Plausible Negative Scenarios by Fund Type

Given that we are in a period of generalized decline in many investment sectors, we reviewed a broad spectrum of ETFs and CEFs by type in terms of plausible negative outcomes, based on 3-year mean return and 3-yr standard deviation of return.

This “360 View” of plausible negative scenarios analysis looks at:

• Countries & Regions
• US Market-Cap & Style
• US & Global Sectors
• Bonds
• Real Estate
• Commodities & Energy
• Currencies

We calculated these levels of possible negative outcome:

• 3-yr mean return less one standard deviation
• 3-yr mean return less two standard deviations
• 3-yr mean return less three standard deviations

The mean return plus or minus one standard deviation of return theoretically establishes a range for about 68% of probable return outcomes.  Plus or minus two standard deviations establishes a range for about 96% of outcomes.  Three standard deviations on each side of the mean establishes a range for about 99% of probable outcomes.

In extreme circumstances, not experienced in the historical period used to develop the standard deviation, this probability approach goes pretty much out the window.  That is the “fat tail” aspect of statistics.

Whether or not the confluence of adverse resource, economic and geopolitical circumstances we are encountering now puts us in the fat tail area only the future will tell.

NOTE:  This report is not a prediction!  It is an attempt to gauge how bad it could become in the absence of the most extreme circumstances.

The results of our study are available for download by clicking the image of the report below:

Comments

[SmartETF:]

Richard, I enjoy your work. To address the fat-tail problem you can do two things, first, convert from measuring the variance of the distribution using standard deviation (in a normal distribution setting) to measuring the distribution's left-side probability of losing money using the concept of Value-at-Risk (VaR). Then replace VaR (based on normal distributions) what is known as CVaR or Expected Shortfall (based on a 'Stable' distribution). The core difference is that normal distributions are arithmetic and stable distributions are logarithmic.

In a Normal Distribution environment, a security move from $1 to $2 equals a 100% gain, but a move from $2 to $3 is only a 50% increase, $3 to $4 is 33%, $4 to $5 is 25%, and so on, the ratio shrinks exponentially; this is why standard deviation moves the probability of return from 1 standard deviation (σ) at 68.3% to 2 σ at 95.4%, and 3 σ at 99.7%. This methodology suggests a 5 σ event will only occur once in 7000 years when it actually occurs every 3 to 4 years. The 87’ crash should have only occurred once in 3 lifetimes of the universe; normal distributions pervert reality.

Stable distributions (logarithmic based) solve this anomaly because a data is properly managed. A security price change from $1 to $2 is a 100% gain, then from $2 to $4, $4 to $8, $8 to $16, all stay at 100% gain. If charted, it would look linear, not exponential.

The second thing you can do is change the way you manage the data to make newer information more valuable; thus avoiding the monster flaws in mean variance. The simplest of choices are to use a rolling moving average or an Exponentially Weight Moving Average (EWMA); the more sophisticated method is GARCH (2002 Noble Laureate winning formula). Keep up the good work!

2008 Jul 14 12:46 PM

[QVM Group:]

I appreciate your comments and will take them under advisement.

One operational issue relating to that approach is that I am using predigested data for larger numbers of securities and don't have the raw data that seems to be necessary to pursue the approach you outlined.

I need to think and read a bit more about the ideas you put out there.

Thanks.

2008 Jul 14 05:20 PM

[Acercher:]

Richard, as usual, thanks for some very interesting hard data. (I suppose it might be even more useful if you follow the first commenter's suggestions, but I can't be the only one who didn't understand even a little bit of it).

My issue is more basic, but goes to the issue of conflating fat tails with (highly) unpredictable events. Fat tails are the unpredictable residue left over from statistical analysis of the past. But unpredictable events can have different degrees of probability based just on common sense (i.e., knowledge not derived solely from statistics).

For instance, under the 2 standard deviation worst case column of your country chart, consider the following pairings:

United Kingdom (17)
Malaysia (17)

Switzerland (8)
Israel (10)

Sweden (30)
Russia (21)

I'm reasonably confident that the possibility of a very bad thing happening in Malaysia, Israel, and/or Russia is significantly higher than in the United Kingdom, Switzerland, and/or Sweden. I'm also reasonably confident the very bad thing would have a very bad effect on that country's stock market.

I find it very counter-intuitive (euphemism for unbelievable) that in essentially 96% of future scenarios, each of the two countries paired above has a basically equivalent downside risk. Comments?

2008 Jul 15 07:24 PM

[QVM Group:]

Achercher:
Interesting point. I need to think about that one. On the one hand "the numbers are the numbers", and on the other hand your logic is compelling.

2008 Jul 16 06:53 AM