I was quite surprised by a paper (The Surprising Alpha From Malkiel’s Monkey and Upside-Down Strategies [PDF] by Robert D. Arnott, Jason Hsu, Vitali Kalesnik, and Phil Tindall) about “inverted” or upside-down[*] versions of some good-looking strategies for better-than-market-cap weighting of index funds.
They show that the inverse of low volatility and fundamental weighting strategies do about as well as or outperform the original strategies. Low volatility index funds still have better Sharpe ratios (risk-adjusted returns) than their inverses.
Their explanation is that most deviations from weighting by market capitalization will benefit from the size effect (small caps outperform large caps), and will also have some tendency to benefit from value effects. Weighting by market capitalization causes an index to have lots of Exxon and Apple stock. Fundamental weighting replaces some of that Apple stock with small companies. Weighting by anything that has little connection to company size (such as volatility) reduces the Exxon and Apple holdings by more than an order of magnitude. Both of those shifts exploit the benefits of investing in small-cap stocks.
Fundamental weighting outperforms most strategies. But inverting those weights adds slightly more than 1% per year to those already good returns. The only way that makes sense to me is if an inverse of market-cap weighting would also outperform fundamental weighting, by investing mostly in the smallest stocks.
They also show you can beat market-capitalization weighted indices by choosing stocks at random (i.e. simulating monkeys throwing darts at the list of companies). This highlights the perversity of weighting by market-caps, as the monkeys can’t beat the simple alternative of investing equal dollar amounts in each company.
This increases my respect for the size effect. I’ve reduced my respect for the benefits of low volatility investments, although the reduced risk they produce is still worth something. That hasn’t much changed my advice for investing in existing etf’s, but it does alter what I hope for in etf’s that will become available in the future.
[*] – They examine two different inverses:
- Taking the reciprocal of each stock’s original weight
- Taking the max(weight) and subtracting each stock’s original weight
In each case the resulting weights are then normalized to add to 1.