Question

Johnny 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 Johnny 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? (Please state your answer in 2 decimal points)

Answer 1

From the given information about Johnny's portfolio calculating weight and weighted average beta.

stock	Investment	Beta	weight	weight*beta
A	150000	1.4	40.00%	0.56
B	50000	0.8	13.33%	0.11
C	100000	1	26.67%	0.27
D	75000	1.2	20.00%	0.24
Totla portfolio	375000		portfolio beta	1.17

So current beta of portfolio is 1.17

if stock A is replaced with stock E of beta 0.75, new beta is

New beta = 0.75*0.4 + 0.8*0.1333 + 1*0.2667 + 1.2*0.2 = 0.91

So, change beta is change by a value of 0.91-1.17 = -0.26