Measuring Industry Beta using a Combination of Black-Scholes model and Grey Theory

Abstract

When investigating projects and companies for investment purposes, most analysts use a discount rate that is derived from CAPM model. The calculated beta of this model is usually a representor of risks and opportunities of the relative industry but has almost no attention to risks and opportunities of the project or firm that is being investigated. This ignorance to risk measurement could make a poor discount rate which would lead to incorrect evaluation and reduction of Equity value. In most cases, correcting for risks and opportunities of beta, would make a big difference in the results. The goal of this paper is to provide a more accurate measurement of systematic risk of investment projects by considering it's relative risks and opportunities.In this research the adjusted beta from the model of Bernardo and others was calculated using 10 years of monthly return of all companies listed in Tehran Stock Exchange and Iran Farabourse. Then by mixing Grey Theory with the model, we tried improving the mentioned model. The grey beta of growth opportunities and grey beta of existing assets was calculated for all firms. Finally, to test the variables, some robustness checks was performed using Durbin test and Wu-Housman test. The results shows better performance of Grey BCG model. The calculated beta could be used to improve risk measurement of industries and firms. It also could help discount rate calculation and valuation of companies, projects and startups.

Keywords

• risk measurement
• growth beta
• existing assets beta
• grey beta
• capm