Question

You own three​ stocks: 600 shares of Apple​ Computer, 10 comma 000 shares of Cisco​ Systems, and 5 comma 000 shares of​ Colgate-Palmolive. The current share prices and expected returns of​ Apple, Cisco, and​ Colgate-Palmolive are,​ respectively, $ 537​, $ 24​, $ 93 and 12 %​, 10 %​, 8 %. a. What are the portfolio weights of the three stocks in your​ portfolio? b. What is the expected return of your​ portfolio? c. Suppose the price of Apple stock goes up by $ 24​, Cisco rises by $ 4​, and​ Colgate-Palmolive falls by $ 13. What are the new portfolio​ weights? d. Assuming the​ stocks' expected returns remain the​ same, what is the expected return of the portfolio at the new​ prices?

Answer 1

	No. of Shares	Share Price	Expected Return
Apple Computer	600	537	12%
Cisco System	10000	24	10%
Colgate Palmolive	5000	93	8%

(a) The above data is provided. We will first calculate the total value of od individual stocks in the portfolio.

Value of stock = No. of shares*Share Price

Value of Apple computer shares = 600*537 = 322200

Value of Cisco Systems shares = 10000*24 = 240000

Value of Colgate-Palmolive shares = 5000*93 = 465000

Total value of the portfolio = Value of Apple computer shares + Value of Cisco Systems shares + Value of Colgate-Palmolive shares = 322200+240000+465000 = 1027200

Weight of Apple computers =W_A = Value of Apple computer shares/Total value of the portfolio = 322200/1027200 = 0.3137 = 31.37%

Weight of Cisco Systems =W_C = Value of Cisco shares/Total value of the portfolio = 240000/1027200 = 0.2336 = 23.36%

Weight of Colgate-Palmolive =W_CP = Value of Colgate-Palmolive shares/Total value of the portfolio =465000/1027200 = 0.4527 = 45.27%

Weight of Apple computers =W_A = 31.37%, Weight of Cisco Systems =W_C = 23.36%, Weight of Colgate-Palmolive =W_CP = 45.27%

(b) Expected Return on Apple Computers = E[R_A] = 12%, Expected Return on Cisco Systems = E[R_C] = 10%, Expected Return on Colgate-Palmolive = E[R_CP] = 8%

Expected Return of the portfolio is calculated using the formula:

E[R_p] = E[R_A]*W_A + E[R_C]*W_C + E[R_CP]*W_CP​​​​​​​ = 12%*31.37% + 10%*23.36% + 8%*45.27% = 9.72%

Expected return of the portfolio = 9.72%

(c) Apple stock goes up by $ 24​, Cisco rises by $ 4​, and​ Colgate-Palmolive falls by $ 13

New share price of Apple = 537+24 = 561

New share price of Cisco = 24+4 = 28

New share price of Colgate-palmolive = 93-13 = 80

Value of Apple computer shares = 600*561 = 336600

Value of Cisco Systems shares = 10000*28 = 280000

Value of Colgate-Palmolive shares = 5000*80 = 400000

Total value of the portfolio = Value of Apple computer shares + Value of Cisco Systems shares + Value of Colgate-Palmolive shares = 336600+280000+400000 = 1016600

Weight of Apple computers =W_A = Value of Apple computer shares/Total value of the portfolio = 336600/1016600 = 0.3311 = 33.11%

Weight of Cisco Systems =W_C = Value of Cisco shares/Total value of the portfolio = 280000/1016600 = 0.2754 = 27.54%

Weight of Colgate-Palmolive =W_CP = Value of Colgate-Palmolive shares/Total value of the portfolio =400000/1016600 = 0.3935 = 39.35%

	No. of Shares	New Share Price	Expected Return	New value	Weights
Apple Computer	600	561	12%	336600	33.11%
Cisco System	10000	28	10%	280000	27.54%
Colgate Palmolive	5000	80	8%	400000	39.35%

New weight of Apple computers =W_A = 33.11%, New weight of Cisco Systems =W_C = 27.54%, New weight of Colgate-Palmolive =W_CP = 39.35%

(d) Expected Return on Apple Computers = E[R_A] = 12%, Expected Return on Cisco Systems = E[R_C] = 10%, Expected Return on Colgate-Palmolive = E[R_CP] = 8%

Expected Return of the portfolio is calculated using the formula:

E[R_p] = E[R_A]*W_A + E[R_C]*W_C​​​​​​​ + E[R_CP]*W_CP​​​​​​​ = 12%*33.11% + 10%*27.54% + 8%*39.35% = 9.88%

Expected Return of the portfolio at new prices = 9.88%