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

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.