Question

PLEASE SHOW IT IN A SIMPLE WAY that is easy to follow! and some explinations for steps if possible. THANK YOU!

You want to create a $65,000 portfolio comprised of two stocks plus a risk-free security. Stock A has an
expected return of 14.2 percent and stock B has an expected return of 17.8 percent. You want to own
$20,000 of stock B. The risk-free rate is 4.8 percent and the expected return on the market is 13.1
percent. If you want the portfolio to have an expected return equal to that of the market, how much
should you invest in the risk-free security?

Answer 1

In order to calculate this, let us assume amount invested in Risk-free security is x.

Now, per formula,

Return of Portfolio = Weight of Stock A * Expected Return of Stock A + Weight of Stock B * Expected Return of Stock B + Weight of Risk free asset * Expected Return of Risk free asset.

Weight of stock B = 20000/65000 = 4/13.

Weight of Risk Free Asset = x/65000

Weight of Stock A, hence = (65000-20000-x)/65000 = (45000-x)/65000

Plugging everything into a mathematical expression:

0.094x = 6390 - 4940

x = $15,425.5. This is the amount to be invested in risk free security