CONCAVE WITH DIMINISHING RETURNS. Similar to the low volatility simulations (Exhibit 7 upper left hand corner), the low volatility + value + momentum simulations (Exhibit 7, lower right hand corner) exhibit a concave function with diminishing returns, however with a much steeper slope. As might be expected the tradeoff between alpha and turnover is quite a bit more favorable, although both exhibit declining marginal benefits.
YES. IT IS LESS EFFICIENT. As shown in Exhibit 7 , in the lower right hand corner, the slope of the multifactor/low volatility (low V) strategy is dramatically steeper than the slope indicated by the single factor/low V strategy (dotted line). This suggests the efficiency as measured by units of alpha gained per unit of turnover for the multifactor/low V vastly exceeds that of the single factor/low V strategy. The authors cite an example where the single factor turnover rate is more than twice that of the multifactor portfolio. Specifically, the multifactor/low V portfolio with an alpha objective of 4.5% delivered a minimum turnover of 15% versus a single factor/low V portfolio with the same alpha objective that delivered a minimum turnover of 35%. On the other hand, fixing turnover at 20% and then 30% produced an additional 2% alpha.
Why does it matter?
Higher turnover in a low volatility strategy can be justified by integrating other factors such as value and momentum. The additional alpha generated thereby can also be done at low trading costs. This is especially true for multifactor approaches, rather than mixing a single factor with low volatility.
The most important chart from the paper
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged and do not reflect management or trading fees, and one cannot invest directly in an index.
An efficient low-volatility strategy only needs a little amount of trading. The empirical literature on low-volatility investing reveals a concave relation between the amount of trading and the risk reduction. Portfolio simulations confirm this non-linear pattern in which each increase in turnover results in smaller marginal reductions in volatility. In general a moderate trading level of 30% is enough to reduce portfolio volatility by 25% compared with the market index. In addition, low-volatility stocks are relatively liquid and cheap to trade, primarily because they are much larger than the average stock. The law of diminishing returns also applies to other alpha factors such as value and momentum and integrating them into a multi-factor low-volatility strategy is an efficient way to increase factor exposure at low trading costs.
Dr. Tommi Johnsen was a past Director of the Reiman School of Finance and a tenured faculty at the Daniels College of Business at the University of Denver. She has worked extensively as a consultant and investment advisor in the areas of quantitative methods and portfolio construction. She taught at the graduate and undergraduate level and published research in several areas: capital markets, portfolio management and performance analysis, financial applications of econometrics, and the analysis of equity securities. Her publications have appeared in numerous peer-reviewed journals.
Performance figures contained herein are hypothetical, unaudited and prepared by Alpha Architect, LLC; hypothetical results are intended for illustrative purposes only. Past performance is not indicative of future results, which may vary. There is a risk of substantial loss associated with trading stocks, commodities, futures, options and other financial instruments. Full disclosures here.