Strategy design and the fallacies of breadth
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ORIGINAL ARTICLE
Strategy design and the fallacies of breadth Leigh Sneddon1 Revised: 14 October 2020 / Accepted: 15 October 2020 / Published online: 12 November 2020 © Springer Nature Limited 2020
Abstract High return correlations between assets have widely and plausibly been said to detract from active performance.The concept of Breadth supports this view. Buckle, however, reported that these correlations improve active performance. Based on three approaches, we report that Buckle is correct. First, we introduce a model of active investing that includes return correlations between assets. Design formulae give the time averages of active risk and return and other portfolio characteristics. Next, we show that Monte Carlo simulations confirm the conclusions of the model. Finally, we provide the investment intuition behind the conclusions. All else equal, active managers should be more aggressive when return correlations are expected to be high, not low. A related widely held belief is that return forecasts with lower correlations between assets provide better performance. The model also includes these correlations. The same approaches show that this consensus too is incorrect: all else equal, correlations of return forecasts between assets improve performance. The design formulae can be used for opera‑ tional strategy design aimed at performance improvements. As examples, we use it to exploit differences in predictive power between sectors and to efficiently incorporate Environmental, Social and Governance controls into active security selection. Keywords Active · Strategy · Breadth · Correlation · Performance · Forecast
Introduction Return correlations have long been a focus in active manage‑ ment (see for example the 1995 edition of Elton et al. 2014), and high correlations have been widely regarded as detract‑ ing from performance (Solnik and Roulet 2000; Kolanovic et al. 2010; Montagu et al. 2010; ETF.com 2007; Rothman 2010; Hatheway et al. 2010; Patel 2011). Buckle (2004), on the other hand, presents a model where correlations improve active performance. His model differs from standard prac‑ tice, however, and the results in some cases include negative Breadths. Which is right, Buckle’s finding or the consensus? An extremely simple scenario, consisting of two assets with one asset return equal to the other plus a constant, sup‑ ports Buckle. The fixed difference means the returns are per‑ fectly correlated. The investment manager will observe one This work was presented at the Chicago Quantitative Alliance, Las Vegas, Nevada conference in April 2018. The author thanks Ron Kahn for his guidance on early versions of the manuscript and Northfield Information Services, Inc. for the data and risk models. * Leigh Sneddon leigh@mayfield‑invest.com 1
Mayfield Investments Solutions, Inc., Mill Valley, CA, USA
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asset consistently outperforming the other. The manager can then give the assets equal but opposite weights and achieve positive return with zero volatility. Fully correlated assets are
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