By LARRY SWEDROE
“Measures of uncertainty that are based on the bell curve simply disregard the possibility, and the impact, of sharp jumps… Using them is like focusing on the grass and missing out on the (gigantic) trees. Although unpredictable large deviations are rare, they cannot be dismissed as outliers because, cumulatively, their impact is so dramatic.”
— Nassim Taleb, The Black Swan: The Impact of the Highly Improbable
Over the course of the first two decades of the 21st century, equity markets faced three “black swan” events: the attacks of September 11, 2001, the Global Financial Crisis that began in late 2007 and the COVID-19 pandemic. Each resulted in steep falls in equity prices. The term “black swan” was a common expression in 16th-century London that described impossibility. It derived from the old-world presumption that all swans must be white—because all historical records of swans reported that they had white feathers. Thus, a black swan was something that was impossible, or nearly impossible, and could not exist. After the discovery of black swans in Western Australia in 1697 by a Dutch expedition led by explorer Willem de Vlamingh on the Swan River, the term metamorphosed to connote that a perceived impossibility may later be found to exist.
With the publication of Nassim Nicholas Taleb’s 2001 book, Fooled by Randomness, “black swan” became part of the investment vernacular — virtually synonymous with the term “fat tail”. In terms of investing, fat tails are distributions in which very low and high values are more frequent than a normal distribution predicts. In a normal distribution, the tails to the extreme left and extreme right of the mean become smaller, ultimately reaching zero occurrences. However, the historical evidence on stock returns is that they demonstrate occurrences of low and high values that are far greater than theoretically expected by a normal distribution. Thus, an understanding of the risk of fat tails is an important part of developing an appropriate asset allocation and investment plan. Unfortunately, many investors fail to account for the risk of fat tails. Let’s look at some evidence on their existence.
Javier Estrada, author of the 2007 study Black Swans and Market Timing: How Not To Generate Alpha, examined the returns of 15 stock markets and more than 160,000 daily returns. He sought to determine the likelihood that investors can successfully predict the best days to be in and out of the market. Following is a summary of its findings:
1. Stock returns are not normally distributed
Black swans appear with far greater frequency than predicted by normal distributions. For example, for the Dow Jones Industrial Average, 29,190 trading days (107 years) produced a daily mean return of 0.02 percent and a standard deviation of 1.07 percent. Under the assumption of normality, 39 days would produce returns above 3.22 percent, and 39 would produce returns below -3.17 percent. However, there were six times the number of returns outside that range—253 daily returns below -3.17 percent and 208 above 3.22 percent. Note that the maximum and minimum daily returns were 15.34 percent and -22.61 percent. The returns exhibited a high degree of negative skewness (the left tail of the distribution curve is larger) and excess kurtosis (fat tails)—clear departures from normality.
2. The tails are fat
While the daily mean return was 0.02 percent, the mean returns of the best 10, 20 and 100 days were 11.10, 9.37 and 5.92 percent, respectively—10.4, 8.8 and 5.5 standard deviations above the mean. The mean returns of the worst 10, 20 and 100 days were -10.46, -8.73 and -5.87 percent, respectively—9.8, 8.2 and 5.5 standard deviations below the mean. Even the lowest of the best 100 daily returns (4.20 percent) was 3.9 standard deviations above the mean. While less than two of these should have been expected, the market produced 100. Similarly, the highest of the worst 100 daily returns (-4.28 percent) was 4 standard deviations below the mean. While less than one should have been expected, the market produced 100.
3. Impact of missing the best and worst days
While 10 days accounted for 0.03 percent of the days, missing the best 10, 20 and 100 days resulted in a reduction of terminal wealth of 65, 83 and 99.7 percent — the terminal value was less than the original investment. On the other hand, avoiding the worst 10, 20 and 100 days increased the terminal wealth 206, 532 and 43,397 percent, respectively. The author concluded: “These figures speak for themselves and should help investors notice the odds they are against when trying to successfully time the market. A negligible proportion of days determine a massive creation or destruction of wealth. The odds against successful market timing are just staggering.”
4. International markets produced the same results
The departure from normal distributions was clear in all 15 countries studied. The countries and the numbers of years through 2006 were: Australia 49, Canada 31, France 38, Germany 47, Hong Kong 37, Italy 34, Japan 52, New Zealand 37, Singapore 41, Spain 35, Switzerland 38, Taiwan 40, Thailand 31, U.K. 38 and U.S. 79. Across all 15 markets, the number of outliers was over five times more than expected—investors assuming normal distributions of returns substantially underestimated risk. Interestingly, with Australia as the lone exception, missing the best 100 days (less than 1 percent) resulted in a terminal wealth lower than the initial capital invested.
Estrada’s results are not new information. Professor Eugene Fama, in his 1964 thesis at the University of Chicago, demonstrated that market returns are not normally distributed. And Nassim Nicholas Taleb discussed the problem of black swans in his 2001 book, “Fooled by Randomness.” His second book, The Black Swan: The Impact of the Highly Improbable, was published in 2007. Taleb called a black swan an event with the following three attributes: “First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable. I stop and summarise the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explain almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives.”
Given that the existence of fat tails was well known, when one arrives, it certainly shouldn’t be a surprise to investors. Yet it is safe to say that the depth and breadth of the bear market we experienced from November 2007 through March 9, 2009, came as a shock to many, if not most, investors—as did the crash caused by COVID-19, which resulted in the sharpest decline in history, with the MSCI World Index falling 34 percent from February 19 to March 23.
The moral of the tale
Just as shipbuilders know that in most cases the seas are relatively safe, they also know that typhoons and hurricanes happen. Therefore, they design their ships not just for the 95 percent of sailing days when the weather is clement but also for the other 5 percent, when storms blow and their skill is tested.
The existence of fat tails doesn’t change the prudent strategy of being a passive buy, hold and rebalance investor. Active managers have demonstrated no ability to protect investors from fat tails. However, their existence is extremely important because of the effect they can have on portfolios. The risk of black swans and the damage they can do to portfolios, especially for those in the withdrawal phase, must be considered when designing one’s asset allocation. With that in mind, consider the following advice:
- Make sure your investment plan accounts for the existence of fat tails.
- Don’t take more risk than you have the ability, willingness or need to take.
- Never treat the unlikely as impossible or the likely as certain.
The information presented herein is for educational purposes only and should not be construed as specific investment, accounting, legal, or tax advice. Certain information contained may be based on third party data which may become outdated or otherwise superseded without notice. Third party information is deemed to be reliable but its accuracy and completeness cannot be guaranteed. By clicking on any of the links above you acknowledge that they are solely at your convenience, and do not necessarily imply any affiliations, sponsorships, endorsements or representations whatsoever by Buckingham regarding third-party websites. Buckingham is not responsible for the content, availability, or privacy policies of these sites, and shall not be responsible or liable for any information opinions, advice, products or services available through them. The opinions expressed by the featured author are their own and may not accurately reflect those of Buckingham Strategic Wealth® or Buckingham Strategic Partners® (collectively Buckingham Wealth Partners, “Buckingham”). LSR-21-43
LARRY SWEDROE is Chief Research Officer at Buckingham Strategic Wealth and the author of numerous books on investing.
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