Work out values and returns for indexes weighted by price, by market capitalisation and equally
The idea
An index's weighting method decides how much each constituent moves it. A price-weighted index sums share prices and divides by a divisor, so high-priced stocks dominate and the divisor must be adjusted after splits to keep the index level unchanged. A market-capitalisation-weighted index weights by price times shares outstanding, so the largest companies dominate and the index rebalances itself as prices move. An equal-weighted index averages the constituents' returns, which tilts it towards smaller companies and requires regular rebalancing. Price return uses price changes alone; total return also adds dividends: (ending value - beginning value + income) / beginning value.
A practice question
A price-weighted index holds three stocks priced at 40, 25 and 85. Over the period they move to 44, 24 and 90. The index's price return is closest to:
- 3.96%Why not: Averaged the three stocks' own returns, which is the equal-weighted index return, not the price-weighted one.
- 2.67%Why not: Reported the change in index points (8 / 3) as though it were a percentage return.
- 5.33% — correct
A price-weighted index moves with the sum of prices: 150 to 158, so the return is 158 / 150 - 1 = 5.33%. Equal-weighting would give 3.96%.
A harder one
Stock A has 100 shares outstanding and moves from 20 to 22. Stock B has 50 shares and moves from 60 to 57. Stock C has 200 shares and moves from 10 to 11. The return of a market-capitalisation-weighted index of the three is closest to:
- 0.00%Why not: Summed the prices without share counts, which is the price-weighted return (90 to 90).
- 3.57% — correct
- 5.00%Why not: Averaged the individual returns of 10%, -5% and 10%, which is the equal-weighted return.
Market values start at 2,000 + 3,000 + 2,000 = 7,000 and end at 2,200 + 2,850 + 2,200 = 7,250, so the return is 7,250 / 7,000 - 1 = 3.57%.
The hardest tier
A market-capitalisation-weighted index rises from 1,250 to 1,300 over a year, and its constituents pay dividends worth 18 index points. The index's total return is closest to:
- 5.44% — correct
- 4.00%Why not: Computed only the price return (1,300 / 1,250 - 1) and left out the dividends.
- 5.23%Why not: Divided the gain plus dividends by the ending value of 1,300 instead of the starting 1,250.
Total return = (1,300 - 1,250 + 18) / 1,250 = 68 / 1,250 = 5.44%. Price return alone is 4.00%; the dividends add 1.44 percentage points.
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