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?The Greatest Anomaly in Finance'

February 14, 2012

by Geoff Considine

The Russell Low Volatility and Low Beta indices are calculated for both the Russell 1000 (large-cap stocks) and Russell 2000 (small-cap stocks), drawing the lowest-volatility or lowest-beta stocks from each index.  The Russell low-volatility and low-beta ETFs in the table are designed to track these indices.

Two unique features distinguish the Russell methodologies from their S&P counterpart. First, their selection of low-beta stocks is derived from projected (rather than historical) beta, which is a more complex but also in some ways more useful approach. Second, their low-volatility selection criterion is trailing two-month volatility for each stock in the respective indexes.

These indices are rebalanced monthly. 

I obtained the stock-by-stock holdings for each of the five low-beta and low-volatility ETFs mentioned above. Because a 40-holding portfolio is the largest my analytical tools can process, the portfolios I used to stand in for these ETFs comprised the largest 40 holdings (by market value) in each of these ETFs, maintained at the same relative weights as they appear in the indexes.  The results of my projections are below.

Trailing three-year risk, return, and correlations of portfolios comprised of the top-40 holdings of these ETFs

3 year risk

The upshot of the simulation is unambiguous – QPP expects the outperformance of low-beta and low-volatility portfolios to persist. This is crucial support for the findings of Baker et al, and strong evidence that the continued outperformance of these stocks is well-grounded in basic market theory.

One might miss the significance of these results if they were to look only at the first result, the return of each portfolio. While the trailing average three-year returns of the low-volatility and low-beta portfolios are less than those of their respective parent indices, we must look beyond that simple measure.

Doing so, we see that their return-to-risk ratio is markedly higher.  The Russell 1000 Low Beta’s projected 149% return-to-risk ratio, for instance, is striking for being higher by almost half than the broader Russell 1000’s 103% projected ratio.

The Russell 2000 Low Volatility selections have the lowest trailing return-to-risk ratio – lower, in fact, than that of the full Russell 2000 – and they also exhibit the least difference in volatility from their parent index. I believe that this is in part due to that index’s use of trailing two-month volatility, which is quite noisy, in selecting and weighting stocks.

Further cause for the decreased benefit seen in low-volatility small-cap stocks, however, is the fact that volatility increases as market cap decreases – a fact that Baker et al. note.  Thus the stocks with lowest volatility will also be among the larger-cap stocks in the Russell 2000.  This reality means seeking out low-volatility Russell 2000 stocks costs us some of the small-cap boost to performance.  For this reason, a small-cap low-volatility index would be the least attractive of these strategies, generally speaking, as the results above suggest.