Question

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?

Answer 1

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.