Oil tail risks and the forecastability of the realized variance of oil-price: Evidence from over 150 years of data

Abstract

We examine the predictive value of tail risks of oil returns for the realized variance of oil returns using monthly data for the modern oil industry (1859:10-2020:10). The Conditional Autoregressive Value at Risk (CAViaR) framework is employed to generate the tail risks for both 1% and 5% VaRs across four variants of the CAViaR framework. We find evidence of both in-sample and out-of-sample predictability emanating from both 1% and 5% tail risks. Given the importance of real-time oil-price volatility forecasts, our results have important implications for investors and policymakers.

Climate risks and U.S. stock‐market tail risks: A forecasting experiment using over a century of data

“…This motivation to use over 125 years of data also makes the choice of the United States an obvious one due to data availability on both temperature and stock price. In this regard, instead of the traditionally used option-implied measures of tail risks (Salisu, Pierdzioch, & Gupta, 2022b), we use a framework based on the underlying returns data measure tail risk, which is understandable due to the unavailability of data on options over the prolonged sample period that we study in this research. Specifically, we estimate tail risk using the popular Value at Risk (VaR) metric at 1% and 5% by employing the conditional autoregressive quantile specification as proposed by Engle and Manganelli (2004), which, in turn, is called the CAViaR model(as a robustness check, we also draw on extreme-value theory [EVT] to estimate a GARCH-EVT-based model).…”

“…Complete details of all these estimations are available from the authors upon request.9 It should be noted that the GARCH-2 model makes the estimate of the volatility of the growth rate of temperature comparable with the one derived from the stochastic-volatility model (which we discuss in Footnote 3.2), which also includes a lag of the growth rate of temperature.10 The technically minded reader is referred to this paper to get an understanding of the details of this methodology.11 Other approaches such as those proposed byBoudoukh et al (1998) andDanielsson and de Vries (2000) are not "extreme enough" to capture the tail distribution.12 Technically minded readers may refer toEngle and Manganelli (2004) for further details on the tail-risk estimation. Also, recent applications of the CAVaiR framework to measure tail risks are documented in the energy-finance literature bySalisu, Gupta, and Ogbonna (2022d),Salisu, Pierdzioch, et al (2022e),Salisu et al (2021),Salisu, Gupta, and Ji (2022a),Gupta (2022b), andGupta (2022c).13 We assume that the DQ test takes prominence over the %Hits and the RQ statistics. In cases where more than one tail risk is statistically insignificant in terms of the DQ test, we consider both the %Hits and the RQ statistics to identify the specification with the best fit.14 We have dropped the time index for notational convenience.15 It should be noted that we do not use the loss function to draw conclusions regarding the "rationality" of forecasts under (as-)…”

“…12 12 Technically minded readers may refer to Engle and Manganelli (2004) for further details on the tail‐risk estimation. Also, recent applications of the CAVaiR framework to measure tail risks are documented in the energy‐finance literature by Salisu, Gupta, and Ogbonna (2022d), Salisu, Pierdzioch, et al (2022e), Salisu et al (2021), Salisu, Gupta, and Ji (2022a), Salisu, Pierdzioch, and Gupta (2022b), and Salisu, Pierdzioch, and Gupta (2022c). …”