3. (20%) Suppose you purchased Spotlight Co.\'s stock on Nov 1, 2015 and held it

Question

3. (20%) Suppose you purchased Spotlight Co.'s stock on Nov 1, 2015 and held it for one year, selling on Oct 31, 2016. What was your annual realized return? Date Price Dividend Nov 01 15 Feb 15 16 Aug 15 16 Oct 31 16 30 28 27 29 1.5 0.5 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? 5, (2096) What is the standard deviation of a portfolio with specified amounts invested in Apple and Target? Standard Deviation 0.5 0.8 Weight Correlation with Apple Apple 0.3 Target 0.7 0.3

Explanation / Answer

Answer 3

Formula for return = New price – old price + dividend received x 100
                                                    old price

= (29-30)+1.5+0.5 x 100 = 3.33%
             30

Answer 4

Part 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


Part 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%


Part 3

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

New weight

Microsoft =   $75000 . = .4167
                   $180000

Pepsi =     $105000   . = ..5833
                   $180000

Answer 5

Formula standard deviation for portfolio = root of (2A2A + 2B2B + 2ABrAB)

Notation for formula

Standard deviation for apple = A
Standard deviation for Target = B
Weight of apple = WA
Weight of Target = WB
Co-relation between stock = r

just put the values in the formula to find the standard deviation of the portfolio

= root of [(0.3)2A*(0.5)2A + (0.7)2B*(0.8)2B + 2(0.3)(0.7)(0.3)(0.5)(0.8)]

= 0.6217

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