As a brief sneak-preview of a white-paper I am writing, I wanted to share the following graph.
Using the current constituents of the S&P 500 (technically, 422 of them based on data availability), this graph plots the rank stability of 1-month realized returns, volatility, and average pairwise correlation compared to historical ranks over an N-month look-back period. The worst-case scenario occurs when realized ranks are exactly flipped historical ranks (i.e. 422 becomes 1, 421 becomes 2, …, 2 becomes 421, 1 becomes 422), leading to a total sum of rank changes of 97,241. For a given look-back length, realized rank-differences are measured as a percent of this worst-case then averaged over all walk-forward cases. The result is plotted below.
Not surprisingly, more data leads to greater stability in ranks — though, in this case, it may simply be an effect of data availability, as the 10-month look-back can walk-forward nearly ~120 months, where the 80-month look-back can only walk-forward ~30 months. Nevertheless, we see that volatility rankings are much more stable than correlation rankings, which are much more stable than return rankings.
This sort of data analysis is a great way to understand the assumptions and vulnerabilities of quantitative methods: a strategy can only be as robust as its weakest link. Perhaps that is why S&P’s SPLV has had demonstrably lower volatility than MSCI’s USMV ETF: SPLV takes only the 100 lowest volatility equities and equally weights them whereas USMV uses factor models to project the variance-covariance matrix and performs an optimization. Since correlations exhibit less stability than volatilities, we may be able to conclude that USMV may exhibit less consistency in the low volatility it achieves relative to SPLV (especially since the equities in question have fairly high correlations anyway).