Statisticians have a term for 20/20 hindsight. It’s “retrospective predictability” and it refers to the idea that previously unfathomable events often seem as if they were actually predictable once they occurred. In a sense, retrospective predictability is what makes stories of “famous last words” so compelling.

Statisticians also have their own take on the phrase “The only thing constant is change itself.” As author Nassim Nicholas Taleb (see related posting), mathematician Benoit Mandelbrot (see related posting) and others have shown change itself is actually* inconsistent*. In other words, volatility is volatile. And so you never really know the likelihood of extreme events.

Spanish academic Javier Estrada brings these two concepts together in this November 2007 article on what Taleb has called **“black swan events”** (in reference to the previously unfathomable discovery of black swans in Australia over 300 years ago).

Black swan events (the subject of Taleb’s best-selling book) cannot be explained by the commonly-made assumption that random events, such as stock market movements, followed the familiar bell curve (normal distribution).

Estrada applies this thinking to 15 equity markets around the world. He calculates the returns from the best and worst 10, 20, and 100 trading days. Then he calculates the returns a passive investor in those markets would have received if they had missed out on these small groups of trading days.

Estrada’s findings confirm the existence of black swans:

“Outliers have a massive impact on long term performance. On average across all 15 markets, missing the best 10 days resulted in portfolios 50.8% less valuable than a passive investment; and avoiding the worst 10 days resulted in portfolios 150.4% more valuable than a passive investment. Given that 10 days represent, in the average market, less than 0.1% of the days considered, the odds against successful market timing are staggering.”

How staggering? A footnote on page 7 says the chances of Black Monday occurring in 1987 – if you believed market returns followed a normal distribution – was 3.98×10^-99. That’s a decimal point followed by 98 zeros then “398”. As a reference point, some estimates peg the number of atoms in the known universe at only 10^80. So the chances of Black Monday happening (again, assuming you felt that market returns were normally distributed) was way smaller than pinpointing one specific atom in the entire universe. (To put it in terms easier to comprehend, that’s about the same as the odds of the Boston Red Sox finally winning baseball’s World Series in 2004 – see posting).

Estrada calculates the ratio of expected outliers to actual outliers (assuming normality and defining “outliers” as daily stock market returns greater than three standard deviations from the mean). In an ironic twist, Australia had the smallest number of black swan events. Yes, in the country that gave birth to this avian metaphor black swans are an endangered species (at least compared to those in other markets). Actual Australian outliers were only 2.9 times more prevalent than a normal distribution would suggest. This compares with an average ratio of around 5 times for the other 14 countries examined. By contrast, Taiwan has a black swan infestation problem.

Australia may get the last laugh on this one. If you missed out on the best 100 trading days in several markets, you’d be in rough shape. Says Estrada:

“Missing the best 100 days in Taiwan and Thailand would have resulted in a loss of virtually all the capital invested; in Germany, Hong Kong, Japan, and Singapore the terminal wealth would have been reduced to less than 10% of the initial capital invested.”

Miss these days in Australia and you’d escape with a whopping 48% of your capital.

So here’s an important message to our Australian readers: “*No worries! Throw another shrimp on the barbie. And don’t worry about spending a few days on the beach. Everything will ‘come good’ .”*

## 3 Comments

December 19, 2007 at 6:56 am## Harry M. Kat

December 20, 2007 at 9:21 am## Greg H M