Financial markets for specific asset classes are typically represented by indices. Exchange-traded funds derived from these indices inherently carry a certain degree of risk. In ideal circumstances, this risk can be quantified through a linear dependency structure of portfolio elements. However, it is widely acknowledged that financial assets, in particular cryptocurrencies (CCs), often exhibit non-linear tail behaviour, and hence there is no guarantee of linear dependency. In this study, optimal CC portfolios are first constructed by minimizing spectral risk measures (SRMs) explicitly tied to different levels of risk aversion. The resulting portfolios and the indices are then projected into two dimensional embeddings using multidimensional scaling (MDS), t-distributed stochastic neighbor embedding (t-SNE), and uniform manifold approximation and projection (UMAP), which makes proximity patterns clear and interpretable. Finally, groupwise proximity is assessed with nonparametric statistical tests. Our central contribution is a visualization first pipeline grounded in SRMs that maps investor risk preferences to CC portfolios and, through low dimensional embeddings and nonparametric tests, provides interpretable evidence to identify which preference parameterized portfolios most closely align with specific CC indices, thereby informing product design and investor profiling.
Financial markets for specific asset classes are typically represented by indices. Exchange-traded funds derived from these indices inherently carry a certain degree of risk. In ideal circumstances, this risk can be quantified through a linear dependency structure of portfolio elements. However, it is widely acknowledged that financial assets, in particular cryptocurrencies (CCs), often exhibit non-linear tail behaviour, and hence there is no guarantee of linear dependency.
In this study, optimal CC portfolios are first constructed by minimizing spectral risk measures (SRMs) explicitly tied to different levels of risk aversion. The resulting portfolios and the indices are then projected into two dimensional embeddings using multidimensional scaling (MDS), t-distributed stochastic neighbor embedding (t-SNE), and uniform manifold approximation and projection (UMAP), which makes proximity patterns clear and interpretable. Finally, groupwise proximity is assessed with nonparametric statistical tests. Our central contribution is a visualization first pipeline grounded in SRMs that maps investor risk preferences to CC portfolios and, through low dimensional embeddings and nonparametric tests, provides interpretable evidence to identify which preference parameterized portfolios most closely align with specific CC indices, thereby informing product design and investor profiling.