Question

You have a $ 2 million portfolio consisting of $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio's new beta be after these transactions?

Answer 1

1/20= 5%
older stock contribution of risk= 0.9*0.05=0.045
New stock contribution of risk= 1.4*0.05=0.07
Now just simply eliminating the effect of older beta and adding the contribution of new beta
1.1-0.045+0.07=1.125

Answer 2

Suppose you manage a $4 million fund that consists of four stocks with the following
investments:
Stock Investment Beta
A $ 400,000 1.50
B 600,000 0.50
C 1,000,000 1.25
D 2,000,000 0.75
If the market’s required rate of return is 14% and the risk-free rate is 6%, what is the
fund’s required rate of return?

Answer 3

Porfolio beta=weight of stock A* beta of stock A+ weight of stock B*beta of stock B+ weight of stock C*beta of stock C + weight of stock D*beta of stock D
=0.1*1.50+0.15*-0.5+0.25*1.25+0.5*0.75
=0.7625
Fund's required rate of return=Risk free rate+(Market return-Risk free rate)*Beta
=6+(14-6)*0.7625
=12.1%