Return Targets and Percentile Fans

Martin L. Leibowitz and Anthony Bova

Financial Analysts Journal, 2010, vol. 66, issue 1, 28-40

Abstract: This article presents a highly intuitive approach for visualizing return distributions for a basic form of cash/equity allocations. This “percentile fan” framework can help clarify some of the key risk–return trade-offs in intuitive ways for a wide set of asset owners. In particular, percentile fans can help investors express their portfolio objectives in terms of return targets or shortfall limits over one or more horizons. For some investors, these intuitive goals, especially when depicted in a visual context, can feel like a more natural approach than the standard mean–variance utility framework.The authors use multiple-percentile “fans” for a range of equity mixtures (described by beta values) to provide a simultaneous view of the prospects for reaching return targets and satisfying prescribed risk limits. In particular, percentile fans can help investors express their portfolio objectives in terms of return targets or shortfall limits over one or more time horizons. For some investors, these intuitive goals, especially when depicted in a visual context, can feel like a more natural approach than the standard mean–variance utility framework.The authors’ findings suggest that to achieve reasonable return targets within the framework of a standard market model, allocations may need to be seriously long-term oriented and yet able to accommodate relatively high levels of year-to-year volatility. Returns from diversifying assets, better-yielding low-risk alternatives, and active strategies can also help in achieving reasonable return targets over the long run but with a potentially greater vulnerability to severely adverse markets.A minimum objective for any risk taking is to surpass the return available from the risk-free rate. In the authors’ analysis, one basically horizontal percentile line always radiates from the risk-free rate. This percentile line acts as a risk floor in the sense that it characterizes a common probability of exceeding the risk-free rate for all portfolios with positive betas. In their basic example, the 60th percentile line delineates this risk floor such that all risky portfolios have the same 60 percent probability of exceeding the risk-free rate. The one exception is the zero beta portfolio, which is 100 percent invested in the risk-free rate itself.Over the long term, a significant probability of achieving decent return targets requires accepting a sufficiently high minimum beta risk. Short-term risk constraints, however, typically set a maximum beta limit. A range of feasible beta values is defined by some combination of a maximum for risk constraints and a minimum for return objectives. The beta range found in their examples roughly approximates the 0.55−0.65 beta values widely seen in practice for most individual and institutional portfolios (even those with high levels of diversification).

Date: 2010
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DOI: 10.2469/faj.v66.n1.7

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