CFA Level IEquity InvestmentsMedium
A price-weighted index consists of three stocks priced at $50, $30, and $100, with a current divisor of 3.00 (so the index level equals 60.00). The $100 stock undergoes a 2-for-1 stock split, reducing its price to $50, with no change in the prices of the other two stocks. To keep the index level unchanged immediately after the split, what should the new divisor be?
- A1.44
- B3.00
- C4.33
- D2.17
Show answer & explanationAnswer & explanation
Correct answer: D. 2.17
Before the split, index = (50+30+100)/3 = 180/3 = 60.00. After the split, new sum of prices = 50+30+50 = 130. To keep index level at 60.00, new divisor = 130/60 = 2.1667 ≈ 2.17.
Why the other options are wrong
- A. This results from dividing the pre-split sum by the post-split sum instead of solving for the divisor correctly.
- B. This is the unchanged divisor, which would incorrectly alter the index level after the split.
- C. This results from inverting the correct ratio (60/130 rather than 130/60).
Price-Weighted Index Divisor Adjustment (Stock Split)
When a component of a price-weighted index undergoes a stock split, the divisor must be adjusted downward so that the index level remains unchanged immediately after the split.
- Stock splits reduce a stock's price but not its economic value, requiring divisor recalculation.
- New divisor = New sum of prices ÷ Pre-split index level.
- Divisor decreases whenever a stock split lowers a high-priced stock, since price sum falls but index level must stay constant.
Memory trick: Split the price, shrink the divisor — the index stays put like a see-saw balancing.