Portfolio diversification plays a crucial role in portfolio management. It can be presented in various ways, but in this thesis, the focus will be on diversification based on uncorrelated sources of risk, presented with principal portfolios. Once we have found uncorrelated principal portfolios, we can use them to present the portfolio's diversification. This can be achieved by using the exponential of the diversification distribution's entropy, which represents an approximate number of uncorrelated sources of risk. On the basis of this value, a maximization can be carried out, with restrictions representing portfolio constraints. Depending on the investor's risk preference, we build multiple optimal portfolios, which we then join into a diversification frontier.
This method is then used in the example of cryptocurrencies, which are highly correlated. With its help, we find the diversification frontier for the cryptocurrencies used. At the same time, we are comparing the diversification according to this method with the one based on optimal Sharpe ratio.