In: Finance
Assume that you hold a. diversified 90,000 portfolio with a beta of 1.20 and that you are in the process of buying 1000 shares of a high tech stock at $10 a share with beta of 1.70 and adding it to this portfolio. also assume that risk free rate is 2% and that the expected rate of return on the market is 10.0% based of the CAPM what would be the expected rate of return. for your portfolio after the purchase of this stock
Step 1: Portfolio Beta
The beta of a portfolio is the weighted average beta of the securities which constitute the porfolio
Weight | Beta | Weight*Beta | |
Portfolio | 0.90(90000/(1000*10) | 1.20 | 1.08 |
High tech stock | 0.10(1-.9) | 1.70 | 0.17 |
Portfolio Beta = Weight*Beta
= 1.08+.17
= 1.25
Using Capital Asset Pricing Model
Expected Rate of Return = Rf + b ( Rm – Rf )
Where,
Rf – Risk free return = 2%
b – Beta = 1.25
Rm – Expected return on market portfolio = 10%
Expected Rate of Return = 2+1.25*(10-2)
= 2+1.25*8
= 2+10
= 12.00%