Centred expected shortfall (CES): a traditional asset manager’s view on decomposing downside investment risk

Erik Kroon, Mehdi-Vincent Hacini and Koye Somefun

Quantitative Finance, 2023, vol. 24, issue 1, 83-104

Abstract: Risk driver contributions are key to understanding portfolio risk. Often, this is done by decomposing portfolio volatility. This is problematic in the presence of non-elliptical distributions. Some asset managers propose switching to value-at-risk (VaR) or expected shortfall (ES) as risk measures. Often the latter is preferred as it deals better with risk in sub-portfolios. However, we argue that the traditional asset management industry should, as a rule, ‘not’ apply ES directly. Instead, expected portfolio return should be first subtracted from it; this Centred Expected Shortfall (CES) forms a natural extension of volatility. The relative breakdowns of both are identical if the underlying multivariate distribution is elliptical. From a practical perspective, we show how to correctly decompose CES and how ES can be misleading. Moreover, we recommend plotting so-called alpha-CES/volatility profiles. These work with distribution-free risk estimates and give a bird’s eye view on the downside impacts of any non-ellipticalities as a function of the portfolio’s left tail size (alpha). Conveniently, these profiles also describe upside tail (surplus) risks. We end with two practical illustrations: A simple assets-only example based on historical data with assets as risk drivers; and a more complex Liability-Driven Investing (LDI) simulation example with factors as drivers.

Date: 2023
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DOI: 10.1080/14697688.2023.2269992

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