Systematic Tail Risk

Abstract

We test for the presence of a systematic tail risk premium in the cross section of expected returns by applying a measure of the sensitivity of assets to extreme market downturns, the tail beta. Empirically, historical tail betas help predict the future performance of stocks in extreme market downturns. During a market crash, stocks with historically high tail betas suffer losses that are approximately 2 to 3 times larger than their low-tail-beta counterparts. However, we find no evidence of a premium associated with tail betas. The theoretically additive and empirically persistent tail betas can help assess portfolio tail risks.

Risk premia: asymmetric tail risks and excess returns

“…This was in fact proposed as a resolution of the Mehra & Prescott "equity premium puzzle" by Kraus and Litzenberger (1976), Rietz (1988) and then in many follow up papers with a similar message, e.g. (Harvey and Siddique 2000, Barro 2006, Santa-Clara and Yan 2010, Bollerslev and Todorov 2011, (see also Kelly and Hao 2013, van Oordt and Zhou 2013, Kozhan et al 2013. Risk premium might be more a question of skewness and negative tail events than related to volatility per se.…”

Can Tail Risk Predict Asia-Pacific Exchange Rates Out of Sample?

“…Tail risk has been studied in predictive models for stocks (Li et al, 2021;Van Oordt & Zhou, 2016). This approach has been employed to measure stocks tail risks (Salisu, Gupta, & Ogbonna, 2021); and oil tail risk (Salisu, Gupta, & Ji, 2021).…”

Systemic risk and bank business models

“…Given some low probabilityp, only a few observations correspond to the tail scenario R s ≤ −VaR s (p). Van Oordt and Zhou (2016) apply this methodology in an asset pricing framework and show that estimates are relatively persistent over time and that historical estimates help to predict which stocks suffer relatively large losses in market crashes. Instead, we estimate T i using an EVT approach.…”

“…This estimator of T i has a smaller mean squared error than an OLS regression if the estimation is based on a few tail observations only. Van Oordt and Zhou (2016) apply this methodology in an asset pricing framework and show that estimates are relatively persistent over time and that historical estimates help to predict which stocks suffer relatively large losses in market crashes.…”