The Downside and Upside Beta Valuation in the Variance-Gamma Model

The paper is aimed to assess the risks and gains of investment portfolio which relate to the impact of a particular asset. We consider the investment portfolios which consist of assets with variance-gamma, gamma distributed and deterministic returns. The returns are assumed to be dependent. We derive analytical formulas for the downside and upside betas in the discussed framework. The established formulas depend on the values of a number of special mathematical functions including the values of the generalized hypergeometric ones.