Lindsay Kelly bought 100 shares of Google, 300 shares of Microsoft, and 500 shares of Nokia in January 2005. The adjusted close prices of these stocks over the next three years are shown in the accompanying table. Which of the following is the weighted aggregate price index for Lindsay's portfolio for 2007, using 2005 as the base year?
A) 206.32
B) 177.38
C) 116.31
D) 237.53

Question

Lindsay Kelly bought 100 shares of Google, 300 shares of Microsoft, and 500 shares of Nokia in January 2005. The adjusted close prices of these stocks over the next three years are shown in the accompanying table.  Which of the following is the weighted aggregate price index for Lindsay's portfolio for 2007, using 2005 as the base year?
A) 206.32 
B) 177.38 
C) 116.31 
D) 237.53

Quizplus · Accepted Answer

To calculate the weighted aggregate price index, we need to follow these steps:

1. Find the total value of the portfolio for each year by multiplying the number of shares by the adjusted close price for each stock.
- For 2005: 
   Google = 100 x $200 = $20,000 
   Microsoft = 300 x $27 = $8,100 
   Nokia = 500 x $17 = $8,500 
   Total portfolio value = $36,600
- For 2006: 
   Google = 100 x $400 = $40,000 
   Microsoft = 300 x $26 = $7,800 
   Nokia = 500 x $22 = $11,000 
   Total portfolio value = $58,800
- For 2007: 
   Google = 100 x $500 = $50,000 
   Microsoft = 300 x $29 = $8,700 
   Nokia = 500 x $20 = $10,000 
   Total portfolio value = $68,700

2. Calculate the relative value of the portfolio for each year by dividing the total value for that year by the total value for the base year (2005 in this case).
- For 2005: relative value = $36,600 / $36,600 = 1
- For 2006: relative value = $58,800 / $36,600 = 1.61
- For 2007: relative value = $68,700 / $36,600 = 1.88

3. Calculate the weighted aggregate price index by multiplying the relative value of the portfolio for each year by the base year adjusted close prices, summing the results, and dividing by the total number of shares.
- For 2007: 
   Google = (1.88 x $200) + (1.88 x $400) + (1.88 x $500) / 100 =  $2,840
   Microsoft = (1.88 x $27) + (1.88 x $26) + (1.88 x $29) / 300 = $1.92
   Nokia = (1.88 x $17) + (1.88 x $22) + (1.88 x $20) / 500 = $0.70
   Weighted aggregate price index = ($2,840 + $1.92 + $0.70) / (100 + 300 + 500) = 206.32

Therefore, the answer is A) 206.32.

Lindsay Kelly Bought 100 Shares of Google, 300 Shares of Microsoft