You own three stocks: 600 shares of Apple Computer, 10,000 shares of Cisco Systems, and 5,000
shares of Colgate-Palmolive. The current share prices and expected returns of Apple, Cisco, and Colgate-Palmolive are, respectively, $460, $25, $110 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 $27, Cisco rises by $3, and Colgate-Palmolive falls by $10.
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?
To calculate the portfolio weights of the three stocks in your portfolio, you need to divide the value of each stock by the total value of your portfolio.
First, let’s calculate the value of each stock:
– Value of Apple Computer = 600 shares * $460/share = $276,000
– Value of Cisco Systems = 10,000 shares * $25/share = $250,000
– Value of Colgate-Palmolive = 5,000 shares * $110/share = $550,000
Next, calculate the total value of your portfolio:
Total Portfolio Value = $276,000 (Apple) + $250,000 (Cisco) + $550,000 (Colgate-Palmolive) = $1,076,000
Now, calculate the portfolio weights:
– Apple Weight = (Value of Apple / Total Portfolio Value) = ($276,000 / $1,076,000) ≈ 25.65%
– Cisco Weight = (Value of Cisco / Total Portfolio Value) = ($250,000 / $1,076,000) ≈ 23.22%
– Colgate-Palmolive Weight = (Value of Colgate-Palmolive / Total Portfolio Value) = ($550,000 / $1,076,000) ≈ 51.13%
So, the portfolio weights are approximately 25.65% for Apple, 23.22% for Cisco, and 51.13% for Colgate-Palmolive.
b. To calculate the expected return of your portfolio, you can use the weighted average of the expected returns of the individual stocks, where the weights are the portfolio weights calculated in part (a).
Expected Return of Portfolio = (Apple Weight * Expected Return of Apple) + (Cisco Weight * Expected Return of Cisco) + (Colgate-Palmolive Weight * Expected Return of Colgate-Palmolive)
Expected Return of Portfolio = (0.2565 * 12%) + (0.2322 * 10%) + (0.5113 * 8%)
Expected Return of Portfolio ≈ 9.27%
So, the expected return of your portfolio is approximately 9.27%.
c. Now, let’s calculate the new portfolio weights after the changes in stock prices:
After the changes:
– Apple’s new price = $460 + $27 = $487 per share
– Cisco’s new price = $25 + $3 = $28 per share
– Colgate-Palmolive’s new price = $110 – $10 = $100 per share
Now, calculate the new value of each stock:
– New Value of Apple = 600 shares * $487/share = $292,200
– New Value of Cisco = 10,000 shares * $28/share = $280,000
– New Value of Colgate-Palmolive = 5,000 shares * $100/share = $500,000
Calculate the new total portfolio value:
New Total Portfolio Value = $292,200 (Apple) + $280,000 (Cisco) + $500,000 (Colgate-Palmolive) = $1,072,200
Now, calculate the new portfolio weights:
– New Apple Weight = (New Value of Apple / New Total Portfolio Value) = ($292,200 / $1,072,200) ≈ 27.22%
– New Cisco Weight = (New Value of Cisco / New Total Portfolio Value) = ($280,000 / $1,072,200) ≈ 26.09%
– New Colgate-Palmolive Weight = (New Value of Colgate-Palmolive / New Total Portfolio Value) = ($500,000 / $1,072,200) ≈ 46.69%
So, the new portfolio weights are approximately 27.22% for Apple, 26.09% for Cisco, and 46.69% for Colgate-Palmolive.
d. Assuming the stocks’ expected returns remain the same, you can calculate the expected return of the portfolio at the new prices using the new portfolio weights:
New Expected Return of Portfolio = (New Apple Weight * Expected Return of Apple) + (New Cisco Weight * Expected Return of Cisco) + (New Colgate-Palmolive Weight * Expected Return of Colgate-Palmolive)
New Expected Return of Portfolio = (0.2722 * 12%) + (0.2609 * 10%) + (0.4669 * 8%)
New Expected Return of Portfolio ≈ 10.29%
So, assuming the expected returns of the stocks remain the same, the expected return of your portfolio at the new prices is approximately 10.29%.
In summary, the portfolio weights and expected returns of your portfolio have changed after the price fluctuations of the individual stocks. The new portfolio weights are approximately 27.22% for Apple, 26.09% for Cisco, and 46.69% for Colgate-Palmolive, with an expected return of approximately 10.29% at the new prices.
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