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Quantitative Equity Research

Challenging the constant leverage paradigm


Executive Summary

This paper focuses on a common approach to building an equity portfolio and shows why it is likely to be suboptimal. In particular, we focus on the question of how to set the overall level of risk in a portfolio, which is critical to generating returns but so far has received little study.1

One commonly-used method to set the level of portfolio risk is to fix the book size (i.e. gross notional exposure) to be a constant. We refer to this approach as Constant Leverage (CL). In contrast, the alternative we present in this paper varies the book size in order to keep the forecast volatility constant. We refer to this method as Volatility Targeting (VT). The main difference between the two methods is how they manage leverage and volatility: CL portfolios have a very tight distribution of leverage and a wide distribution of realized volatility, while VT portfolios have a wide distribution of leverage and a tight distribution of realized volatility

The Constant Leverage approach has some clear advantages over Volatility Targeting: it is simpler to implement and generally has lower turnover. However, what is often overlooked is that CL’s wide distribution of realized volatility has two important drawbacks. The first is the risk of underperformance from either taking too much risk when performance is poor or taking too little risk when performance is good. Volatility Targeting avoids this by maintaining a constant level of risk. The second drawback, and the focus of this paper, is that a Constant Leverage approach will tend to generate inferior risk-adjusted performance when compared to a Volatility Targeting approach.

We demonstrate this expected decrease in riskadjusted performance by means of a stylized model of strategy performance and market volatility. Our model shows that in order for a Constant Leverage implementation to have the same expected Sharpe ratio as a Volatility Targeted implementation, risk-adjusted return expectations need to increase by more than 40% when market volatility rises. This required increase in Sharpe ratio during high volatility regimes represents an enormous hurdle for Constant Leverage implementations to overcome.

To see if the Constant Leverage approach can regularly overcome this hurdle, we evaluate a set of market neutral strategies using both VT and CL portfolio construction approaches. We find that for most of the strategies, the Sharpe ratio of the CL strategy is worse than the Sharpe ratio of the VT strategy, indicating that Sharpe ratio expectations in high volatility environments are insufficient to justify a Constant Leverage approach.

Thus, we conclude that for most strategies, Volatility Targeting is a more appropriate approach to equity portfolio construction.

“Everything should be as simple as it can be, but not simpler” – A. Einstein2

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