You own a portfolio that has a total value of $130,000 and a beta of 1.28. You have another $49,000 to invest and you would like the beta of your portfolio to decrease to 1.18. What does the beta of the new investment have to be in order to accomplish this

Answer:βB = 0.9147=beta of new investment

Explanation:

Total investment = $130,000 + $49,000 = $179,000

Using

Portfolio beta (βp) = wA * βA + wB * βB

Where βp is the portfolio beta coefficient,

wA is the weight of the first investment,

βA is the beta coefficient of first investment;

wB is the weight of the second investment,

βB is the beta coefficient of second investment

but weight of investment is stock value / total investment x 100

wA = 130,000 / 179,000X 100=72.63%

WB = 49,000/179,000 X100=27.374%

Portfolio beta (βp) = wA * βA + wB * βB

1.18 = (72.63%*1.28) + (27.374% XβB)

1.18=0.9296+0.27374βB

βB i = (1.18-0.9298) / 0.27374

βB = 0.9147=beta of new investment