Abstract: This disclosure details methods for measuring and analyzing diversification of portfolio of assets. A dimension is a logical and quantitative means to measure diversification. As the number of dimensions increases so does diversification. Strong asset correlations among each other detract from the notion of independence. A positive correlation increases risks and is therefore undesirable. Assets are embedded into a high dimensional Euclidean vector space. The entire portfolio is interpreted as a set of points whose ambient dimension is the number of assets in the portfolio. The Karhunen-Loève expansion is used to quantify the KL dimension of the geometric object induced by a portfolio. The associated dimension is taken as the measure of diversification accounts for both the number of assets and the commonality within them. This ensures that measuring diversification as a dimension accounts for the complete diversification affect of the portfolio and is thus a valuable portfolio management tool.

Abstract: This disclosure details methods for measuring and analyzing diversification of portfolio of assets. A dimension is a logical and quantitative means to measure diversification. As the number of dimensions increases so does diversification. Strong asset correlations among each other detract from the notion of independence. A positive correlation increases risks and is therefore undesirable. Assets are embedded into a high dimensional Euclidean vector space. The entire portfolio is interpreted as a set of points whose ambient dimension is the number of assets in the portfolio. The Karhunen-Loève expansion is used to quantify the KL dimension of the geometric object induced by a portfolio. The associated dimension is taken as the measure of diversification accounts for both the number of assets and the commonality within them. This ensures that measuring diversification as a dimension accounts for the complete diversification affect of the portfolio and is thus a valuable portfolio management tool.

Abstract: This disclosure details methods for measuring and analyzing diversification of portfolio of assets. A dimension is a logical and quantitative means to measure diversification. As the number of dimensions increases so does diversification. Strong asset correlations among each other detract from the notion of independence. A positive correlation increases risks and is therefore undesirable. Assets are embedded into a high dimensional Euclidean vector space. The entire portfolio is interpreted as a set of points whose ambient dimension is the number of assets in the portfolio. The Karhunen-Loève expansion is used to quantify the KL dimension of the geometric object induced by a portfolio. The associated dimension is taken as the measure of diversification accounts for both the number of assets and the commonality within them. This ensures that measuring diversification as a dimension accounts for the complete diversification affect of the portfolio and is thus a valuable portfolio management tool.