RiskMetrics method for estimating Value at Risk to compare the riskiness of BitCoin and Rand

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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.

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    • Figure 1. Plot of BTC/USD prices (left) and one-day log returns (right)
    • Figure 2. Plot of ZAR/USD prices (left) and one-day log returns (right)
    • Table 1. Error distribution functions
    • Table 2. Descriptive statistics of exchange rate price returns
    • Table 3. Optimal RiskMetrics estimate parameters for BTC/USD
    • Table 4. Optimal RiskMetrics parameter estimates for ZAR/USD
    • Table 5. VaR estimates
    • Table 6. Kupiec’s test p-values
    • Conceptualization
      Delson Chikobvu, Thabani Ndlovu
    • Formal Analysis
      Delson Chikobvu, Thabani Ndlovu
    • Methodology
      Delson Chikobvu, Thabani Ndlovu
    • Project administration
      Delson Chikobvu
    • Resources
      Delson Chikobvu
    • Supervision
      Delson Chikobvu
    • Writing – review & editing
      Delson Chikobvu, Thabani Ndlovu
    • Data curation
      Thabani Ndlovu
    • Investigation
      Thabani Ndlovu
    • Software
      Thabani Ndlovu
    • Validation
      Thabani Ndlovu
    • Writing – original draft
      Thabani Ndlovu