Even if that argument doesn’t convince, he does mention an interesting trade, which is to buy September 30 or 32.50 VIX (Chicago Board Options Exchange volatility index) puts and hedge with at the money SPY (ETF that tracks the S&P 500, whose implied volatility is measured by VIX) puts. What happens is, if the VIX drops as the market rises, the VIX puts make money, but the SPY puts lose value. If the market drops, the SPY puts increase in value, but the VIX puts lose value.

Now the question is, how much of each to buy?

Vega

What we have to look at is, for a move of, say, ten points down in the S&P 500 (which is equal to one point in the SPY) which would make our SPY puts more valuable, how much would VIX drop, which would make the VIX puts less valuable?

How much would the value of the SPY puts increase for a 1 point drop in SPY? Since their delta is near -0.5, they would increase in value by half a dollar.

That is one piece we need.

We need to figure out how much the VIX puts drop in value when SPY drops. To do that we use the SPY vega. Vega of SPY is 0.12 so the change in the implied volatility of SPY would be given by the change in the SPY option value divided by the option’s vega, or 0.5 / 0.12 or 4% for a 1 point drop in SPY. But this is 4% of the implied volatility. Since the implied volatility is 27, this gives a change of the implied volatility of 4% of 27 which is about 1. So the implied volatility would go from 27 to 28.

This change is the underlying that moves the VIX puts. So since the VIX 30 puts have a delta of -0.7, that would change the value of the VIX puts by (-0.7) * (1) = -0.7

So it is these two changes in value that we want to hedge. It looks like we would need about 7 SPY puts for every 5 VIX puts (7 SPY * 0.5 + 5 VIX * (-0.7) = 0).

Where Does The Profit Come From?

One way to figure that out is to look at the vega of the SPY puts and compare it to the delta of the VIX puts. That way, we are looking at the change in the value of the SPY puts when their implied volatility changes (that is what vega measures), and comparing that to the change in the VIX puts when its underlying (the implied volatility of the SPX index) changes.

The vega is the change in the value of the option for a small change in the implied volatility. For the 99 or the 98 SPY put, vega is $0.12 and the delta of the September 30 VIX put is -$0.71. For the September 32.50 VIX put the delta is -$0.89. So we would have to buy six times as many SPY puts as VIX puts. That would make us immune to movements in the implied volatility.

If we bought 7 SPY for every 5 VIX, we would profit from the change in implied volatility calculated above. The VIX puts are six times as sensitive to changes in implied volatility of the SPX as the SPY puts are. If the S&P implied volatility drops, the vega measures the change for the SPY while it is delta that changes the value of the VIX puts.

The underlying for the VIX is the futures contracts so, for example, calendars do not work the same way. The out month moves independently of the near month.

The 30 day historical volatility of the VIX is 84% while the at the money options, at 25, have an implied volatility of 64%. Right now VIX is trading just below 25, so it would be a coin flip if the puts end up in the money or not.

Here is the chart from his post:

SPX on top, VIX in the middle, and CSFB skew index bottom

Adam Warner doesn’t see that the CSFB skew index adds much value.   He points out the huge dip in CSFB last October when VIX was hitting the 80s.  That has put many people off this index, why would there be a dip there?

CSFB tells you what your deductible would be on the put side if you were paying for it with a 10% out of the money call three months out.  What that means is, find the price of the call three months from now that is 10 % above the market.  Then look for the put three months out that sells for the same amount.  How far is that below the market?  That is CSFB for today.

To put on a zero- cost collar with options that expire in three months, sell the 990 call (SPX at 900) and that will finance  the put 19% below, at 729.  This is about 2/3rds of the max skew that CSFB has seen.

So last October, all the puts had high vol so the skew was low.   Counterintuitve, but possible.

One detail straight off is that the comparison should be with the VXV not VIX since VXV and the skew index measure three months out. Here is what VXV looks like:

S&P 500 Options Volatility Three Months Out

Not very different than VIX, a little higher, but still at a low point of the last six months.

Seems plausible,  but being skeptical, I wanted to test it.

Here is a plot of daily trading volume in SPY, the proxy for the S&P 500.

SPY Volume (20 day Simple Moving Average)

I’ve plotted the 20 (trading) day simple moving average. That smooths the plot and I use it to compare the daily volume to the moving average to get a measure of high volume or low volume.

As you can see, it has been rising since 2000. Since the volume has been rising, I compare the daily volume to the MA to see if the daily volume is high or low.

SPY Daily Volume (20 day Moving Average)

To measure the volatility, I take the daily range as a percent of the opening price.

SPY Daily Range

The correlation coefficient for the full time series, from 31st January 2000 to 29 June 2009 is 0.273; while for the smaller sample, 3rd January 2007 to 29 June 2009 it is 0.234. Pretty much the same.

Perfect correlation would be +1 and perfect anticorrelation would be -1. 0.27 is pretty good for financial time series. When I trimmed the outliers, the correlation for the full series went to 0.22. So the result is robust.

(You trim away the outliers, those points that are far away from the mass of points, because they have too large an influence on the correlation.)

The plot of the full time period looks like a solid mass, so I just plotted the shorter time period.

This is the table he published:

One feature of this portfolio is that a large move down, 50% or greater, will wipe out the BGU part of the portfolio, leaving the cash.  But now, the portfolio is all cash, so it doesn’t participate in the market anymore.

The table is correct if you make the move in one step. If you get there in two steps the second portfolio lags to the upside and does better to the downside, if the two steps in the downward move are both down. If one step is up and the other down, then the BGU / cash portfolio lags. The following table illustrates the point for a net 20% down move.

The first column is a one step move down 20%. The second column is a step down 10% and then another step down 11.1% which is a total loss of 20%. The third column is a step up of 7%, then a step down of 25.23%.  Why does the BGU portfolio have this seemingly erratic behavior?

It has to do with compounding.  The reason compounding grows faster than an arithmentic growth is the multiplying of terms.  So the IWM portfolio grows in two steps to

$100 * (1 + r1) * (1 + r2) = $100 * [1 + (r1 + r2) + r1 * r2]

The first term is the principal, $100.  The second term is the arithmetic return, r1 + r2, and the third term is what compounds the returns, r1 * r2.  Usually, r1*r2 is small.  If they are both one percent, multiplying them gives one hundredth of one percent, tiny.  If both returns are ten percent, then r1*r2 is one percent.  Now, it is beginning to matter.  In the BGU portfolio, this term is multiplied by 3.  So two ten percent moves will contribute 3% to the overall return.

It is this term, and all higher order terms, that is different between the two portfolios.  When there are several big moves, these terms are large because they have the powers of 3 multiplying them.

If this won’t make Cramer spit out that coffee, not sure what will (hat tip Kieran in the comments)

Direxion, a pioneer in providing alternative investment strategies to sophisticated investors, announced today that it will execute a 1-for-2 reverse split of the shares of Direxion Daily Mid Cap Bear 3x Shares after the closing of the markets on Wednesday, June 24, 2009. MWN shares will begin trading on NYSE Arca, Inc. (NYSE Arca) on a split-adjusted basis on Thursday, June 25, 2009.

No one’s exactly sure why they picked MWN to reverse-split first. It’s a $33 stock, and it’s way off the radar. But the implication is that more popular names like our friends FAS and FAZ will reverse split as well.

Clearly though 2:1 won’t do the trick for them, perhaps 10:1 would make more sense. Or better still, issue new one’s from scratch. There was also some thought about creating new one’s with longer reset periods, like say one month as opposed to 1 session. But alas, that becomes problematic too as we saw a month with a greater than 33.3% gain in financials as recently as March. In fact last time we ran numbers, we saw that if Direxion had issued monthly FAS and FAZ when they issued the originals, FAS would be lower than it is now and FAZ would have gone under zero.

And in other news, Finra has officially requested that Ultra ETF’s now only sell with a warning label.

The Financial Industry Regulatory Authority has reminded brokers and registered investment advisers about their fiduciary duties when selling ETFs that offer leverage, are designed to perform inversely to the index or benchmark they track, or both. In a notice posted to its Web site earlier this month, Finra reminded the brokers and advisers that these instruments are complex and typically unsuitable for retail investors who plan to hold them longer than one trading session.

“While such products may be useful in some sophisticated trading strategies, they are highly complex financial instruments that are typically designed to achieve their stated objectives on a daily basis,” the notice said. “Due to effects of compounding, their performance over longer periods of time can differ significantly from their stated daily objective.”

It goes on to note that if your Ultra ETF is still up 4 hours after you buy it, consult a physician. Do not operate heavy machinery if you buy and hold these.

And no, I have no idea what is in that picture, although it looks like something out of Sleeper.

Not sure I said that exactly, but let me clarify the point.

The VIX will likely understate “real” implied volatility for the next couple weeks. Remember the VIX is a statistical calculation designed to give an estimate of the volatility of an SPX ATM option with 30 days until expiration. But not all time is created equal. The stretch from June expiration through the July 4th weekend is about the worst “time” to own. It encompasses 16 calender days this year, so this over half the time that VIX of last Friday covered is a seasonally low volume and low volatility stretch. Traders tend to lower bids ahead of it not so much as anticipation of lower volatility estimates going forward, rather just an acknowledgment that the time value of a July option right here right now is less than the calendar would indicate. Those lowered bids have the effect of making any volatility calculation a bit low.

But of course, markets move. And this market moved way lower Monday. And the VIX shot up. Does this make this whole point wrong? Not really. My suggestion is more that the VIX understates “real” volatility. And that “real” volatility picked up notably on Monday.

Longer dated volatility measures better express volatility right now. Such as VXV which we discussed yesterday (90 day VIX) and VXX (the VIX ETN). VXX is very new, but we (well, Bill Luby and I) suspect it will track an average of 40-50% of the VIX move. It lifted 4% on Monday, which implies “real” VIX lifted something like 8-10%, less than the 11.5% actual VIX lift, but still a pretty impressive move.

So long as we’ve dredged up a little Cramer, how about we at least have a takeaway from it.

Allen was kind of enough to post this Howard Simons response to the “Great Ultra Market Knockdown” discussion over on Real Money.

Variance Swaps and ‘They’
6/22/2009 4:03 PM EDT

Charles, recall how when W.C. Fields was asked by the rube, “Is this a game of chance?” he was told, “Not the way I play it.”

One of the bigger contributors to end-of-day extensions is position-squaring by market makers in variance swaps. Variance moves as the square of volatility, so on such a day as this when the VIX is up about 10.7%, these market makers have to sell ever-greater quantities of stock at ever-lower prices to hedge. This process works in reverse, too, and I believe much of the kick higher after March 10, 2009, was attributable to the unwinding of such hedges.

But you have to get with the program. Buyers are not “they.” Sellers are “they.” And that extends to the various leveraged ETFs, too: Leveraged-down is bad, and leveraged up is, well, not so bad.

Now I can’t verify his numbers are correct, but the principle is spot on. Consider “they” as anyone effectively short market volatility in some fashion. Be it variance swaps, SPX straddles, whatever. And yes, even Ultra ETF’s. A third party that creates them for Direxion or ProShares is effectively short all he has created. Not every player in every product flattens out at exactly the close of each day, but it’s certainly a force on the margins. And the bigger the move, the more you need to hedge, so it can feed upon itself. Cramer’s Evil Cabal is often a quant-ish trader or hedge fund simply evening up. And yes, that evening up can take the form of shorting into weakness and chasing strength.

Now hedgies and traders not actually short volatility can indeed pile on, knowing they can squeeze the aformentioned players. Or at least try to squeeze them. But it’s not a layup to buy at 3pm every strong day and sell 3pm every weak day. It’s perhaps a good odds move, but it’s a risk trade that gets squeezed too in it’s own right.

And we haven’t even touched on actual longs selling stocks. That’s been known to happen too.

Bottom line is it makes better TV to have some Sith Lord sitting around controlling every market in the world, but it’s a bit more complex in reality.