Question

1/ You invest in a portfolio that has 2 assets: T-bills and a risky asset that has a beta of 1.6. If you
want a portfolio with a beta of 1.2, how much should you invest in each asset?

2/ An analyst at MGK Inc tells you that if you invest in CitrusJuice shares today, you will receive of a
return of 11%. Should you invest in the share based on this advice? Why or why not? Beta of
the stock = 1.1, risk free rate = 3% and market risk premium = 7%.

Answer 1

Dear student, only one question is allowed at a time. I am answering the first question

1)

Let the Investment in T-bills ( Weight of T bills in the portfolio ) be X

Now, since the portfolio will be only consisting of T-bills and the risky asset, the total weight of the portfolio which is sum of weights of all the assets of the portfolio = 1

So, Weight of T bills + Weight of risky asset = 1

So, Weight of risky asset = 1 - Weight of T bills

= 1 – X

As T-bills are risk free, their beta is always = 0

Portfolio Beta is the weighted average of betas of the assets of the portfolio

= Beta of T bills x Weight of T bills + Beta of risky asset x Weight of risky asset

So,

0 x X + 1.6 x ( 1 – X ) = 1.2

So, 0 + 1.6 – 1.6 X = 1.2

So, 1.6 X = 1.6 – 1.2

So, X = 0.4 / 1.6

= 0.25

So, Weight of T bills is 0.25 or 25% and 25% of the Investible amount will be invested in T bills

So, Investment in risky asset

= 1 – Investment in T bills

= 1 – 0.25

= 0.75 or 75%

So, 75% of the Investible amount will be invested in the risky asset