Change it had to come.
We knew it all along.
We were liberated from the fall that’s all.
But the world looks just the same.
And history ain’t changed…

Meet the new boss.
Same as the old boss.

- The Who

One of the cornerstones of modern portfolio theory is that security prices are normally distributed – more specifically, that they follow a “random walk” with normally distributed increments.  As a result, portfolio managers have grown accustomed to viewing returns as being normal.  This allowed for portfolio managers to find an optimized trade-off between risk and return (mean variance optimization).

But alternative investments threw a wrench in the works.  Since they held highly irregular instruments such as options, derivatives and structured products with non-normal return distributions, their returns tended not to fit the usual models.  As a result, academics and practitioners developed new techniques to analyze these investments and to optimize portfolios made from them.  Today, many in the alternative investment industry scoff at the supposedly naive simplicity of the “normality assumption.”  Indeed, even practitioners of traditional investing seem to have come to reject this central theorem of modern portfolio theory.

But have we thrown out the baby with the bathwater?  Is this “new normal” really just the same as the old one?  David Esch of New Frontier Advisors writes in the Journal of Investment Management that it essentially is – that the normality assumption is still a safe bet in most circumstances.

His article in the First Quarter 2010 edition, “Non-normality facts and fallacies” defends the use of the normality assumption on a number of compelling grounds.  In fact, his arguments are so compelling that it is about to be placed on the required reading list for the Chartered Alternative Investment Analyst (CAIA) Designation (for complete current reading list, click here).

In a nutshell Esch rejects “the popular fallacy that normal models cannot be valid or useful because return distributions have marginal non-normal distributions.”

He takes specific aim at “extreme value theory” (see related post), higher moments (see related posts), and copulas (see related post) saying that while these techniques do account for extreme events, they can “easily backfire.”  He also criticizes the popularized notion that “correlations go to one” in times of financial calamity (see related post).

He basically argues that investors should not begin “rejecting standard models in the face of one or even several unusual observations.”

For example, he points out that if a return distribution has a positive skew ceteris paribus its mode may be negative.  In other words, the most likely outcome of a random draw from a positively skewed distribution is one that is below the mean.  (see illustration from his JOIM article below)

Esch acknowledges that many investors see benefits in positive skew.  But if you compare a normal distribution with a mean of 0 and a standard deviation of 1 (lower curve) to a positively skewed distribution with the same mean and standard deviation (the peaked curve), you can see that the positively skewed distribution is more likely to deliver a negative return.  This means a manager who attempts to increase skewness while keeping mean and standard deviation constant would under perform his/her peers most of the time.  As Esch points out “fund managers are routinely fired for such underperformance.”

The same can be said of kurtosis (a.k.a. “fat tails”).

Note that a highly kurtotic, “fat tailed” distribution (the peaked curve) actually has a lower probability of a one standard deviation move from the mean than a corresponding normal distribution with the same mean and standard deviation.  Excess kurtosis means that the distribution gathers in two areas: a) in the centre and b) in the tails.  But without also having a higher standard deviation, a “leptokurtic” distribution like this will mean the tails are relatively closer to the centre than the tails of a normal distribution.

This is similar to the argument made by author (and CAIA Board Member) Alexander Ineichen in his book Asymmetric Returns when he says (on p. 126):

“…we believe volatility matters more than excess kurtosis. Excess kurtosis as a risk measure indicates that the distribution deviates from normal distribution.  The statistic is often used as an indication that there is a “higher” probability of a far-from-equilibrium event.  However, it does not address the issue of how severe the undesirable event might be…”

It’s also similar to the argument made by Todd Brulhart and Peter Klein in the 2005 AIMA Canada/Hillsdale Research Award winning paper.  Report Brulhart and Klein:

“Since the variance of hedge fund index returns is much lower than for equity indices, alternate measures, such as higher moments and magnitude and length of draw downs, are also considered. Based on these alternate measures we conclude that the true magnitude of extreme returns is actually lower for hedge fund indices as compared to equity indices.”

This suggests to us that one of the problems with ignoring kurtosis entirely is that when investors see a leptokurtic distribution, they are more likely to want to lever it up – thus increasing the standard deviation and exposing themselves to even larger losses.

Although it may seem that “correlations go to one” in these fat tail events, Esch points out that:

“…net of this dominating effect, there are idiosyncratic risk factors within assets which will be once again observable after the storm. When datasets are corrected for systematic effects, the “correlations go to one” effect will largely disappear. In other words, residual returns from suitable risk models do not show correlations going to 1 during extreme market volatility.”

In other words, the sun will come up tomorrow.

This is an important issue for risk managers who may have overhauled their models in the wake of 2008 only to have guaranteed themselves lower returns until the next time the market falls out of bed.  Then again, selling insurance isn’t a bad gig.  A report by Financial News last week said that Nassim Taleb’s Universa Investments is closing in on a major allocation from China Investment Corp. (CIC) despite his funds negative returns in 2010 and 2009.

Why?  According to Financial News, it’s because “Such an approach represents an extreme downside hedge for China, whose export-heavy economy depends on global growth.”  And last time the global economy tanked (2008) Universa was reportedly up 100%.

As usual, the debate about whether to account for black swans boils down to whether you want to be long or short volatility.  And that’s a pretty “old normal” debate.