Question

Assume that rf= 5% and rm = 15%. What are the expected returns of projects that have a beta of 2.0, 1.5, 1.0, and 0.5? What are the expected returns of projects that have a beta of 0 or -0.5?

Answer 1

Part 1:
Expected return=Risk free rate+Beta*(Market return - Risk free rate of return)

Given that the risk free rate=5% and market return=15%
When Beta values are 2.0, 1.5, 1.0, and 0.5 the value of expected returns will be:

When beta=2
Expected return=5% +2*(15%-5%)=5% +2*(0.1)=0.05 +0.2=0.25=25.00%

When beta=1.5
Expected return=5% +1.5*(15%-5%)=5% +1.5*(0.1)=0.05+0.15=0.2=20.00%

When beta=1
Expected return=5% +1*(15%-5%)=5% +1*(0.1)=0.05 +0.1=0.15=15.00%

When beta=0.5
Expected return=5% +0.5*(15%-5%)=5% +0.5*(0.1)=0.05+0.05=0.1=10.00%

Part 2:
Expected returns of projects that have a beta of 0 or -0.5

When beta=0
Expected return=5% +0*(15%-5%)=5%

When beta=-0.5
=5% +(-0.5)*(15%-5%)=5%-0.5*(0.1)=0.05-0.05=0%