CFA Level 1

Securities Markets - Computing Indexes


The methods of calculating the various weighting schemes is best explained by example:

Example: Price Weighted Series
Given the following series data, calculate the price weighted return over a one-year period.

Stock Price Info for Series 1


Answer:
To calculate the return over a one-year period, first calculate the price weighted series value at each date.

Price weighted index12/31/2003 = (15 + 25 + 40 + 80) = 40
                                                           4
Price weighted index12/31/2004 = (10 + 30 + 40 + 100) = 45
                                                           4

The one-year return for the price weighted series would thus be (45/40)-1 = 12.5%


Example: Market Weighted Series
Given the following series data, calculate the market weighted return over the one-year period.


Stock Price Info for Series 2

Answer:
Market weighted return = 390,000 x 100 = 109.59
                                     355,000

The 1-year return for the market weighted series would thus be (109.59/100)-1 = 9.59%.


Example: Unweighted Series
Given the following series data, calculate the unweighted return over a one-year period.


Stock Price Info for Series 3

Answer:
Geometric Average = (1.05 * 1.25 * 1.00 * 1.30)1/4 = 1.143



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