A SIMPLE TRAFFIC LIGHT APPROACH TO BACKTESTING EXPECTED SHORTFALL NICK COSTANZINO AND MICHAEL CURRAN Abstract. We propose a Traffic Light approach to backtesting Expected Shortfall which is completely consistent and analogous to the Traffic Light approach to backtesting VaR initially proposed by the Basel Committee on Banking Supervision in their 1996 consultative document [1]. The approach relies on the generalized coverage test for Expected Shortfall developed in [2]. Contents 1. Introduction 1 2. Traffic Light Approach to Expected Shortfall 3 3. Some Comments 5 4. Conclusion 5 References 5 1. Introduction Let {t i } N i=0 be a sequence of historical trading days and {L i } N i=1 the correspond- ing realized trading losses. The most basic approach to assess the accuracy of the VaR forecast calculation for those trading days is to backtest using the VaR Cov- erage Test. This leads to the Traffic Light approach to backtesting VaR originally proposed by the Basel Committee for Banking Supervision in [1] which we describe below. For each i =1, ..., N , let VaR i (α) denote the forecast VaR at level α defined by (1.1) VaR(α) := inf {z ∈ R : F L (z) ≥ α} where F L is the cumulative distribution of the random loss variable L. For each trading day i we define the VaR breach indicator X (i) VaR : [0, 1] →{0, 1} as (1.2) X (i) VaR (α) := {Li≤VaRi(α)} =  0 if L i > VaR i (α) 1 if L i ≤ VaR i (α). That is, X (i) VaR keeps track of whether a breach occurred for trading day i. Then the total number of breaches over all N trading days, denoted by X N VaR : [0, 1] → {0, 1, 2, ..., N } is Date : May 7, 2015. 1