Question

You own a portfolio that has a total value of $215,000 and it is invested in Stock D with a beta of .86 and Stock E with a beta of 1.39. The beta of your portfolio is equal to the market beta. What is the dollar amount of your investment in Stock D?

Answer 1

Answer:  BP = BD(WD) + BE(WE)

                   1 = 0.86(1-WE) + 1.39WE

                   1 = 0.86-0.86WE + 1.39WE

                   1 = 0.86 + 0.53WE

                 -0.53WE = -0.14

                  0.53WE  = 0.14

                         WE   = 0.14/0.53

                         WE   = 0.2641509434

                         WD = 1 - WE

                         WD = 1 - 0.2641509434

                         WD = 0.7358490566

The dollar amount of investment in stock D = 0.7358490566 x $215,000

                                                                         = $158,207.54

Explanation: The beta of the portfolio is 1, which corresponds to the beta of the market. The beta of the portfolio equals beta of each stock multiplied by the percentage of fund invested in each stock(weight). The weight of stock D is equal to 1 - weight of stock E. Therefore, we need to make weight of stock E the subject of the formula by solving the problem mathematically and collecting the like terms. The weight of stock E is 0.2641509434. The weight of stock E will be subtracted from 1 so as to obtain the weight of stock D, which is 0.7358490566. The dollar amount of stock D equal to $215,000 multiplied by 0.7358490566, which is $158,207.54.