The Investors’ Behavior towards the Relationship between Bitcoin, Litcoin, Dash Coins, and Gold: A Portfolio Modeling Approach

Abstract

This study considers a market-based economy that is composed of two asset classes: one is a digital, cryptocurrency, and the other is real, gold. We demonstrated that coins like (BTC, LTC, and DASH) can substitute a traditional safe haven “gold” in an intertemporal investment portfolio to become a new form of safe haven. The cryptocurrency follows a Jump-diffusion process. However, gold prices follow an Ornstein-Uhlenbek process to characterize the stochastic nature of the market. The stochastic optimal control approach, combined with the strategic asset allocation and the intertemporal utility theory, are used through the derivation of a Hamilton-Jacobi-Bellman (HJB) equation to determine an explicit solution of the optimal allocation problem for investors with CRRA utility function. We considered the Gamma Lévy process to solve the optimization problem. By using the secant method, we determined numerically the optimal percentage invested in the two asset classes at each time over the holding period. Our results showed that an investor can substitute gold by coins (BTC, LTC, DASH) from an investment portfolio perspective. Although Gold is supposed to be the traditional safe-haven asset, the digital currency seems to emerge as a new form of safe-haven value in a risky environment.