ABSTRACT
Cryptocurrencies are virtual
currencies employed in blockchain transactions. They are particularly worthy of
theoretical examination, given the limited academic literature on the subject.
This paper constructs valuation models of bitcoin and altcoins, both as single
investments and components of mutliple-asset portfolios. As single investments,
cryptocurrencies are valued at the confluence of Legendre utility functions,
with Esscher transformed Geometric Levy pricing processes. As part of
portfolios, cryptocurrencies are contained in traditional Markowitz portfolios
which are varied by increasing the proportion of the riskless asset, shorting
the risky asset, or adding currency options. Theoretical formulations show that
Markowitz models combined with bitcoin, located on the Capital Market Line
(which we term CML portfolios), have
low returns, mainly due to the presence of the riskless asset. Such portfolios
are appropriately suited to the investment goals of risk-averse traders, while
overlooking the preferences of risk-takers. To satisfy less risk-averse investors,
we propose a high-return portfolio with 9 asset choices, consisting of risky
assets, cryptocurrencies, US dollars, soybean futures, Treasury bond futures,
oil futures, currency options on the US dollar, currency options on the Mexican peso, and technology, or
biotechnology stocks. Laplace transforms are employed to suppress
volatility, skewness, or kurtosis of returns, which empirical studies have
found to contribute to tail risk contained in outliers in fat-tailed
distributions.