Downside Risk Evaluation with the R Package GAS

Abstract

Financial risk managers routinely use non-linear time series models to predict the downside risk of the capital under management. They also need to evaluate the adequacy of their model using so-called backtesting procedures. The latter involve hypothesis testing and evaluation of loss functions. This paper shows how the R package GAS can be used for both the dynamic prediction and the evaluation of downside risk. Emphasis is given to the two key financial downside risk measures: Value-at-Risk (VaR) and Expected Shortfall (ES). High-level functions for: (i) prediction, (ii) backtesting, and (iii) model comparison are discussed, and code examples are provided. An illustration using the series of log-returns of the Dow Jones Industrial Average constituents is reported.

On the Elicitability and Risk Model Comparison of Emerging Markets Equities

“…The relationship between the FZL function and the generalised autoregressive score (GAS) models (Creal et al [42]; Harvey [43]) is exploited as they both use loss function as an impetus of time-variation in the parameters (Ardia et al [44]).…”

“…GAS(p, q) gives dependence of the driving mechanism in (3) on the scaled score vector in (4). We use GAS(1, 1) in this study for all estimations (see Creal et al [42]; Ardia et al [44]). It may be worthwhile to compare the GAS models with generalised autoregressive conditional heteroscedasticity (GARCH) models of various dimensions, however, the outputs from our estimations in this study are overly voluminous (the tables presented are compressed) for brevity reasons.…”

Value at Risk estimation using GAS models with heavy tailed distributions for cryptocurrencies

“…The aim of backtesting analysis is to assess the precision of the prediction by splitting the estimation and evaluation period. VaR backtesting procedures evaluate the true coverage of the unconditional and conditional left-tail of a log returns distribution (Ardia, Boudt and Catania, 2018). The correct unconditional coverage (UC) was first considered by Kupiec (1995) and the correct conditional coverage (CC) was first considered by Christoffersen (1998).…”

“…Bitcoin, one of the most widely traded cryptocurrencies, was first introduced and documented by Satoshi Nakamoto in 2008. Cryptocurrencies were established to promote the use of decentralized control so that electronic payments between individuals can be made without transacting via a third party (Ardia et al, 2018). This reduces transaction costs to an almost zero cost and/or price and allows for speedy buying and selling.…”

“…The analysis was done using data from July 2010 to April 2014 and it was discovered that Bitcoin has high annualized volatility, but when transaction volume was taken into account, it proved to be more stable. Ardia et al (2018) used Markov-switching GARCH (MSGARCH) models to explore the existence of regime changes in the GARCH volatility dynamics of Bitcoin log returns. Daily Bitcoin mid-prices from August 2011 to March 2018 were used in the investigation.…”