please help me with questions 4. (20%) Suppose you buy 2,500 shares of Microsoft

Question

please help me with questions

4. (20%) Suppose you buy 2,500 shares of Microsoft at $20 per share and 3,500 shares of Pepsi at $35 per share. If Microsoft's stock goes up to $30 per share and Pepsi stock falls to $30 per share and neither paid dividends, (1) What is the new value of the portfolio? What return did the portfolio earn? (2) Show that Eq. 11.2 is true by calculating the individual returns of the stocks and multiplying them by their weights in the portfolio. (3) If you don't buy or sell any shares after the price change, what are the new portfolio weights?

Explanation / Answer

Answer 1

Working Note 1
First we will calculate the present value of the portfolio i.e. before price change.

Microsoft = 2500 * $20 = $50,000
+
Pepsi       = 3500 * $35 = $1,22,500

Total                              = $1,72,500

Answer
New value of portfolio i.e. after price change

Microsoft = 2500*$30 = $75,000
+
Pepsi      = 3500*$30 = $1,05,000

Total                            = $1,80,000

Explanation = To find new value of portfolio just multiply the number of share by the new value of the share.

Return on portfolio --- It is % of what we earned over and above original investment.

Formula of return= New value – old value   x 100
                                         old value


Return =    $180000 - $172500 . x 100 = 4.35%
                          $172500


Answer 2

Just as we calculated portfolio return in the similar manner we will calculate individual return.

1. Microsoft = $30 - $20 =   $10 . x 100 = 50%
                                            $20

2. Pepsi = $30 - $35 =   -$5 . x 100 = -14.286%
                                      $35


Working note

we will calculate the old weight of the portfolio

To calculate weight just divide the individual share amount by total amount of investment

weight of Microsoft =   50000/172500 = 0.29

weight of Pepsi = 122500/172500 = 0.71


Total = .29+.71 = 1

Continuing answer

calculating return by multiplying individual return by respective weight

= .29 x 50% + .71 x -14.286%

= 4.35%


Answer 3

To calculate new weight just divide respective share amount by total amount after share price

New weight

Microsoft =   $75000 . = .4167
                   $180000

Peps =     $105000   . = .5833
                   $180000

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