Question

You have $150,000 to invest in a stock portfolio. Your choices are stock A with an expected return of 16% and stock B with an expected return of 10%. Your goal is to create a portfolio with an expected return of 14%. How much money do you invest in stock B?

Answer provided: $50,000

Why, what is the formula?

Answer 1

Total weight of the portfolio is always 1

So, Investment weight of stock A + Investment weight of stock B = 1

So, Investment weight of stock A = 1 – Investment weight of stock B

Now, Weighted average of returns of stocks in a portfolio is the expected return of the portfolio

So, Expected return of the portfolio

= Weight of stock A x Return of stock A + Weight of stock B x Return of stock B

So, 0.14 = (1 – Weight of stock B) x 0.16 + Weight of stock B x 0.10

So, 0.14 = 0.16 – 0.16 x Weight of stock B + 0.10 x Weight of stock B

So, 0.06 x Weight of stock B = 0.16 – 0.14

So, Weight of stock B = 0.02 / 0.06

= 0.3333 or 1/3^rd

So, Value of investment in stock B

= Total investment amount x Weight of stock B

= $150,000 x 1 / 3

= $50,000