Risk measurement models for top 10 cryptocurrencies: A comparison of VaR and volatility models

Value-at-risk (VaR) is the most common and widely used risk measure that enterprises, particularly major banking corporations and investment bank firms employ in their risk mitigation processes. The purpose of this study is to investigate the value-at-risk (VaR) estimation models and their predictive performance by applying a series of backtesting methods on BRICS (Brazil, Russia, India, China, South Africa) and US stock market indices. The study employs three different VaR estimation models, namely normal (N), historical (HS), exponential weighted moving average (EMWA) procedures, and eight backtesting models. The empirical analysis is conducted during three different periods: overall period (2006–2021), global financial crisis (GFC) period (2008–2009), and COVID-19 period (2020–2021). The results show that the EMWA model performs better compared to N and HS estimation models for all the six stock market indices during overall and crisis sample periods. The results found that VaR models perform poorly during crisis periods like GFC and COVID-19 compared to the overall sample period. Furthermore, the study result shows that the predictive accuracy of VaR methods is weak during the COVID-19 era when compared to the GFC period.

This paper uses a Multiple Attribute Decision Making (MADM) model to improve the out-of-sample performance of a naïve asset allocation model. Under certain conditions, the naïve model has out-performed other portfolio optimization models, but it also has been shown to increase the tail risk. The MADM model uses a set of attributes to rank the assets and is flexible with the attributes that can be used in the ranking process. The MADM model assigns weights to each attribute and uses these weights to rank assets in terms of their desirability for inclusion in a portfolio. Using the MADM model, assets are ranked based on the attributes, and unlike the naïve model, only the top 50 percent of assets are included in the portfolio at any point in time. This model is tested using both developed and emerging market stock indices. In the case of developed markets, the MADM model had 24.04 percent higher return and 53.66 percent less kurtosis than the naïve model. In the case of emerging markets, the MADM model return is 90.16 percent higher than the naïve model, but with almost similar kurtosis.

South Africa’s economy has faced many downturns in the previous decade, and to curb the spread of the novel SARS-CoV-2, the lockdown brought South African financial markets to an abrupt halt. Therefore, the implementation of risk mitigation approaches is becoming a matter of urgency in volatile markets in these unprecedented times. In this study, a hybrid generalized autoregressive conditional heteroscedasticity (GARCH)-type model combined with heavy-tailed distributions, namely the Generalized Pareto Distribution (GPD) and the Nolan’s S0-parameterization stable distribution (SD), were fitted to the returns of three FTSE/JSE indices, namely All Share Index (ALSI), Banks Index and Mining Index, as well as the daily closing prices of the US dollar against the South African rand exchange rate (USD/ZAR exchange rate). VaR values were estimated and back-tested using the Kupiec likelihood ratio test. The results of this study show that for FTSE/JSE ALSI returns, the hybrid exponential GARCH (1,1) model with SD model (EGARCH(1,1)-SD) outperforms the GARCH-GPD model at the 2.5% VaR level. At VaR levels of 95% and 97.5%, the fitted GARCH (1,1)-SD model for FTSE/JSE Banks Index returns performs better than the GARCH (1,1)-GPD. The fitted GARCH (1,1)-SD model for FTSE/JSE Mining Index returns is better than the GARCH (1,1)-GPD at 5% and 97.5% VaR levels. Thus, this study suggests that the GARCH (1,1)-SD model is a good alternative to the VaR robust model for modeling financial returns. This study provides salient results for persons interested in reducing losses or obtaining a better understanding of the South African financial industry.