Abstract

This study presents an analysis of the impact of asset price bubbles on the markets for cryptocurrencies and con-siders the standard risk management measure Value-at-Risk (“VaR”). We apply the theory of local martingales, present a styled model of asset price bubbles in continuous time and perform a simulation experiment featuring one- and two-dimensional Stochastic Differential Equation (“SDE”) systems for asset value through a Constant Elasticity of Variance (“CEV”) process that can detect bubble behavior. In an empirical analysis across several widely traded cryptocurrencies, we find that the estimated parameters of one-dimensional SDE systems do not show evidence of bubble behavior. However, if we estimate a two-dimensional system jointly with an equity market index, we do detect a bubble, and comparing bubble to non-bubble economies it is shown that asset price bubbles result in materially inflated VaR measures. The implication of this finding for portfolio and risk management is that rather than acting as a diversifying asset class, cryptocurrencies may not only be highly correlated with other assets but have anti-diversification properties that materially inflate the downside risks in portfolios combining these asset types. We also measure the model risk arising from mispecifying the process driving cryptocurrencies by ignoring the relationship to another representative risk asset through applying the principle of relative entropy, where we find that across all cryptocurrencies studied that the distributions of a distance measure between the simulated distributions of VaR are almost all highly skewed to the right and very heavy-tailed. We find that in the majority of cases that the model risk “multipliers” range in about two to five across cryptocurrencies, estimates which could be applied to establish a model risk reserve as part of an economic capital calculation for risk management of cryptocurrencies.

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