Value at risk and returns of cryptocurrencies before and after the crash: long-run relations and fractional cointegration

Cryptocurrency has become an increasingly important investment vehicle, thus the long-run relationship between risk and return of cryptocurrency is vital for both investors and policy-makers. We apply the Fractionally Cointegrated Vector Autoregression (FCVAR) model and investigate the risk-return relationship. This has not been studied previously, much less disintegrating the series into periods of pre-crash, post-crash, and the full sample. Empirical results indicate that risk series in all eight cryptocurrency markets exhibit long-memory property, and there is a long-run fractional cointegration relationship between the risk of altcoins and Bitcoin. Most importantly, though a positive risk-return tradeoff is found in the full sample, there are big differences between results of pre-crash and post-crash. The time horizon set to 14 days, all the eight currencies exhibit traditional risk-return tradeoff after the crisis, whereas the effect doesn’t exist before the crisis, with the exception of Dash and Doge. In the same vein, there is no leverage effect in all eight currencies before the crisis but this effect is present in three cryptocurrencies after the crisis. The differences indicate that investors are more cautious, increasing risk awareness and demanding higher compensation for risk after the crash. The above results are robust when time horizon is 30 days.