Where the Black Swans Hide & the 10 Best Days Myth via SSRN

Mebane T. Faber

Cambria Investment Management

August 1, 2011

Cambria – Quantitative Research Monthly, August 2011

Abstract:

Below we examine market outliers in financial markets. How much effect do these outliers have on long term performance? Can the investor prepare for these anomalies, or are they truly ‘black swans’ that cannot be managed? In this issue we examine numerous global financial markets on daily and monthly time frames. We find that these rare outliers have a massive impact on returns. However, these outliers tend to cluster and the majority of both good and bad outliers occur once markets have already been declining. We critique the “missing the 10-best-days” argument proffered by advocates of buy and hold investing, demonstrating that a significant majority of the 10 best days and the 10 worst days occur in declining markets. We continue to advocate that investors attempt to avoid declining markets where most of the volatility lies, and conclude that market timing and risk management is indeed possible, and beneficial to the investor.

Where the Black Swans Hide & the 10 Best Days Myth

Nassim Taleb, author of Fooled by Randomness and The Black Swan, popularized the concept of the black swan – namely, the occurrence of utterly unforeseeable events that are thought of as not being possible based on previous experiences.

Taleb defines a black swan as:

  1. Outlier outside the realm of regular expectations because nothing in the past can convincingly point to its occurrence.
  2. The event carries an extreme impact.
  3. Explanations for the occurrence can be found after the fact, giving the impression that it can be explainable and predictable.

Many market commentators have latched on to this term to describe all financial market events. However, the existence of large outlier events known as fat-tailed distributions in financial market returns has been well documented for over 40 years (Mandelbrot 1963, Fama 1965). While the financial media have only recently re-visited the fat-tail concept (due largely to the occurrence of the internet bust in 2000-2003 as well as the global financial meltdown in 2008 and 2009), it has been a thoroughly studied field in finance over the past several decades.

Investors should realize that normal market returns are extreme. Individuals that continue to believe in the Gaussian (bell-shaped) distribution, or ignore empirical results will continue to be surprised by future events. Roughly 40% of all yearly returns in US stocks are greater than 10% or less than -10%. Bear markets are common, and markets can and do decline from 50-100%.

Financial market return distributions are similar to fractal systems that follow a power law distribution (which is useful in describing events like earthquakes and volcanic eruptions). Below is a chart from the book The Failure of Risk Management by Hubbard that illustrates the inability of the Gaussian models to account for large outlier moves in financial markets. In a normal distribution world a 5% decline in the Dow in a single trading day should not have happened in the past 100 years. In reality, it has happened nearly 100 times.

black swans market outlier

Unfortunately, many investors have come to the conclusion that rare events are impossible to predict, and therefore, there is nothing to do other than buy and hold their investments and wait out any negative outliers. However, this explanation simply rids the investor (advisor) of any responsibility – the fatalistic attitude becomes “it was a black swan, it’s not my fault!”

In this article we examine market outliers, their effect, but more importantly when they occur and if the investor can do anything to protect against them.
While we are not going to spend much time on a literature review, the appendix has a list of books and papers on market bubbles, financial market return distributions, and investment history. The next few issues of Cambria Quantitative Research are going to expand on some of the topics mentioned here (bubbles, forecasting, etc).