In: Finance
Stock Amount Beta
A 25,000 0.2
B 20,000 1.0
C 30,000 1.8
D 25,000 1.6
Risk-free rate is 3% and the market risk premium is 8%.
If stock E with its beta of 0.6 and has an expected return of 8.2% should it be added to the portfolio?
Portfolio Beta = weighted average of beta of the stocks in the portfolio where weights are the proportion of stock in the portfolio .
Total amount of stocks invested in portfolio = 25000 + 20000 + 30000 + 25000
= 100000
Weight of stcok A = 25000 / 100000 = 25%
Weight of stock B = 20000 / 100000 = 20%
Weight of stock C = 30000 / 100000 = 30%
Weight of stock D = 25000 / 100000 = 25%
Portfolio Beta = 0.25 * 0.20 + 0.20 * 1 + 0.30 * 1.8 + 0.25 * 1.6
= 1.19
Aas per the CAPM ,
Required rate of return = risk free rate + market risk premium * beta
= 3 + 8 *1.19 = 3 +9.52 = 12.52%
The amount of stock E is missing so lets assume amount to be $20000
Total amount of stocks invested in portfolio = 25000 + 20000 + 30000 + 25000 + 20000
= 120000
Weight of stcok A = 25000 / 120000 = 20.83%
Weight of stock B = 20000 / 120000 = 16.67%
Weight of stock C = 30000 / 120000 = 25%
Weight of stock D = 25000 / 120000 = 20.83%
Weight of stock E = 20000 / 120000 = 16.67%
Portfolio Beta = 0.2083 * 0.2 + 0.1667*1 + 0.25*1.8 + 0.2083*1.6 + 0.1667*0.6
= 1.98
Revised expected return = 3 +8 * 1.98 = 18.84%
The required rate of rteurn will increase hence we can add it to portfolio.