Mathematical and statistical methods for assessing the stabilizing role of stablecoins in cryptomarkets
The "code.zip" folder contains the different programming codes in Matlab and R, as well as the sample data necessary to carry out the dynamic portfolio optimization problems related to the inclusion of stablecoins in traditional cryptocurrency base portfolios. Specifically, these codes and raw data help to explore the diversification capabilities of stablecoins on cryptocurrency portfolios during the COVID-19 pandemic. We consider a risk-averse investor with a defensive profile whose preferences are modeled by a CARA-type utility function. Making use of the Taylor expansion, we obtain a functional form of the investor's certain equivalent which is a function of the first four conditional moments of the portfolio returns. These in turn are obtained from the conditional co-moment tensors of the assets in the portfolio, which are estimated using the GO-GARCH model. We also form minimum variance portfolios as a benchmark. The risk of base portfolios composed solely of traditional cryptocurrencies is compared to the risk of portfolios that include a stablecoin by means of modified VaR, an extension of Gaussian parametric VaR that includes conditional skewness and kurtosis terms of the portfolio returns. The results of the risk estimates are contrasted by means of different backtesting tests commonly used in the literature. The obtained results show that dollar-backed stablecoins have a strong ability to reduce the tail risk of cryptocurrency portfolios, especially by reducing their volatility, which is supported by very low conditional correlations between stablecoins and traditional cryptocurrencies. Moreover, the considered stablecoins induce a systematic reduction of portfolio kurtosis. Finally, our findings show that not considering higher order moments in cryptocurrency portfolios can lead to an underestimation of risk.