Question

Rf=2%, Rm= 10%

An equal weighted portfolio of stock X and Rf yields a return of 10%

A portfolio of stock Y and Rf with a 75% investment in stock Y yields a return of 6.5%

What is the market beta of a portfolio if we invest 40%in X, 20% in Y, 20% in Rf and 20% in the market?

Answer 1

Weight of X = 0.5

Weight of Rf = 0.5

Expected return of Portfolio = Weight of X*Expected return of X+Weight of Rf*Expected return of Rf

10 = Expected return of X*0.5+2*0.5

Expected return of X = 18

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

18 = 2 + Beta * (10 - 2)

Beta = 2

Weight of Y = 0.75

Weight of Rf = 0.25

Expected return of Portfolio = Weight of Y*Expected return of Y+Weight of Rf*Expected return of Rf

6.5 = Expected return of Y*0.75+2*0.25

Expected return of Y = 8

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

8 = 2 + Beta * (10 - 2)

Beta = 0.75

Weight of X = 0.4

Weight of Y = 0.2

Weight of Rf = 0.2

Weight of Market = 0.2

Beta of Portfolio = Weight of X*Beta of X+Weight of Y*Beta of Y+Weight of Rf*Beta of Rf+Weight of Market*Beta of Market

Beta of Portfolio = 2*0.4+0.75*0.2+0*0.2+1*0.2

Beta of Portfolio = 1.15