Tuesday, June 15, 2010

The Story of “New Normal” and the Fat Tail

Prior to 2007, few people had heard of Nassim Taleb and his Black Swan. Some people had heard of fat tails, but most were quant modelers and academics with seemingly boundless mathematical knowledge. Additionally, the predictability of the distribution curves was an easy sell when three standard deviations encompasses nearly all outcomes, four, five, and six standard deviations were hardly worth considering.

But the question that continues to arise is whether or not there is a "new normal" and, if so, is it more dangerous than the "old normal"? Will the "new normal" carry greater volatility and risk? The short answer is probably.

As we know, volatility can come in many forms but it is always descriptive of a range of outcomes. Whether it is implied, historical or expected, volatility is described by a percent annualized standard deviation. In other words, if over the last year a $100 stock traded with a 25% volatility, we can be reasonable sure that 68% of that time it traded between $75 and $125. Similarly, if we expect the stock to have a 25% range over the next year, we are expecting 68% of outcomes to fall between $75 and $125.

With the flash crash a recent memory and the near collapse of the financial system (the verdict is still out on that one, in my opinion) having occurred in the not so distant past, I asked myself, "Has there really a broad increase in volatility over the years or is it just a passing fancy?"

Obviously, I needed a lot of data to answer this question; fortunately, we have this thing called the internet. So I pulled the historical prices for the S&P 500 from Yahoo! from Jan 1962 to present day, put them on a spread sheet and went to work.

The first thing I thought was that if volatility is increasing we should see an increase in the standard deviation of daily percentage returns, meaning that overall the range of outcomes probable on a daily basis should expand. With over 12,000 data points, I decided some summary was in order so I broke the information down into annual groups.

Along the bottom of the chart there are the average daily percentage returns for each year. This is fairly constant with average returns in the +/- 1.5% range for each year.

The spiky reddish orange line is the standard deviation of the close to close changes for each year. Not unexpectedly, the largest increases in range occur in down years (2008, 2002, 1987, etc.). Additionally, there are higher highs and higher lows which are suggestive of a long term up trend. That trend can be seen easily with the overlay of the linear regression line (royal blue). Since 1962, the standard deviation of daily returns has more than doubled on an annual basis from .0575% to 1.25%. That's a fair sized increase and certainly evidence of more volatile markets. Remember, this is only close to close and does not take into account any increases in intraday volatility.

Now knowing the mean (average) daily return and standard deviation for each year gives us all the information we need to understand the annual distributions of returns for any given year. Unfortunately, that only applies to normal distributions and the stock market has never been so kind as to keep things simple. To really reinforce my thesis of increasing volatility I wanted to know more about the distributions.

This is about skew and kurtosis. These are descriptive statistics that provide you with additional information about the distribution in question. Briefly, skew can be positive or negative with the direction reflecting which side the fatter tail is on. Positive skew reflects a plethora of outcomes just below or to the left of the mean, with outliers, when the occur tending to be far right of the mean. Negative skew reflects the majority of outcomes just above or to the right of the mean, with outliers tending to occur at the extreme of negativity or far to the left of the mean. The broad stock markets tend to trade with a slight negative skew, with the majority of outcomes resulting in a small percentage gains, but the large moves, when they occur produce large daily losses.

Our other statistic, kurtosis, can also be positive or negative. Positive excess kurtosis indicates that the majority of outcomes are clustered around the mean with a number of both positive and negative outliers fattening the tails of the distribution. As a result, there are fewer median outcomes than would be found in a normal distribution or bell curve, a condition known as leptokurtosis. Negative excess kurtosis, or platykurtosis, is characterized by few outliers (thin tails) and a roughly even probability of outcomes around the mean. The broad markets tend to exhibit leptokurtosis.

My intention here was to determine whether over time the tails, and in particular the downside tail was increasing; were getting fatter by means of increasing kurtosis and decreasing (more negative) skew. However rather than examine each year individually, I grouped them together 6 years at a time. This was somewhat arbitrary, but it allowed for an easy to deal with 8 data sets.

Before we get into the results, take a look at the above chart for a little more understanding on skew and kurtosis. The period from May 1998 through May 2004 (red line) most resembles a normal distribution with the lowest skew and second lowest kurtosis of the 8 periods. It is compared to the April 1986 to April 1992 which had the highest kurtosis and most negative skew.

Hopefully you can see that the red hand drawn mean line virtually bisects the red distribution, which would be typical of a normal distribution. Whereas the blue median line shows the largest number of outcomes just to the right or the median with more bumps on the far left (negative skew). Additionally, the blue distribution is much narrower while also having more outliers (leptokurtosis). This chart isn't indicative of anything, but will hopefully help you better visualize the numbers in the table below.

Although I would not consider this conclusive, the four most recent periods (April 1986 to present) have a higher average excess kurtosis and a more negative skew compared to the prior 24 years. Obviously this is heavily influenced by the inclusion of the April 1986 to April 1992 data, which was unquestionably extreme.


Never the less, the table does add additional weight to the theory that increasing volatility with fatter tails is the new normal. I would feel remiss however if I didn't propose some fundamental explanation as to why this might occur.

First, globalization has increased correlations between countries, businesses, and other entities. As we saw with our own financial crisis and now the crisis in Europe, when things start going wrong they go wrong for more people. It is like a pebble falling off a cliff into a pool of water. It used to be that when something failed it would fall by itself, maybe dragging a few smaller rocks along as well causing some nominal ripples. Now, the little pebbles are chained to rocks which are chained to boulders, and the ripples are more like the waves caused when a chuck of glacier falls into the ocean. No matter the level of regulation, if you feel that helps, this interconnectedness is not going to change.

Second, electronic trading and penny increments have diminished liquidity, in my opinion. While I admit this is an arguable point, back in the day, when stocks were quoted in fractions, size would build up on the bid and the offer because they were relatively wide spreads. Even if there is a thousand bid and offered on a stock that is only a penny wide, it is much scarier to execute a large order of 10,000 shares or more. Before, you might find 10-15,000 up on a market that was $50 - $50.25, now with 1000 at each penny you are not sure where you will get the order filled and once the buying or selling begins, algorithms are likely to jump on board in the same direction putting additional pressure on the stock. Furthermore the same computers that are following the momentum are also canceling liquidity providing orders on the other side. This also is not going to change.

This is not a doom and gloom piece, this is about knowing and understanding that the markets are evolving. So keep those puts pumped, don't take relative calm for granted, and enjoy the glacial waves.

Friday, June 4, 2010

Testing the 200

From the low around 1040 on the S&P to the recent test of the 200 day and likely lower, this video seems to sum it up.

Wednesday, June 2, 2010

An Historical Perspective on Volatility Spikes

This past month has produced a rare event: a spike in the VIX of more than 40%. While I was aware that this was unusual, I wasn't sure how unusual until I started playing with the numbers. As it turns out, there have only been 10 such events since January of 1990 when records for the VIX began. So let's take a walk down memory lane.

January 1990

The VIX spikes 47% during the month as concerns about the economy mount. The first George Bush was beginning his second year in office and for those of you who follow election cycles and its impact on the markets, the second year in office has the worst record historically. The S&P 500 (SPX) found a temporary bottom approximately 5% below its 200-day simple moving average (SMA) near the end of January and moved higher into the summer. The SPX put in a double top in June and July of 1990 before plunging from mid-summer into the fall.

August 1990

The VIX spikes 41% after moving 36% higher in July as the SPX dropped 20% from its July high until its October low, finally bottoming 12% below its 200 day SMA. Economic woes continued to mount as the second year of the election cycle led the market down roughly 7% for the year.

There is a long break in extreme moves as the market began a solid multi-year advance.

July 1996

1996 was shaping up to be a decent year, until the SPX dipped 5% in July and the VIX jumped more than 42%. This began a month long battle with the 200 day SMA before the SPX resumed its climb finishing the year up 20%. Oh and for those too young to remember, health care debate was coming to a close as Congress passes HIPAA, the Health Insurance Portability and Accountability Act protecting coverage for workers and families when they lose or change jobs. Additionally, the rupee was struggling as a Javanese earthquake shook the region, but the distressed currency may have been a precursor to the all out crisis in 1997.

October 1997

The Asian currency crisis is in full swing and the SPX falls as much as 13% during the month as the VIX leaps 53%. Once again, the index found intraday support around its 200-day SMA. But nothing could hamper the go-go '90s as the market tacked on more than 30% for the year.

August 1998

Long Term Capital Management requires a Federal bailout as its volatility and currency bets spiral out of control. The VIX soared a then record 78% over the month as the SPX plunged from a 14% premium to its 200-day SMA to a 9% discount. During the month of September 1998 the index returned to test the average before setting a double bottom and finishing the year strong. The '90s were unstoppable with the market tacking on another 28% for the year.

Interestingly, as the internet bubble burst and we moved through the 2000-2003 bear market there were no month over month volatility spikes greater than 28%.

May 2006

By the end of May 2006, the SPX was in negative territory for the year and the jumped more than 41% setting off a summer long back and forth battle with the 200-day SMA. Although the Iraq war was in full swing and the infractions at Guantanamo Bay were coming to light, there was little headline financial news to send the markets into turmoil. By the end of the summer, not only had the SPX regained positive territory, but it began a move that would but it up 13% for the year.

February 2007

The real estate cookie was beginning to crumble, durable goods orders were declining, and China's growth was in question. The VIX leapt nearly 48% on the month mostly driven by a 4.1% disaster of a day on the 26th which constituted the largest one-day point decline for the Dow Industrials since 2001. But there were still plenty of late comers who wanted in and the SPX found support around the 1380 level before moving to its peak later in the year.

July 2007

The VIX jumped by 45% after moving up 24% in June. Sub-prime mortgages were collapsing and John Paulson was making a mint. Although the July high for the SPX was not the ultimate high, we had to wait for October 2007 for that, it was the first of a double top from which the markets have yet to fully recover.

September – October 2008

The only time in the 20 year history of the VIX that it increased by more than 40% in two consecutive months. The 90% record one month spike in September was followed by a 52% jump in October. But let's face it, the world was coming to an end. No one knew if the US would have a financial system left and the poorly worded TARP legislation was little comfort. The SPX plunged nearly 50% in a scant two months; even the bursting of internet bubble caused less short term damage. Additionally, after this spike occurred the time to the March 2009 low was the longest before the market found at least a temporary bottom.

May 2010

The VIX jumped 45% last month preceded by a 25% move in April. Two consecutive months with greater than a 20% month over month move in volatility have occurred 5 times including the most recent. In the prior 4 instances the VIX has been roughly 10% lower 2 months later while the S&P 500 has gained less than 1% over the same 2 month period.

Even when the spikes are relatively isolated, the SPX has taken a month or two to find new direction.

The conclusion today is that there is some historical suggestion that selling volatility out into July may be the preferred move, albeit from a very small sample size. With the Average True Range (20) of the SPX at the highest level since December 2008, there is certainly some room for volatility to come in. However, there are a number of exogenous factors that could tip the markets. Foremost on my mind, is the devastation that an early season hurricane could wreak on the Gulf Coast including the western coast of Florida, depending on trajectory. I don't believe that the economic impact of the oil spill has been fully priced into the market, but that may take time. The same goes for the as yet unresolved European debt issues and the overall state of the US economy. But the bottom line is that although intraday volatility may not be going away, the current battle with the SPX 200-day SMA is likely to continue into the middle of the summer, so if you have stock positions, long or short, that you have been waiting to sell options against, now may be a good time to do it.