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?
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 |
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