Bill Brodsky stands at a crossroads. He looks up and sees two signs.

“Left: Amass large trading volume with deep fee discounts.”

“Right: Attempt to muscle in on rivals’ most popular contracts.”

Bill, and the Chicago Board Options Exchange, forsake both alternatives and forge their own path.

This may be unfair to Nasdaq OMX PHLX – king of the dividend arbitrage strategy, stimulated by flat fees, in which market makers can harvest dividends from unexercised options – and to the International Securities Exchange, which battled CBOE for four years for the right to list competing Standard & Poor’s and Dow Jones index options.

But it is fair to say that CBOE, more than any other options exchange, has championed product innovation. Witness the rapid growth in 2010 in its Volatility Index options and futures, and its more recent addition, the S&P 500 Implied Correlation Index, which won an FOW Award for Innovation in December.

Then at the beginning of January, CBOE began publishing volatility values on five of the most liquid US stocks.  

So what is the next move from the pathfinder? Word on the street says it’s skew and that it’s due any day now. (Should FOW quickly trademark the name Six?)

The Edwin Starr argument rebuffed

An option, huh, yeah, what is it good for? Absolutely nothing.

Or maybe not.

For as long as there have been derivatives crises – whether caused by crime (Leeson, Kerviel, Madoff) or bungling (Orange County, LTCM, synthetic CDOs) – cynics have questioned their use.

Is it a naïve fallacy that derivatives can actually help companies and individuals hedge and reduce the risks they face? Are options really just elaborate toys for highly numerate speculators?

No, cynics, they’re not.

That’s not my opinion. That is what skew tells us. Skew offers circumstantial evidence to suggest that derivatives, options in this instance, are indeed hedging tools first and speculative vehicles second. How does it do that?

If the Vix charts the price of risk, you could say that skew chronicles the price of extreme risk – tail risk. Skew asks a specific question: how likely is a 10% correction in the next few months?

Look at the skew in pricing between a three month S&P 500 option at 90% of the spot price and one at 110%.

It shows that the market deems a 10% fall almost twice as likely as a 10% rise, despite the general bullishness in the underlying equity market.

A recent Gallup poll, quoted by Bloomberg, of 1,000 investors, analysts and traders found: “More than two of five of those surveyed say they are seeing more opportunities to make money. That’s the highest level since the poll began… and compares with less than one in three still hunkering down. The rest describe the economic environment as getting back to normal.”

Despite such bullishness the options market has not lost sight of its primary function. Favourable sentiment has not altered the bias of skew, which shows the prevalence of downside hedging among derivatives users.

The twisted smile

To understand skew, think about the volatility smile. Imagine a smiling Mr Vol strolling through the FX and commodity markets, observing on his travels fairly balanced volatility regimes. Now imagine Mr Vol stumbling into the equity option space, being consumed by its fatalistic nature and suffering a stroke down his right side. That smile is now skewed.

Skew is not unique to, but is most commonly observed in, equity options. Société Générale labels it “crashphobia”.

“Lab studies,” SG avers, “suggested that losses are twice as powerful emotionally and psychologically as gains. Reflecting this fear of loss, equity puts are consequently better bid than calls.”

More people want to buy defensive put options for strikes below the present price of an index or stock than want to buy bullish calls. This means the option writers can demand higher premiums for the former.

Plug those premiums into the standard option pricing model and it spits out a reading that the implied volatility of the out-of-the-money puts is higher than that of calls with strikes equally far above today’s price.

In other words, the dear pricing of these popular puts implies that the option writer is at greater risk of having to pay out on the puts than on the calls. The model reads that as saying the underlyings are more volatile on the downside than on the upside.

Let’s use some real numbers. Under the put-call parity theory, at-the-money calls and puts on the same instrument should have the same implied volatility.

For example, a March at-the-money call on the S&P at 1290 has implied vol of 14.7% – and so does the equivalent put.

But further from today’s price, divergence sets in. A 10% out-of-the-money call, on the S&P hitting 1420 in March, has implied vol of 15.0% – only slightly dearer than the at-the-money call. This is one side of the volatility smile.

The opposite put, on the S&P sinking to 1170 by March, has implied vol of 24.6% – a much steeper increase from the at-the-money, giving a skewed smile. Yet both contracts put the writer at risk of a payout if the S&P budges by 10%.

Quite something, eh? Equity option investors are a fearful lot.

Take the vol of the out-of-the-money call, 15%, and subtract it from the vol of the opposite put, 24.6%, and you get 9.6%. That’s today’s (January 25) three month skew on the S&P.

Now watch how that number changes day by day. If it rises, investors are growing more fearful. If it falls, the opposite is true.

More than nerves

As SocGen tells it, the crash of 1987 precipitated this preference for fear over optimism.

But surely there is more to the outsized vol on puts than just crashphobia?

After all, the credit crunch has demonstrated that any asset class can fall by 10%. Why aren’t commodity or FX options traders as cautious as their equity brethren?

Mariana Capital strategist Daniel Hawkins explains. “It’s not that any one group of traders is more conscientious than another,” he says. “It’s more a reflection of the fundamentals of the asset classes. Take commodities – these are supply-constrained assets. Therefore the greater risk is usually of a jump up in price, not a slump lower. Meanwhile, currencies tend to have symmetrical volatility smiles. They’re traded in pairs, so if skew existed it would create an arbitrage opportunity.”

As so often in equity derivatives, structured products issuers are partly responsible. Their business makes them naturally long volatility, so they want to sell volatility to hedge themselves. Much of this is done by writing calls and call spreads, pushing down premiums on the call side of the market and hence increasing skew.

Why don’t they write puts instead? Even after all these years the lesson of Long Term Capital Management still haunts volatility traders. As the market fell, the fund is believed to have lost as much as $1bn on puts it had written. No one wants to “pick up pennies in front of a steam roller”.

Finally, there is an empirical underpinning for skew. Research shows that in any given period, a strike price 5% below today’s price is more likely to be hit than one 5% above. This is because, when stocks rise, they tend to rise gradually, whereas when they fall, it is sudden and steep. Market participants’ emotional hatred of falling prices is reflected, not just in skewed pricing for options, but in skewed behaviour of the equity underlyings.

Wanted: crystal ball

Come on CBOE. You know what we want. We want an investable index that will predict the future. Is that too much to ask?

So does skew predict the future?

Barclays Capital is on hand to crush our dreams: “One of the urban myths regarding volatility skew that we wish to examine is whether it has any predictive properties, ie. do changes in volatility skew (however it is measured) have any bearing on subsequent market performance?”

The conclusion: “There is no clear empirical relationship.”

Rats.

So, apart from demonstrating how equity option traders are chicken, what does skew tell us?

Well, it tells us when puts are relatively cheap and expensive. That’s useful for equity portfolio managers. If your portfolio is protected by $500m worth of puts and you have to roll that exposure monthly, you can opt to roll more on days when skew is falling (and puts are cheap) and less on days when it’s rising (and puts are expensive).

Is skew a better indicator, or a better hedge, than the Vix?

Swings and roundabouts… Skew doesn’t rise as much when stockmarkets are falling. So it’s not quite such a powerful hedge as the Vix. Day traders might have less interest in a skew ETF than a Vix ETF.

On the other hand, skew doesn’t fall as fast when markets are rising, making the pain of holding it as a hedge less acute.

Fair enough, sounds interesting, when’s the index being launched?

Sadly, CBOE declines to comment. However, it’s a columnist’s prerogative to speculate. So let me do that.

CBOE’s next move

Catherine Shalen, a director at CBOE, declared at a conference last summer that the exchange’s skew index was not correlated with volatility. In other words, it was not just another Vix.

This statement is more revelatory than it may seem. There are several ways to calculate skew. Some simple (as I have demonstrated above), some complex – don’t let’s get started on variance skew.

The simple mainstream skew calculation is correlated with volatility. So, taking Shalen’s words at face value, perhaps CBOE’s calculation is that bit more sophisticated. What does this mean for the forthcoming index?

One should ask Abhinandan Deb and Aaron Brask, the Barclays Capital men who published a report on the pros and cons of different ways of calculating skew. At a basic level it shows that CBOE might not be going for the mainstream version of skew with its index.

Single stock volatility… correlation… skew… Who is CBOE aiming these products at?

Exciting as CBOE’s innovation is, the exchange runs the risk of being too clever for its own good. Might Brodsky be overestimating the intellectual capacity of the investing public?

My hunch is no. He’s a smart cookie.

To come to my point – and feel free, at this stage, to call it a guess or a conspiracy theory.

I contend that the Vix and the skew index are complementary, not competing products.

If we see a liquid CBOE skew future trading this side of 2012, I’ll eat my hat. Creating these indices is designed to push more attention towards Vix – the golden goose.

CBOE has successfully entrenched a common understanding of what volatility is. It is the Vix. To protect that success, CBOE wants ancillary indices to help sophisticated investors further understand when and why to take opportunities in trading the Vix.

In other words, the CBOE is creating indices that say “TIME TO TRADE THE VIX” every day in every way. It’s a smart move, and maybe it says something about where this company goes next.

The options exchange business in the US is getting more vicious. Dogs have not quite begun to eat dogs, but they are undercutting each other.

As the market grows, the CBOE needs to keep rolling out new ideas and having those ideas licensed to keep its edge. Vix, it believes, is the future. Skew is just another way of broadening its appeal.

Theo Casey is a Futures and Options Intelligence columnist.