14. Consider the following security information for 4 securities making up an index: Price Shares Security time = 0 time = 1 Outstanding 8 13 20 million 2 22 25 50 million 3 35 30 120 million 4 50 55 75 million What is the change in the value of the index from time = 0 to time = 1 if the index is calculated using a valueweighted arithmetic mean? Solution: For a valueweighted arithmetic mean, the change is calculated as follows: First, the market value at time = 0 is calculated as: Price Shares Market Security time = 9 time = 1 Outstanding Value 1 8 13 20 million $ 160 2 22 25 50 million $1,1{H} 3 35 30 120 million $4,213!) 4 5t} 55 "I5 million $3350 $9,2i0 The change is then calculated as: [138 160 25 22 \"DD 3035 4200 5550 3750] x +>