Question

Your client wants to invest in a portfolio of two stocks, A and B. Stock A has a beta of 1.15 while Stock B has a beta of 0.75. If you construct a portfolio that has the same systematic risk as the market, what percentage of the portfolio must be invested in Stock A?

Answer 1

Given about two stocks,

Beta of stock A, Ba = 1.15

Beta of stock B, Bb = 0.75

To construct a portfolio that has the same systematic risk as the market, portfolio beta is 1

let weight of stock A in portfolio is w

then, Weight of stock B is (1-w)

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

So, portfolio beta = Wa*Ba + Wb*Bb

=> 1 = w*1.15 + (1-w)*0.75

=> 1 = 1.15w + 0.75 - 075w

=> w = 0.25/0.4 = 0.625

So percentage of the portfolio must be invested in Stock A is 62.50% or 0.625