CFA Level IEquity InvestmentsEasy
A price-weighted index consists of three stocks priced at $40, $60, and $80, with a current divisor of 3.0. The stock priced at $60 undergoes a 2-for-1 stock split, and no other prices change. What must the new divisor be so that the index level remains unchanged immediately after the split?
- A1.5
- B2.0
- C2.5
- D3.0
Show answer & explanationAnswer & explanation
Correct answer: C. 2.5
Before the split, the index level is (40+60+80)/3 = 60. After the split, the $60 stock becomes $30, so the new sum of prices is 40+30+80 = 150. To keep the index at 60, the new divisor must satisfy 150/D' = 60, so D' = 2.5.
Why the other options are wrong
- A. This divisor would overstate the index (150/1.5 = 100).
- B. This divisor gives an index of 75, not the required 60.
- D. Using the old divisor would understate the index after the split (150/3 = 50).
Price-weighted index divisor adjustment
When a stock in a price-weighted index splits or a constituent changes, the divisor must be adjusted so the index level does not change due to the mechanical event.
- Index level = sum of prices / divisor
- Splits and constituent changes require divisor recalculation
- Only price changes (not corporate actions) should move the index
Memory trick: Split happens, price drops, divisor shrinks to keep the index steady.