Question

7.You have a $1,000 portfolio which is invested in stocks A and B plus a risk-free asset. $400 is invested in stock A. Stock A has a beta of 1.3 and stock B has a beta of 0.7. You want a portfolio beta of 0.9.

a.How much needs to be invested in stock B?

b.How much needs to be invested in the risk-free asset?

Answer 1

Given about a portfolio,

Total investment = $1000

investment in stock A = $400

Weight of stock A, Wa = investment in A/Total investment = 400/1000 = 0.4

Let investment in stock B be W, then investment in risk free asset Wf = 1 - 0.4 - W = 0.6-W

Beta of stock A Ba = 1.3

Beta of stock B Bb = 0.7

Beta of risk free assets Bf = 0

So, beta of the portfolio is weighted average beta of its assets.

a). So, portfolio beta = Wa*Ba + Wb*Bb + Wf*Bf

0.9 = 0.4*1.3 + W*0.7 + (0.6-W)*0

=> W = 0.5429

So, investment in stock B is W*total investment = 0.5429*1000 = $542.90

b). So, investment in risk-free asset = 1000 - 400 - 542.90 = $57.10