The Power Law, 80/20 Rule, and Concentration of Returns – What It Means for Money Managers

The power law has been become a strong fascination to me. We have been trained to generally think about the normal distribution. The law of large numbers has been pounded into our psyche since our first class in statistics but as you look more closely, the more relevant the power law becomes. Now, a normal distribution will produce extreme values. However, in a power law the extremes follow certain characteristics such that the “top few” are unbundled or more likely to have an extreme, (as opposed to a normal distribution where the “top few” are exponential and bounded).

• Let’s look at the construction and return performance of the leading equity indices:
  • There is the NASDAQ 100 but the top names represent a significant amount of the index. The FAAMG equals about 45%.
  • For the SPX, the FAAMG will equal 14.5% of the total market capitalization. The performance will be skewed by the gains in these high market cap stocks.
  • Amazon has accounted for 7% of the SPX growth over the last five years.
  • The returns of the major equity indices have been influenced disproportionately given the weighting and actual returns. Performance data shows that over the long-run just a few names will have a meaningful impact on performance. See the seminal work of Hendrik Bessembinder.)
  • Analysis suggests that large up days will make all of the difference in index gains. Miss a few days and you see a marked decline in performance. Missing the top ten days would have reduced returns by close to 40%.
• Let’s look at some numbers in venture capital:
  • A recent study shows that venture cap is like playing long shot bets. Most deals go bad with a few big winners. As quoted by Peter Their the tech venture capital leader, “We don’t live in a normal world, we live under a power law”.
• Let’s look at importance of key days in bond markets:
  • Studies have shown the high concentration of return around just a few days when the Fed makes an announcement.

The power law and the short hand 80/20 phrase (Pareto Principle) is everywhere, yet we likely spend more time on the 80% than the 20% of the total.  So what  do we do about it?

• Know the extremes and when the power law applies.
  • These extremes are everywhere.
  • These extremes will create significant return influence.
  • These extremes are seen in all major indices; passive investors are subject to the power law.
  • However, the extremes are dynamic and change over time.
• When you see these extremes, spend more time studying them.
  • Don’t make the mistake of focusing on the average the 80/20 rule requires 80/20 work effort.
  • Realize that the return patterns of indices or active managers are the same – concentrated in spite of their best efforts.
    • Trend followers, for example, see most of their returns concentrated in a few trades.
    • Given this pattern, it is all the more important to act on the power law. Ride the profits and sell the losers.