You hold a diversified $100,000 portfolio consisting of 20 stocks with $5,000 invested in each.The portfolio's beta is 1.12.You plan to sell a stock with b = 0.90 and use the proceeds to buy a new stock with b = 2.50.What will the portfolio's new beta be? Do not round your intermediate calculations.
A) 1.032
B) 1.260
C) 1.476
D) 1.200
E) 1.236

Question

Quizplus · Accepted Answer

1. Calculate the portfolio's current beta:
Portfolio Beta = (Weighted Beta of all stocks)
Weighted Beta of all stocks = (Beta of Stock 1 x Weight of Stock 1) + ... + (Beta of Stock 20 x Weight of Stock 20) 
 = (1.12)

2. Calculate how much the sale of the old stock will affect the portfolio's beta:
Change in Portfolio Beta = (Amount to be sold / Current Portfolio Value) x Beta of old stock
 = (5000 / 100000) x 0.90 
 = 0.045

3. Calculate how much the purchase of the new stock will affect the portfolio's beta:
Change in Portfolio Beta = (Amount to be bought / Current Portfolio Value) x Beta of new stock
 = (5000 / 100000) x 2.50 
 = 0.125

4. Calculate the portfolio's new beta:
New Portfolio Beta = Current Portfolio Beta + Change in Portfolio Beta
 = 1.12 + (0.125 - 0.045)
 = 1.20

You Hold a Diversified $100,000 Portfolio Consisting of 20 Stocks