摘要：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.
