As I write on June 16, the CBOE Volatility Index is trading at 25.87 – down 10% on the day.

The Vix is the ‘fear gauge’ that measures the prices of in-, at- and out-of-the-money calls and put options on S&P 500 shares. The implied volatility it measures is inversely correlated with underlying equity prices.

It may seem natural, then, that today’s drop in the Vix is commensurate with recent gains in equity markets. Having rallied for six days on the trot, the S&P 500 is putting together its longest winning streak so far in 2010. And since rising markets exert a downward pull on the Vix, this rapid plunge in the Vix seems par for the course. But it’s not.

The up and down surges in recent months of implied volatility – one of the most important elements of option pricing – are far from ordinary.

Take a look at the left hand graph below. It shows, for the period March-June 2009, on how many days the Vix moved by a certain percentage, up or down. What you’ll notice is that the most common result, on 26 out of 61 working days, was a modest 2%-5% fall in the Vix. So far, so normal, considering that during those months the S&P was rising fairly steadily.  

Fast forward to the present (graph 2), and you’ll see a very different picture. And maybe not the one you were expecting.

It’s not so much that the Vix has changed direction – in geek-speak, swapped from a positive skew (counter-intuitively, this means a pattern of falling more often than rising) to a negative skew (vice versa).

It’s that the range of outcomes has become much more varied. The distribution extends further from the midpoint in either direction, and with more outlying events. This is a classic example of ‘excess kurtosis’, or, to use its stage name, the ‘fat tail’.

Fat tails, as popularised by The Black Swan author Nassim Nicholas Taleb, are events occurring outside the ordinary. And in the Vix, they are happening far more often now than they were 12 months ago.

These fat tails are causing some very unusual outcomes for investors. The extreme rates of change in implied volatility are producing some truly bizarre goings-on in options markets.

Just last month came a particularly weird example – equity call options that rose in price while the stockmarket was selling off.

Hysterical Thursday’s hysterical outcome

The ‘flash crash’ on May 6 – dubbed Hysterical Thursday by Bloomberg BusinessWeek magazine – has spawned many important talking points.

Equity market grandees have attacked the role high frequency traders are said to have played in the rout. But the figures from that fateful day reveal something just as puzzling.

The S&P 500 Index fell 3.2% from 1165 to 1128 on the session. Thus, it was a day when one would expect a long options portfolio to take losses. But that was not to be. Equity call options began to fall upwards.

Take Procter & Gamble. Our example is the $70 October contract. With three months till expiry, it was three strikes out-of-the-money, as the share price had closed at $62.16 on May 5.

On May 6, P&G shares plummeted to as low as $39.37 in the afternoon, before closing at $60.75, down 2.3%. On a horrific day like that, it’s unlikely that any holders of this 12% out-of-the-money call were expecting a bump in their contract’s value. However, the call’s price actually rose 20% by the session’s close.

And P&G was not the only one. Kraft, Pfizer, PepsiCo and Abbott Laboratories were among the plethora of companies whose calls were also falling up. Abbott Labs’ call premium rose an eye-watering 146% in the $60 strike, though the shares fell from $50.15 to $49 on the day, via a low of $45.60.

Then, the storm of volatility vanished as quickly as it had come. The Vix’s rise to 40.95 on May 7 was countered by a fall to 28.8 on May 10. That’s a 26.9% fall after a 24.8% rise in two sessions – “the largest single day decline in the 17 year history of the Vix and in the 20 years of reconstructed Vix data,” to quote Barron’s commentator Bill Luby.

The week of the flash crash, naturally, was one of the most extreme cases of such anomalies – but not an isolated one. Excess swings like this, as the graph shows, are more and more common.

Another instance of this type of rogue optionality occurred in 2008. Dean Curnutt, president of Marco Risk Advisors, has written in his daily note to clients on one of his favourite anecdotes from the financial crisis: “We were buying calls on a customer’s behalf as a financial stock crashed. Despite the stock in seeming freefall, the value of calls was actually rising rapidly – that’s not something you see every day.”

Stampeding this way and that

Just as in 2008, the market is now trading wildly. Correlation – a factor input of volatility – is rising, both between otherwise unrelated stocks and between sectors.

The implied correlation index on US stocks has risen 21% in the last four months. This demonstrates that investors are thinking in binary terms – every signal is interpreted as good or bad, buy or sell, risk-on or risk-off.

This bizarre range of outcomes has been hell to trade. To quote Jim Cramer, the excitable host of CNBC’s Mad Money: “Let’s speak truth... People hate this market. I hate it. You hate it. Everybody I talk to hates it because it’s one way each day, not connected to any other day.”

But hating the market is not enough. We need to understand why this is happening and what we can do about it.

I have a few theories as to why the market is behaving so spasmodically.

Theory 1: It’s just noise

One could take the view that today’s fat tails in volatility are just a natural result of the changes in the stockmarket in the past year.

The Vix is a mean-reverting index. Implied volatility tends to overstate the realised historical volatility experienced. Besides, if volatility did not revert to mean, and was a trending force, we’d have 15% moves in the S&P every day.

So whenever the Vix is at historically high levels, the next big move is more likely to be down than up. Twelve months ago, implied volatility was still coming down from the all time high of 81 that it touched in late 2008.

Therefore, it should be no surprise that in the second quarter of 2009 it was falling fairly steadily.

And now that it has reached a lower base, closer to its mean, it is trending less strongly and bouncing up and down more.

But this argument fails to account for the fact that the Vix is a lot more choppy now than at other times when equity prices have been moving sideways, such as in 2005-6, or even during the boom and bust of the late nineties and early noughties.

Theory 2: Trading in the dark

The rapid changes in volatility could be a consequence of the dire economic outlook.

This is a tepid economic recovery, with no consensus as to what is coming next. Economists, analysts and business leaders can’t seem to agree on anything. Depending on whom you listen to, now is the time to ramp up dividends and buy back shares, or go on an M&A spree, or remain heavily overweight in cash.

This makes for a severe lack of visibility for traders and investment managers. And when you don’t know what tomorrow might bring, you’re more likely to over-react to what’s happening today.

So that’s a second reason why implied volatility may be behaving so strangely. It’s the binary, risk-on or risk-off mentality that leads to today’s fat tails.

Theory 3: Policy

Policymakers always exert an influence on markets, but in the past two years this has been exceptional – and with exceptional results.

In recent months, the 10 year dollar swap spread has dipped into negative territory for the first time – a sign that US government risk is actually seen as worse than that of banks. The credit spreads over Treasuries of several blue chip corporate bonds have also turned negative.

While some of this is technical noise, government stimulus – with the huge increases in national debt that it entails – must have played a part.

The last 18 months have produced the $700bn Tarp, the £200bn Bank of England Asset Purchase Facility and the €440bn European Stabilisation Mechanism. This is to say nothing of central banks’ near-zero interest rates around the world.

These sentiment-soothing bailouts have done just what they were supposed to do – calm markets, quickly. No wonder the Vix is more variable than ever.

Which way to jump?

I could go on with the theories... But regardless of the reason for this fat-tailed volatility environment, what really matters is what we do about it.

It’s very hard to say. But it is apparent that both sides of the coin are fraught with risk for options traders.

Conventional wisdom says that when volatility is ‘cheap’, meaning low, a rational investor should buy options.

However, as we have discussed, it is very hard to know whether to buy calls or puts. Momentum trades are non-existent right now because the stockmarket itself has no momentum. When stocks keep flying up and thumping down again, how do you take sides?

Treacherous riches

Conversely, when volatility is ‘rich’, ie. high, the standard investment is to sell options, whether calls or puts, to reap the high premiums.

When volatility is extremely high, an investor can write options further out of the money for the same pay-off.

The problem here is the generic risk of option-writing – assignment. That is, the risk that the strike price gets struck. The investor would then take a loss, or be unable to participate in the momentum of the underlying asset. And, when the array of outcomes is so varied, the risk of assignment nullifies the efficacy of writing options, even those that are out-of-the-money.

Of course, high volatility, high premiums and high risk of assignment usually go together. But what the options writer is looking for is moments when implied vol and the options price are higher than is justified by recent history – the historical or realised volatility. In other words, for volatility arbitrage opportunities.

In recent months, this has been hard to achieve, as realised volatility has had plenty of bite, rising just as fiercely as what is implied.

So what’s an investor to do?

Invest from the bottom up, not the top down. Even at times of excess kurtosis – wild, marginal behaviour in the markets – there will always be individual deep value stories.

If the rogue call options demonstrate anything, it’s that it’s possible to find compelling value, irrespective of the macro headwinds.

Failing that, at least there’s a good excuse for trading losses – it really is rough out there!

Theo Casey is editor of The Fleet Street Letter and a columnist for MoneyWeek.