Question

A portfolio exists that contains equal weights of Five securities: A stock with a beta of 1.5, B stock with a beta of 2.0, C stock with a beta of -0.8, Dis a US Treasury Bond, and E is a security that tracks the market exactly. What is the beta of this portfolio?

What is the expected return of the A stock from the question assuming the Treasury Bond has a 1.72% yield and the expected return of the market is 5.16%?

Answer 1

The beta of the portfolio is :

So, the weights of the securities will be 1/5 = 0.2 as it is an equally weighted portfolio.

Beta of Portfolio A : Weight of security A* beta of security A  + weight of security B * beta of security B + weight of security C* Beta of security C

1/5 * 1.5 + 1/5 * 2 + 1/5 * -0.8 + 1/5 * 0 + 1/5 * 1 ( The beta of treasury bond will be zero, because it is free from any risk and the beta of the stock which tracks the market will be 1).

= 0.3 + 0.4 - 0.16 + 0 + 0.2

= 0.74

So,the beta of the portfolio is 0.74.

The expected return of Stock A as per the CAPM model is :

Re(A ) = Rf + beta (Rm - Rf)

= 1.72 + 1.5* ( 5.16 - 1.72)

= 6.88%

So, the expected return form Stock A is 6.88%.