Question

Suppose Ms. Heiress has a Portfolio Q made up of $2.8 million invested in Endicott Energy stock, and $1.2 million invested in Tyson Foods. Portfolio Q has a beta of 1.47. Ms. Heiress wants to sell the stock of Tyson Foods which has a beta of 0.93, and replace it with the stock of Phillip Morris which has a beta of 1.15, without altering the investment weights. What will be the new beta of Portfolio Q after this transaction?

Answer 1

Value of Portfolio Q
= Amount Invested in Endicott Energy stock
+ Amount Invested in Tyson Foods
= $2,800,000 + $1,200,000
= $4,000,000
Weight of Endicott Energy stock in Portfolio Q
= Amount Invested in Endicott Energy stock / Value of Portfolio Q
= $2,800,000 / $4,000,000
= 0.70
Weight of Tyson Foods in Portfolio Q
= Amount Invested in Tyson Foods / Value of Portfolio Q
= $1,200,000 / $4,000,000
= 0.30
Beta of a Portfolio is the weighted average beta of the stocks in the portfolio.
So,
Beta of Portfolio Q
= Beta of Endicott Energy stock*Weight of Endicott Energy stock
+ Beta of Tyson Foods*Weight of Tyson Foods
1.47 = Beta of Endicott Energy stock*0.70 + 0.93*0.30
1.47 = Beta of Endicott Energy stock*0.70 + 0.279
Beta of Endicott Energy stock*0.70 = 1.47 - 0.279
Beta of Endicott Energy stock*0.70 = 1.191
Beta of Endicott Energy stock = 1.191/0.70
Beta of Endicott Energy stock = 1.70
Now,
Weight of Phillip Morris in Portfolio Q
= Weight of Tyson Foods in Portfolio Q
= 0.30
New Beta of Portfolio Q
= Beta of Endicott Energy stock*Weight of Endicott Energy stock
+ Beta of Phillip Morris*Weight of Phillip Morris
= 1.70*0.70 + 1.15*0.30
= 1.19 + 0.345
= 1.535