Icfai P. A. Application Of Portfolio Theories

Application of Portfolio Theories in Investment Risk Appraisal Exercises 1. A pharmaceutical company is considering a Fertilizer project to diversify its surplus funds. It has got a debt-equity ratio of 2:1, cost of debt is 14% and tax rate is 46%. It is considering Bhagya Fertilizers as a proxy company which has a debt-equity of 2, an asset beta of 0.69 and an effective tax rate of 34%. If the risk-free rate is 10% and the expected return on the market portfolio is 16%, what is the required rate of return for the fertilizers project as per the CAPM model if it intends to propose 2:1 leverage in the new project? 2. The existing investments of a firm consists of two projects 1 and 2 and have the following characteristics. σ1 =10,000; σ2 = 8,000 and ρ12 = 0.5 The firm is considering three new projects 3, 4 and 5 which have the same Standard Deviation of their net present value(i.e.) σ3 = σ4 = σ5 = 15,000. The coefficient of correlation between these new projects and the existing investments are Project 3 4 5

1 ρ31 = 0.6 ρ41 = 0.5 ρ51 = -0.6

2 ρ32 = 0.8 ρ42 = 0.0 ρ52 = -0.7

Required: Determine the standard deviation of NPV of various possible portfolios. Which portfolio reduces the total risk of the firm and why? 3. A portfolio consists of 3 securities 1, 2 and 3. The proportions of these securities are X1 = 0.3, X2 = 0.4, X3 =0.3. The standard deviation of returns on these securities are σ1 = 16, σ2 =19, σ3 = 8. The correlation coefficients among returns are ρ12 = 0.1, ρ13 = 0.5, ρ23 = -0.2. Calculate the standard deviation of the portfolio return.