Problem 1:
Hologram Corporation is a holding company with four main subsidiaries. The percentage of its business coming from each of the subsidiaries, and their respective betas, are as follow:
Subsidiary
Percentage of Business
Beta
Water Company 60% , .70
Cable Company 25% , .90
Real estate 10% , 1.30
Technology companies 5% , 1.50
Part 1: What is the company's beta?
Portfolio Beta = (percentage of water company x beta of water company) + (percentage of cable company x beta of cable company) + (percentage of real estate x beta of real estate) + (percentage of technology companies x beta of technology companies)
Portfolio Beta = (.60 x .70) + (.25 x .90) + (.10 x 1.30) + (.05 x 1.50)
Portfolio Beta = .42 + .225 + 0.13 + .075
Portfolio Beta = 0.85
Part 2: Assume that the risk-free rate is 6% and that the market risk premium is 5%. What is the holding company's required rate of return?
Beta (B) = .85
Risk Premium (RP) = .05
Risk Free Rate (RF) = .06
Rate of Return = RF + B(RP)
Rate of Return = .06 + .85(.05)
Rate of Return = .06 + .0425
Rate of Return = .1025 or 10.25%