this mean? Sure higher prices mean more risk, but  why then does the VIX not rise with SKEW? Again there are holes in both the black swan and the VIX sentiment argument. The reason is “arbitrage.” If vol does not equal IV gamma or option selling should make money.

So I am attempting to argue that SKEW reflects more than simple “downside distribution,” it affects theoretical correlation of IV to price (according to SABR theory). Just think when the VIX hit 80 or so the SKEW went to 0 because (1) there is obviously little downside risk after an epic collapse, but also consider what IV at 80% was pricing in? Risk was priced in, and SKEW was low. You can see my line of thought…. IV may reflect complacency, but the SKEW is an adjustment for option selling risk. Furthermore in 2008 the panic priced in high volatility, but one would ALSO expect the correlation of IV to price to weaken (say go near -40 as opposed to -99). Why? Well there was a large risk that prices could fall and IV not rise much above 80. Both the VIX:VXV ratio and actual results confirmed this in MAR of 2009. The VIX did not make new highs when the SPX made new lows- vol was 30% not 80%.

This further supports that skews and time spreads (VIX:VXV) also likely are affected by other variables such as actual volatility and correlation of IV to price.

As for corn, we know it tends to explode up and down along with volatility… but the correlation is mostly positive with IV; hence, the IV smile is slightly positive- especially when there is a break in price. So corn and the S&P may actually have similar downside tail distributions, but the smiles are different due to the different inherent correlations of IV to price.

Now another thing that many confuse is the VIX:VXV ratio (IV time spread). Yes it reflects market makers and sentiment, but it also is an adjustment for theoretical mean reversion of volatility (just like the lower low in SPX and lower high in VIX comment).  Ever wonder why it is so seasonal? Or why it follows price? Volatility dries up around holidays, so 1M vol drops and 3M vol rises (relatively speaking).  Ok so that explains the holidays, but why is the IV time-spread correlated to price?

Here is my best explanation (using SABR theory). (1) the market grinds higher and many know that can’t last forever so they bid up back-dated IV (just like skew). So volatility is low now, but common sense tells us the risk of it rising is high; therefore, the IV spread widens as volatility drops. Actual volatility forces the VIX lower, but estimated mean reversion volatility stays higher in the VXV.

This also explains why both corn and spx smiles go crazy into expiration. Here how the smile changes over time for corn.

Here is what the SPX looks like. You can see that time affects the smile. Moneyness means “% in the money.” Given that prices are “lognormal” we us ln(strike/current price); this is also the first part of the BSM pricing equation.

Here is another cool view.

Why does the smile change? The reasoning is the underlying properties of  the smile change.

Volatility of Volatility is the primary reason for this change. Or volatility of the VIX, “volvol.” If volvol is low the spread remains high- or in English if SPX is grinding higher volvol drops and the VIX goes discount to VXV.

Here is some empirical evidence supportive of SABR theory of volvol.

Here you can see the correlation. VOLVOL affects time spreads for the most part. So this explains much IMO. IV smiles must account for correlations of IV to price- which also happens to account for SKEWS at the same time.

Now for the final question I often get? ” Why in general does the SPX VIX trade discount to VXV and yet Corn IV structures are the opposite?” E.g. why is DEC corn IV less than JUL corn IV? Most commods are this way just FYI.

This is complicated but the SABR does have some theoretical explanations. First off spot commodity months are more volatile than deferred commodity contracts. That is price discovery at its best, more information comes available for JUL relative to DEC; thus, more volatility for nearby months.. Very simple explanation and reasoning. As for the SPX DEC is fixed to SEP based on an arbitrage-able dividend yield. Corn spreads are a function of supply and demand differentials.

This chart is average IV (of say the smile), not ATM IV for DEC corn. ATM IV is actually much more range-bound (as previous charts above show). You can also see the crop reports here as well- notice how IV is bid up before the report, before volatility rises- no free lunch here!

BOTTOM LINE: My point is that different smiles occur on different commodities and different time horizons based upon different underlying correlations in conjunction with historical price distributions. So when you look at the MMR stuff, you now know what is really going on. This means for you rats attempting to buy OTM puts on the SPX betting on a IV spike and a price drop will not get the return you desire. You  maybe better off buying vix futures or selling the S&P due to “smile risk.”

So there may be simple answers to the smile questions, but I do think there is quantifiable evidence for other influences.

For those of you wondering if I use SABR to model my stuff- no- I am an old fashioned modified (creative) cubic spline model guy. I just think there is evidence of the SABR theory when one steps back and compares corn to the S&P.

Also, on a side note, check out the CME data-suite. It is FREE (once you sign up) and they give live quotes for options and some futures. Here is what the calender corn spread options look like. Cool stuff if you like being creative.

Best of luck unbiased (and now creative) trading,

-Volar

## Convexity – It’s Evil Too

So I (volar) do not have much to say for a market outlook- though the VIX 8 day stat worked out well (with hindsight and inductive reasoning bias).

Banking coin is never easy- but avoiding stupid decisions really makes the difference. Convict keeps it simple- and frankly that is why he is solvent.  Solvent traders have a better probability to make coin than the insolvent ones (law of large numbers- just saying). This post is not simple- and will be difficult for a non-options skooled persons, but it should at least give one reason to not stick one’s private parts in a blender (e.g. trading options without the proper tools/knowledge).

I figured this would be one of those informational/discussion threads. THIS IS NOT  ACADEMIC- this is real world options trading. Option theory and retail option platforms- yes even TOS- are “cool,” but they will still FUBAR your account.

I am first going to list some caveats for retail platforms and general option trading fallacies- many of which are found in one of my favorite math reads, Dynamic Hedging. Following that, I will discuss them- of course- that means charts from Volar.

Caveat A: SPX options are not the same as corn options.

Caveat B: Option skews, smiles, and decay term structures will rape you.

Caveat C: Not one, not a single greek, can be compared to another greek- even on the same commod on the same contract. This is a function of the “shadow greeks.”

Caveat A:

Bottom line for caveat A: you have to have a model for each instrument. If your model does not account for correlations and spread differentials- well you are dead in the water.

Caveat B: Option skews, smiles, and decay term structures will rape you.

This chart is Corn IV over time. Clearly nothing is linear here. Notice that anything less than the 80% IV in the put tail of the first chart is not even readable in the second chart.

This chart is near expiration- yikes.

So my point is that the “VIX” is and “average” but averages the curve. The curve changes options differently. This is the largest reason for novice options traders failing- especially when they use TOS or retail option platforms. Sure your platform may give you a greek number, and even allow you to shift VOL, Time, and Price, but it wont model the IV smile term structure/decay.  Toyota has breaks and a gas pedal, but it is not a Ferrari. Even if TOS did model IV term-structure/smile decay- how could you trust it when we know that each commod is different?

Caveat C:

The smile affects option valuations over time.  This is where things get hairy- shadow greeks. All retail models use BSM (black scholes merton)- but none account for the curve.

So let’s say one is short a JUL corn call (say 750 handle today). Delta may be -0.10 but that value only holds for today- technically for about 5 minutes. A typical model, presuming no change in price, will make about 3 (priced near 4 today) with 5 days till expiration (45 trading days from today). However, when adjusting for the smile (aka what volar code does), one will lose 3 cents. This is a 6 cent or 100% difference in valuation. Why? real world vs. academics.  The IV for tails rises- there is no free lunch. Smiles occur for liquidity and “non- normal” distribution reasons. In any case, nobody holds till expiration, yet they make decisions as if they were holding till expiration. If one do not hold till expiration, one will not get expiration results. Many times OTM options (sold) will make one most of one’s money in 1 day- and waiting till expiration to capture a penny usually ends badly due to bid-ask differentials and IV premiums. Bottom line here- if one’s model does not adjust for reality.. one loses coin.

Many think front month contracts decay more than back month. Some think the back months have more premium to sell and front months are relatively cheap. Neither is correct or wrong. Both are worthless ” all encompassing” statements- like most CNBC stuff.

A good option model should cover sensitivity to the following:

Here is the dilemma.  Is one analyzing 1 day or 1 month? The changes are not linear and they change each other. And each change is multiplied by each other (negative or positive). Yes this looks like crap- but notice that delta is the linear slope of 1 point (chart  below). This chart shows that vega moves opposite to decay, and that up gamma is not the same as down gamma. Also a gamma changes on a vol spike or time decay.

Ok so you see delta only matters at (1) a point in time (2) at a particular price (3) given a certain time (4) given a certain IV (Vol)

Now let’s look at an IV spike:

You can see the Curve is less steep, thus the gamma (delta change) is reduced.

Here is a time decay shift:

So… this goes to show that things change. Gamma up is not the same as gamma down. And gamma up for an OTM is utterly different than gamma down.  Gamma (delta sensitivity) is inverse to Theta (time decay). The math is 1/2* gamma* (vol)*(Contract price^2). This implies that not ALL front month options, when adjusted for the IV curve structure, will not decay (example above). Secondly, one is exchanging decay risk for price risk.

Consider this with 2 options on two different contracts- each has about 20 moving curves at different rates.

This means one must manage the shadow greeks (bleeds, dvol dtime, ddelta dvol, etc…). Below are the ones I follow on a spread trade. BUT one must adjust this for the IV curve. So when I input the trades I know all of the shadow greeks and I model the IV curve. Also remember the spread may not move 1:1 with front month price….

Below are a list of Greeks and bleeds (or changes to greeks for a list of options). In all reality, scenario analysis encompasses all of this into one value, but one must be able to see what and why things change.

No, retail models do not do this correctly.

I suggest using heat maps for calendar spreads- once one adjusts for the code/IV smile of course. Here is a scenario map for 1 particular point in time. When one starts to analyze options, correctly, they will find that scenario analysis is the most optimal choice.

* test the good, the bad, the ugly. Never test the great. Stay frosty.

The top is the contract spread (JUL- DEC corn), the left is CN (JUL corn).

Here is 2 different vegas (price sensitivity to change in IV) for a JUL , DEC calender corn spread. Notice that front month VEGA declines relative to DEC. This means that those who “think” deferred options carry more “premium” is bull crap. The greeks are less sensitive- even though our above example showed that the IV smile spike/shift offsets the decay.

This means one must learn to trade the greeks and shadow (future) greeks. If one plans out the option scenarios one will find that most “common” ideas from brokerage houses are stupid.

So differed options have less sensitivity, but the gamma is higher and the theta lower.

Another stupid comment I hear is that 90% of option expire worthless. I must say logic like that is pure ignorance. (1) any 400% OTM option may or may not trade, consequently how do you even run stats on an infinite number? Secondly,  if margin calls made one bankrupt 30 days before expiration (like MF global, LTCM etal), well expiration did not matter now did it?

Bottom Line: many think they are playing in the kiddy pool when they are actually swimming with a bag of meat on their back offshore Africa in shark infested waters.

Volar

## VIX Up 8 Days?

Well to my knowledge the VIX has never closed up 8 consecutive days. Here is the stats and occurrences for 7 consecutive days.

Occurrences.

Results:

Careful here- virtually all of this data is during the dot.com boom (eg upward biased I presume).

In any case- not exactly bearish.

Here is how many times the VXO has closed 8 consecutive (mind you we are not nearing 8 today, but 5). 4 data points- neutral results.

In any case- the data appears favorable, but some caveats.

(1) There is a ~88-90% chance the VXO is >=13 in APR-JUN time frame (using implied lognormal distributions of seasonal data).

(2) There is a ~59-64% chance the VXO is <=20 in APR-JUN time frame (using implied lognormal distributions of seasonal data).

(2) There is a ~43-48% chance the VXO is >=20 in APR-JUN time frame (using implied lognormal distributions of seasonal data).

This simply implies the VXO generally does not explode here, but also has remained very very low.

Finally here is the hourly SPX- not bullish if you ask me. That trend line should be watched.

I will talk more on options later this week- I think it will be an eye opener into some greeks.

-volar

Mole here: Thank you for a kick ass post, mate – I found another juicy setup for the subs and decided to tack it onto this one:

More charts and cynical commentary below for anyone donning a secret decoder ring. If you are interested in becoming a Gold member then don’t waste time and sign up here. And if you are a Zero or Geronimo subscriber it includes access to all Gold posts, so you actually get double the bang for your buck.

Please login or register for Zero Data Feed (non-recurring) or Zero Data Feed (recurring) or ES Gold (non-recurring) or ES Gold (recurring) or geronimo/ES (recurring) to view this content.

Cheers,

## Some Sentiment, Some Stats, And Some Energy Spreads

This is volar with a quant and sentiment update. That being said, I did something different today- I added some “fundamental” data on the bottom. I did this- not for trading, but bc the news is lame, CNBC is full of retards and koolaid, and frankly its nice to hear sound thoughts- even if its my own voice. I understand most of this may seem like it does not go together (sory in advance per the 20 charts)- but we are talking markets and what else do you have to do this weekend? Beer and free data- sheesh I might read my own post- jk.

For those that are not subs- you get a freebie- heck I bummed 2 charts.

Anyway as for the market, I cannot say I could agree more with Fearless’s last post. Longer-term there is much potential given the panic (VIX and volume for that matter) in August. Yet, some red flags are prevalent. Let us have an unbiased look.

First sentiment, then stats, then spreads.

The CBOE equity put/call ratio is low and my daily sentiment data is off-the-charts. The NASDAQ daily is the highest since 2000- and here is what Jason at ST says “Hulbert Nasdaq Newsletter Sentiment was 75% net long again this week.  The 3-week average is now 75%.  That’s the highest average over a 3-week period since July 14, 2000.”

As always my hats of to SentimenTrader.

Unreal.

Unreal.

And… unreal. Now on to stats…

A ton more of Volar’s charts and cynical commentary below for anyone donning a secret decoder ring. If you are interested in becoming a Gold member then don’t waste time and sign up here. And if you are a Zero or Geronimo subscriber it includes access to all Gold posts, so you actually get double the bang for your buck.

Please login or register for Zero Data Feed (non-recurring) or Zero Data Feed (recurring) or ES Gold (non-recurring) or ES Gold (recurring) or geronimo/ES (recurring) to view this content.

Not sure all of that should go in one post – but now you have something to do this weekend besides get off on Ben Bernanke.

-Volar

## Let’s Short This Bitch

When I fell out of bed today I looked at the tape and had sort of an epiphany. We now have ourselves a kick ass shorting opportunity via a bonafide Scott’s Retest Variation Sell setup. I’m going to make this a freebie to get the rest of you retail rats a taste of how we roll here at Evil Speculator:

Exhibit A is my volume profile on the spoos which shows us no volume participation at all just a few handles above. The tape simply has not much opportunity to run here.

Exhibit B are my Net-Lines on the spoos – the hourly is just about to run into resistance and the daily is soon going to bump its head into a NLBL at 1329.75 – the recent highs. The closer we get to that on little participation (just watch the tiny signal range on the Zero Lite) the better our benefit/risk ratio.

Let’s also take a peek at the AUD/JPY – similar picture but not as extreme. Frankly this thing could run a bit higher on the daily side. However, that does not mean the spoos or the SPX are going to follow suit. Let’s also note that equities have been leading the currency side here, usually a bad sign (for equities).

I already mentioned that the signal range on the Zero Lite has been tiny – I’m seeing almost no participation/momentum strength here. Also remember Sentimentrader’s hedging volume chart I posted yesterday.

This morning Volar posted his RYDEX EFT ratio chart again and the boat seems tilted mightily to one side here. And I have an inkling the sharks are already circling… oh boy…

HOWEVER, despite all this the prevailing medium term trend has been strong and that only gives us a roughly 50/50 chance for a reversal here. Nevertheless (and I can just speak from prior experience – Volar can you quant this?) IF we get a reversal here the odds of it being relatively strong are rather high – I would ‘guesstimate’ it at near 75%. Which means we are looking at a low odds high reward RTV sell setup right here and right now.

So this is what I’m going to do. VIX is relatively low right now and barely scraping 20. Which means OTM options are looking mighty juicy and (if we drop) would benefit nicely from exploding vega:

Here’s an example – obviously you want to be ITM when you close them out, so pick whatever suits you best. I think there’s a decent chance we could drop into SPX 1250 and even if I’m not ITM by then vega is going to boost those premiums just nicely.

Again, and let me play broken record here: This is a low probability high yield setup. But it’s cheap – you have a stop just a few handles away (as I’m typing this the spoos are hanging around 1223, roughly 1227 on the SPX). VIX is low and thus premiums are very affordable. Set your stop a few ticks above the recent high at 1229.75 (you can do that in ThinkOrSwim on a SPY option – research it) and then forget about the trade. Most likely we’ll get our asses stopped out but if we not then it should be madly profitable. Worth a crap shoot with a handful of OTM SPY (or SPX) puts with a stop very nearby. If stopped out our loss should be minimal, assuming of course you stick with SPY, SPX, or any other high volume options, which means your b/a spread is reasonable.

Here’s one quick reminder for my intrepid subs:

More charts and cynical commentary below for anyone donning a secret decoder ring. If you are interested in becoming a Gold member then don’t waste time and sign up here. And if you are a Zero or Geronimo subscriber it includes access to all Gold posts, so you actually get double the bang for your buck.

Please login or register for Zero Data Feed (non-recurring) or Zero Data Feed (recurring) or ES Gold (non-recurring) or ES Gold (recurring) or geronimo/ES (recurring) to view this content.
Cheers,

## More On Quant

Mole did a nice piece this weekend- and I do not have much to share for an outlook- but thought I might elaborate more the stats. I know none of you just want to be quants, but it will (1) help you understand my stat data; and (2) will help you formulate ideas about trading the tape.

The reason I like stats, is that it rids me of bias, but many use it as a false crutch IMO. Heck many give probabilities, but do not consider the real underlying distribution. Let us start with some robust growth rates compounding over say 14 periods.

This is why many use logged SPX charts when going back to 1950. Things look flat at the beginning, but they were not; the blue line is constant growth. Here is the natural log of the data- do you see the difference? This is the dilemma with regular statistics- we presume that returns are “normal” or “lognormal.” However, I am going to give you some charts to show you that the stock market is a bit more complex than meets the eye.

This shows us why so many use LN (natural log) to adjust PRICE for ROBUST growth rates. Again we are adjusting price for growth.

So here is the SPX price vol. and VXO distribution since 1986.

Clearly this does not look like a good bell curve- now this is vol, not asset returns – there is a difference as VOL is always positive and it cannot go negative. Consequently we use lognormal (LN) distribution.

So here is the adjusted data (natural log of VOL).

So I know you are confused- but the point is that vol needs to be looked at on a natural log basis. The fit is actually very good. This means that the VIX and actual SPX vol are both lognormal- but if they are lognormal we have proved the SPX returns must not be normal. So go re-read this again and notice how I said we use LN to adjust PRICE for robust growth. Here we are adjusting VOL for robust growth- not price. I know your head hurts, but let me bring this to real world practicality.

(1) we know from Mole’s post that the SPX has different distributions when VXO>25 or less than 25; moreover, we know that the market has kurtosis. This means markets tell traders to buy low and sell high, and little moves are common. However, that is not a good idea IMO.

(2) we know from the chart above that (a) both SPX and VIX vol are lognormally distributed; and (b) the VIX distribution is > than the SPX in terms of VOL- aka IV trades at a premium to actual SPX vol.

(3) All of this proves that William Eckhardt and Nassim Taleb’s beliefs. The market is more exponential than you will ever believe. So find a way to use this to your advantage.

(4) You must understand this to survive trading. How can one have an opinion or expectation on the market if one does not understand how markets work?

(5) Nothing is ever simple, but it probably is seasonal.

Here is a horrid chart of monthly implied lognormal VXO distributions. My point here is that all VXO distributions are normal- but none have the same shape. This means that one cannot apply the population to the sample- the sample IS a separate population! Notice below the huge differences between the summer and fall.

Now here is a more practical chart. I will just say the JUN is the complete opposite of OCT.

This shows us that in OCT a VXO >30 is has over a 20% probability- whereas JUN is < 5%. Get my point? Also, OCT has a higher probability of the VXO being less than 12- just to make you more confused. That my friends is the difference between an AUG sell-off and a SEP sell-off. In any circumstance- each month is different.

Ok so I know your head hurts, but keep the main points in the back of your mind. Things LOOK one way and act another. Distributions can be 1 seasonal and 2 conditional. In any case there is more than meets they eye. So when it comes to trading, I suggest building ideas that reflect the true nature of the market.

-Volar

## Mole’s Weekend Musings

After seeing two excellent posts from both Fearless and Scott (thank you very much) I really do not have too much of value to add this weekend. The medium and long term perspectives on equities, gold, silver, the Dollar, etc. as reported earlier in the week stand and I’m not going to regurgitate the same material just so produce a post. Instead we’re going to do something a bit different today. Volar responded to Fearless’ post with some very good material on volatility and fat/thin tail distribution. Reading it confirmed some of my own theories related to the cyclical nature of the tape which you may find valuable. So what I’m going to do is to quote Volar’s write up and then basically add my own perspective if you will.

If you run the math you will find that on a daily basis – annually – the skew is close to normal, and but  KURT (i.e. kurtosis) is  large. That is due to compounding error of the VIX distribution and overlapping seasonality data. But nothing is black and white – I believe in conditional statistics and offsetting tail distribution. Common sense tells us that when the VIX is > 25 the market will exhibit a different distribution than when below – especially when you run it seasonally.

Let’s cover some of this as there is a ton of really good information in there. By kurtosis Volar refers to thin tail vs. fat tail distribution. For instance – on a weekly basis what are the percentages of times you get a +/- 0.5% move. What are the percentage of times you get a more violent 2% move? A thin tail market gives you a higher concentration of moves within a small percentage range, let’s say between 0% – 0.5%. A fat tail market gives you a more spread out profile where you see a lifting of the shoulder ranges (i.e. 1% – 2%) and a drop in the middle range (i.e. 0% – 1%). So now that we covered the basics let’s talk about the weather.

Yes, I am not kidding. Every morning you subs get a TICK TrendDay alert – that is your daily weather report based on statistical information captured via the TICK within the first 45 minutes of the NYSE session. Quite often the report nails it on the head and sometimes (like Thursday and Friday) it is completely off the mark. But it’s an attempt to gauge the ‘type of the market’ to expect for the day. Is it going to be a volatile day? Is it going to be a down or up day? When watching the Zero or your own indicators – should you trade divergences or is the short term trend so strong that they don’t matter and VWAP touches are nothing but buying (or selling) opportunities?

The work Volar has been putting together is purely statistical by nature and let me tell you that over 60% of institutional traders use nothing but statistical analysis for their trading. I think that needs to be repeated – a majority of the prop desks run by big institutional players do not care about indicators, golden crosses (or showers), technical analysis in general. If they do then it’s only a minor aspect of what drives their trading algos. It’s almost purely statistical mixed with some AI, genetic algos, HFT stuff, you name it.

For those quant boys ‘conditional statistics’ is everything – I call it the weather. You can express the daily weather in the markets in various ways via statistical conditions – maybe it’s a small number of parameters and maybe it’s hundreds. In the end the system will produce a set of odds for you and perhaps a trading range, entry points, exits, etc. It’s like figuring out if you’re going to take a drive to the mall or take the kids to the park for soccer practice – it all depends on the weather. Only retail rats use the very same algos (i.e. indicators and charts) every single day. Institutional traders have long figured out that what really matters are the ‘road conditions’ and they adjust their trading accordingly.

Which is why I keep telling you guys to pick your markets. The Zero for instance is a very simple tool, obviously geared toward retail traders. It kind of took over where the old ticker tape left off – instead of listening to the racket of the ticker the Zero gives us a feeling of participation and momentum of the trend. That is very valuable I think and it has kept us out of a lot of trouble in the past.

When Volar talks about the VIX being over or under 25 then he refers to essential market conditions that affect the way we should trade. I myself have figured that out when I started writing black box trading systems like Geronimo and evil.rat. Geronimo for instance does very well when the VIX is below 30 but if it’s above then it starts having issues and I actually disable it. It’s the opposite with evil.rat (which I haven’t run for a while now for obvious reasons) – it kicks ass especially during extended high volatility periods as for instance during 2008.

This is what I mean by picking your markets and I am considering extending my work on that end in collaboration with Volar. My vision would be to produce daily and more sophisticated weather reports based on seasonality, volatility, and other essential parameters.

Above graph shows us non seasonally adjusted distributions. By offsetting distribution i mean the holiday’s narrow tails overlap the fall fat tails. (now the VIX complicates this even more as it compounds the data). So things may look “Gaussian” when they are actually not- they are two different distributions. If you break out the months – the aug-oct period is far far from normal and highly skewed to the downside with large fat tails. Where as the “holiday” period is the opposite – it is narrow tailed and not skewed. So the holidays are also not normal, but narrow. I will also add that the high correlation among stocks also breaks the rule of normal distribution and portfolio theory- moreover, non constant distribution of both beta and correlation both imply that gaussian statistics have limits on how one can use them. Or bottom line on gaussian: only use conditional statistics to measure an expected outcome given 2-3 conditions; moreover, never use portfolio theory or VAR because the variables are ever dynamic and not constant.

Basically there are essentially two market conditions that take turns during the year – do you recall Volar’s seasonality charts? There are ‘easy’ times (e.g. the Santa Rally) and then there are more turbulent times. BTW, when I refer to ‘easy times’ then I mean more contained and uni-directional markets. A tough time would be a large correction followed by a fast short squeeze – can be extremely profitable but it’s not easy to trade. If you try then you most likely will have to abandon habits/strategies that work very well during ‘easy times’. There are also months when there is little edge to be had and you should just stay the heck out (i.e. summer IMNSHO).

When Volar talks about the ‘holidays’ then he refers to November until the end of December. Vacation starts after May and that may be a good time to dip into low volatility strategies. The fireworks (i.e. fat tail moves) usually happen in the August to October time frame – I’m sure you are aware of the concentration of market crashes and large corrections that have all occurred in fall.

As for volatility being non-uniform that is my whole point the overlapping non-uniformness makes much look normal or gaussian, when in fact there is 2-8 actual separate, underlying distributions. The other thing i will say is when you run conditions – e.g. if sma > sma_2 or something, the outcome of that particular trade may have normal distribution – regardless of actual market distribution. Which is why I run stats on outcome of conditions – because there is a reason for a normal distribution, not overlapping randomness. I mean if the market is 7% >100ema with the VIX<16 versus the market 15%< 100ema and VIX > 40 those markets will have utterly different expected outcomes- and for good reason. I will say if you are going to test the golden cross or ma’s (on a daily basis) you need to test the slope of the MA (eg. up or down) and then you need to test whether or not the market has made a new high or not. The stats will be much more clear.

Gaussian – if you have used Photoshop you may remember the Gaussian noise filter. It’s basically if you have a more randomness and there’s no clear pattern. Gaussian distribution also measures how many and what concentration of data points fall within a particular measured range – you usually get a bell shaped curve with dropping shoulders toward the 2nd and 3rd standard deviation.

Now what Volar is saying here is key – and in plain old English it means that the outcome of running your statistics depends on the type of market conditions you are looking at. I give you an example – you may find that a simple moving average cross makes you money for months on end but suddenly it starts breaking. What happened? Most likely it’s the market conditions that changes. Perhaps volatility dropped below a threshold, maybe the number of stocks above/below their 200-day SMA reached a certain threshold, or perhaps it’s a combination of factors. The trick here (and that’s the holy grail for the quant crowd) is to come up with a number of test conditions that allow you to find an edge for a particular ‘type’ of market.

It’s very tempting to go overboard and keep adding a boat load of test conditions – after all the more better, right? Well, wrong! I actually do have some experience with that from my time of writing software for a living. Back then we wrote a piece of code and then wrote a few small tests for it to make sure we weed out the majority of bugs early on. You can try to test for everything you can think of but usually the 80/20 rule applies – you catch 80% of the bugs with just some basic and tried test conditions. The same type of thinking applies to writing trading strategies – the root of all evil is premature optimization. Instead of adding more rules or conditions I always try to first figure out why a strategy does not work well during a particular time period. And often it’s the (market) weather that has a bigger effect than shifting/optimizing the strategy’s test parameters. Which means a particular strategy has its time to be active and its time to be silent.

If it snows outside then you’re probably not thinking of heading to the beach for a skinny dip. And if it’s 90 degrees and 80% humidity then soccer practice may not be high on your list and shopping for clothes in that air conditioned mall with your girlfriend may be much less of a painless endeavor. You need to approach the market with a similar perspective – when looking at the tape try to give the weather a bit of consideration. Try to remember which types of trades worked best in what market conditions and you are already light years ahead of the average retail retard.

Again, time permitting Volar will continue to post weekly statistics here but even the seasonal charts I keep putting up are extremely valuable to boot. I hope my musings were of value to you guys and explained some the ways I approach the market and why I sometimes tell you guys to just stay out or to strike without emotions when the odds appear to be on our side.

Cheers,