A share split in two differently weighted indices
Series XXI-B case study · set 3, case 4 of 6 · 5 questions · 2 marks each
Question 1 of 5Case practice
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A miniature market contains only two companies. Company A has 100 shares outstanding at ₹100 each. Company B has 300 shares at ₹50 each. A price-weighted index equals the sum of the two share prices divided by its divisor, initially 1.5, giving a level of 100. A separate market-capitalisation-weighted total market index also starts at 100. A then completes a two-for-one split: its shares double and its price halves, with no economic value change. The price-weighted divisor must be adjusted to preserve index continuity. After the split adjustment, A’s price rises from ₹50 to ₹55 while B stays at ₹50. There are no dividends, new issues, other corporate actions or free-float adjustments.
All amounts and contract terms in this case are hypothetical.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A miniature market contains only two companies. Company A has 100 shares outstanding at ₹100 each. Company B has 300 shares at ₹50 each. A price-weighted index equals the sum of the two share prices divided by its divisor, initially 1.5, giving a level of 100. A separate market-capitalisation-weighted total market index also starts at 100. A then completes a two-for-one split: its shares double and its price halves, with no economic value change. The price-weighted divisor must be adjusted to preserve index continuity. After the split adjustment, A’s price rises from ₹50 to ₹55 while B stays at ₹50. There are no dividends, new issues, other corporate actions or free-float adjustments.
All amounts and contract terms in this case are hypothetical.
Q1What is A’s initial weight in the capitalisation-weighted index?
Option A. 66.67%
Why it is wrong: This uses share prices alone, not market capitalisations.
Option B. 40% — Correct answer
Option C. 25%
Why it is wrong: This uses the share-count proportion alone.
Option D. 50%
Why it is wrong: The companies do not have equal market values.
Answer: B. A’s value is 100×₹100 = ₹10,000. B’s is 300×₹50 = ₹15,000. A’s weight is ₹10,000/₹25,000 = 40%. Remember: Market-capitalisation weighting includes both price and share count.
Hint, shown before you answer in practice mode: Multiply each company’s price by its own shares outstanding.
XXIB-S3-C04-Q1mediumnumerical
Q2Before the split, what is A’s weight in the price-weighted index?
Option A. 50%
Why it is wrong: The share prices are initially unequal.
Option B. 66.67% — Correct answer
Option C. 40%
Why it is wrong: This is the capitalisation weight.
Option D. 33.33%
Why it is wrong: This is B’s initial price weight.
Answer: B. ₹100/(₹100+₹50) = 66.6667%. Share counts do not determine this index’s weights. Remember: Different index construction rules create different exposures.
Hint, shown before you answer in practice mode: For this index, use A’s price divided by the sum of prices.
XXIB-S3-C04-Q2easynumerical
Q3What divisor keeps the price-weighted index at 100 immediately after the split?
Option A. 1.5
Why it is wrong: Keeping the old divisor would cause an artificial index fall.
Option B. 0.75
Why it is wrong: This halves the divisor although only one of the two prices halves.
Option C. 1.0 — Correct answer
Option D. 2.0
Why it is wrong: This would make the index level 50.
Answer: C. The new divisor must satisfy (₹50+₹50)/divisor = 100. Therefore divisor = 1.0. Remember: Adjust a price-weighted divisor to prevent a split being mistaken for a loss.
Hint, shown before you answer in practice mode: After the split, the price sum is ₹50 + ₹50.
XXIB-S3-C04-Q3mediumnumerical
Q4What is the price-weighted index return when A then rises to ₹55 and B is unchanged?
Option A. −30%
Why it is wrong: This incorrectly retains the old pre-split divisor.
Option B. 10%
Why it is wrong: This is A’s individual share-price return.
Option C. 4%
Why it is wrong: This is the capitalisation-weighted index return.
Option D. 5% — Correct answer
Answer: D. The new level is (₹55+₹50)/1 = 105. From the maintained level of 100, the return is 5%. Remember: Calculate market returns only after neutralising mechanical corporate actions.
Hint, shown before you answer in practice mode: Use the adjusted divisor and the post-adjustment starting level.
XXIB-S3-C04-Q4mediumnumerical
Q5By how many percentage points does the price-weighted return exceed the capitalisation-weighted return in the final price move?
Option A. 0 percentage points
Why it is wrong: The post-split index weights differ.
Option B. 5 percentage points
Why it is wrong: This assumes the capitalisation-weighted index did not move.
Option C. 1 percentage point — Correct answer
Option D. 6 percentage points
Why it is wrong: This incorrectly compares the index with A’s share return.
Answer: C. Total capitalisation rises from ₹25,000 to 200×₹55 + 300×₹50 = ₹26,000, a 4% return. Price-weighted return is 5%, giving a 1-percentage-point gap. Remember: Index construction can explain return differences even when both indices hold the same names.
Hint, shown before you answer in practice mode: After the split A has 200 shares. Compare total market values before and after the final price move.
XXIB-S3-C04-Q5hardnumerical
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