Thabani Ndlovu

This paper uses theValue at Risk (VaR) and the Expected Shortfall (ES) to compare the riskiness of the two currency exchange rate volatility, namely BitCoin against the US dollar (BTC/USD) and the South African Rand against the US dollar (ZAR/USD). The risks calculated are tail-related measures, so the Extreme Value Theory is used to capture extreme risk more accurately. The Generalized Pareto distribution (GPD) is assumed under Extreme Value Theory (EVT). The family of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models was used to model the volatility-clustering feature. The Maximum Likelihood Estimation (MLE) method was used in parameter estimation. Results obtained from the GPD are compared using two underlying distributions for the errors, namely: the Normal and the Student-t distributions. The findings show that the tail VaR on the BitCoin averaging 1.6 and 2.8 is riskier than on South Africa’s Rand that averages 1.5 and 2.3 at 95% and 99%, respectively. The same conclusion is made about tail ES, the BitCoin average of 2.3 and 3.6 is higher (riskier) than the South African Rand averages at 2.1 and 2.9 at 95% and 99%, respectively. The backtesting results confirm the model adequacy of the GARCH-GPD in the estimation of VaR and ES, since all p-values are above 0.05.

In this study, the RiskMetrics method is used to estimate Value at Risk for two exchange rates: BitCoin/dollar and the South African Rand/dollar. Value at Risk is used to compare the riskiness of the two currencies. This is to help South Africans and investors understand the risk they are taking by converting their savings/investments to BitCoin instead of the South African currency, the Rand. The Maximum Likelihood Estimation method is used to estimate the parameters of the models. Seven statistical error distributions, namely Normal Distribution, skewed Normal Distribution, Student’s T-Distribution, skewed Student’s T-Distribution, Generalized Error Distribution, skewed Generalized Error Distribution, and the Generalized Hyperbolic Distributions, were considered when modelling and estimating model parameters. Value at Risk estimates suggest that the BitCoin/dollar return averaging 0.035 and 0.055 per dollar invested at 95% and 99%, respectively, is riskier than the Rand/dollar return averaging 0.012 and 0.019 per dollar invested at 95% and 99%, respectively. Using the Kupiec test, RiskMetrics with Generalized Error Distribution (p > 0.07) and skewed Generalized Error Distribution (p > 0.62) gave the best fitting model in the estimation of Value at Risk for BitCoin/dollar and Rand/dollar, respectively. The RiskMetrics approach seems to perform better at higher than lower confidence levels, as evidenced by higher p-values from backtesting using the Kupiec test at 99% than at 95% levels of significance. These findings are also helpful for risk managers in estimating adequate risk-based capital requirements for the two currencies.