Question

Consider a portfolio of 250 shares of rm A worth $30/share and 1500 shares of rm B
worth $20/share. You expect a return of 4% for stock A and a return of 9% for stock B.
(a) What is the total value of the portfolio, what are the portfolio weights and what is
the expected return?
(b) Suppose rm A's share price falls to $24 and rm B's share price goes up to $22.
What is the new value of the portfolio? What return did it earn? After the price
change, what are the new portfolio weights?

Answer 1

no. of shares of rm A = 250

Share price of rm A = $30

Expected return of rm A = 4%

no. of shares of rm B = 1500

Share price of rm B = $20

Expected return of rm B = 9%

a)

Total Value of the portfolio = Value of rm A + value of rm B

= no. of shares of rm A * share price of rm A + no. of shares of rm B * share price of rm B

= 250*$30 + 1500*$20 = $7,500 + $30,000 = $37,500

Weight of rm A = value of rm A / total value of portfolio = $7,500/$37,500 = 0.20

Weight of rm B = value of rm B / total value of portfolio = $30,000/$37,500 = 0.80

Expected Return of Portfolio = Weight of rm A * Expected Return of rm A + Weight of rm B * Expected Return of rm B

= 0.2 * 4% + 0.8*9% = 0.8% + 7.2% = 8.0%

b)

New share price of rm A = $24

New share price of rm B = $22

New Total Value of the portfolio = Value of rm A + value of rm B

= no. of shares of rm A * new share price of rm A + no. of shares of rm B * new share price of rm B

= 250*$24 + 1500*$22 = $6,000 + $33,000 = $39,000

Return Earned = Change in Portfolio Value / Initial Portfolio Value = ($39,000-$37,500)/$37,500

= $1,500/$37,500 = 4.00%

New Weight of rm A = value of rm A / total value of portfolio = $6,000/$39,000 = 0.1538

New Weight of rm B = value of rm B / total value of portfolio = $33,000/$39,000 = 0.8462