The consequences of the Basel III requirements for the liquidity horizon and their implications for optimal trading strategy

In this study we propose a formula-based approach for determining the optimal liquidity horizon used in scaling the base expected shortfall under the Basel Committee’s market risk capital requirements. Specifically, the “half-life†formula introduced by Almgren and Chriss in 2000 is used to compute optimal liquidity horizon values and construct an optimal expected shortfall measure. Unlike the regulatory approach, which scales expected shortfall across aggregated groups of risk factors, as laid out in the Basel Committee’s 2019 “Minimum capital requirements for market risk†, our method enables scaling at the level of individual securities, thereby improving estimation accuracy. To evaluate performance, we compare optimal expected shortfall with the regulatory expected shortfall using returns data from the Standard & Poor’s 500 and Dow Jones Industrial Average indexes. Employing the regression-based expected shortfall backtesting technique of Bayer and Dimitriadis, we find that optimal expected shortfall produces unbiased estimates, while regulatory expected shortfall systematically overstates the true magnitude of expected shortfall.