Title: Mapping Cryptocurrency in the Financial Market using Manifold of Positive Definite Matrices Professor. In-Jae Kim Department of Mathematics and Statistics Minnesota State University, Mankato Date: 2023.08.9(Wed) Time: 4:00 pm venue: AORC Seminar room Abstract: A cryptocurrency is a form of digital asset. There has recently been a growing public interest in trading cryptocurrencies as part of their financial portfolio. However, its identity as an asset class is not clear. In this talk we examine the proximity of cryptocurrencies as an asset class to traditional ones. To estimate the proximity, we select five representative assets from each of twenty-eight subcategories of asset classes and compute the corresponding correlation matrices of asset returns. Using the fact that these correlation matrices belong to a mathematical structure, called Riemannian manifold, we compute a non-Euclidean distance between the 28 correlation matrices representing the 28 subcategories of asset classes. To visualize relative positions of the 28 subcategories in the 2-dimensional Euclidean space, we use the multi-dimensional scaling. For clustering of the 28 projected points in the 2-dimensional Euclidean space, we use -means clustering. This clustering illustrates that cryptocurrency acts more like securities than commodities when it comes to price movement. Our study of comparing cryptocurrency with the other asset classes using Riemannian distance provides investors with the information that is useful to construct a well-diversified portfolio.