## Portfolio theory using cryptocurrencies

2018-02-5 last edited: 7/10/18

During the 2018 developer weekend in SF one of the objectives was to make an app relating to cryptocurrencies in some capacity. In my view one of the shortcomings of the cryptocurrency field is how open it is too speculation, and that there is an absence of long term perspectives amongst those who call to invest in cryptocurrencies. Exemplified by the emphasis on the moonshot effect; how cryptocurrencies rapidly appreciate in value when they first become popular. Our team sought to address this shortcoming by preforming a modern portfolio theory analysis on a selection of more mature and higher market cap cryptocurrencies. The model was solved using cvxpy library which is able to address quadratic optimization problem at the heart of modern portfolio theory. Further the library can implement various constraints, so it is possible to take into account restrictions on short selling and other complicating factors.

The graphed curve represents the collection of portfolios which have the lowest risk, defined as standard deviation of return, for any given return. The predicted performance (over one year!) of any given portfolio is defined as $e^{\mu+\sigma\epsilon}$ where $\mu$ is the y axis coordinate of the portfolio and $\sigma$ is the x axis coordinate. To examine various portfolios hover over the dots on the curve and the new portfolio with its specific mixture will be rendered to the right.

One aspect that can be observed is that the scale of the graph is absolutely insane. A unit of one for expected returns corresponds too a $100*(e^1-1)=172/%$ gain in one year. The most extreme portfolio, has a claimed rate of return of 2.7 and a risk of 3.0. This means the $-1\sigma$ return is -30% and the $+1\sigma$ return is 29800%. This, at first pass, sounds rather incredulous. However recalling the history of bitcoin which was at one point worth a few dollars and not that long ago worth north of 20,000 it is clear there is a president for massive appreciation, which would then also appear in any naive application of portfolio theory to cryptocurrencies. However, with bitcoin now worth around 100 billion it is unlikely that bitcoin will see similar appreciation again. Similarly every cryptocurrency that we modeled also went through a period of high growth that is unlikely to occur again, otherwise the currency would not have found its way into our model, as such in our analysis there is a persistent bias in the data. A bias towards high growth that only an early adopter, not a conservative investor using modern portfolio theory, would achieve. Thus any future analysis of how to intelligeltly hold a long position in mature cryptocurrencies will require a careful handling of this moonshot effect.