Question

Paul McLaren holds the following portfolio: Stock Investment Beta A $150,000 1.40 B 50,000 0.80 C 100,000 1.00 D 75,000 1.20 Total $375,000 Paul plans to sell Stock A and replace it with Stock E, which has a beta of 0.75. By how much will the portfolio beta change? a. −0.260 b. −0.286 c. −0.190 d. −0.211 e. −0.234

Answer 1

Stocks	Value	Weight (A)	Beta (B)	Portfolio Beta (AXB)
Stock A	150000	0.4000	1.4	0.560
Stock B	50000	0.1333	0.8	0.107
Stock C	100000	0.2667	1	0.267
Stock D	75000	0.2000	1.2	0.240
Total	375000			1.173
CALCULATION OF THE REVISE OF BETA OF PORTFOLIO WITH STOCK E
Stocks	Value	Weight (A)	Beta (B)	Portfolio Beta (AXB)
Stock E	150000	0.4000	0.75	0.300
Stock B	50000	0.1333	0.8	0.107
Stock C	100000	0.2667	1	0.267
Stock D	75000	0.2000	1.2	0.240
Total	375000			0.913
Net Change in Beta of Portfolio = Beta of portfolio with Stock E - Beta of Portfolio with Stock A
Net Change in Beta of Portfolio = 0.913 - 1.173
Net Change in Beta of Portfolio = - 0.260
Answer = Option A = - 0.260