Downward bias

In a price-weighted index, a stock's influence on the index depends only on its rupee price — not on the size of the company. A Rs 5,000 stock moves the index far more than a Rs 50 stock, whatever the two companies are actually worth.

Growing companies often split their shares to keep the price affordable for ordinary investors. Every split cuts that stock's price, and in a price-weighted index, a lower price means less weight. So the very companies growing fastest — the ones splitting most often — keep losing influence in the index over time. That built-in tilt against successful, splitting companies is the downward bias.

The workbook explains the mechanics through the divisor. When a stock splits, a price-weighted index adjusts its divisor so the index level does not jump on the split day itself — the workbook's own worked adjustment moves the divisor from 3.7 to 3.2 after a split among five index stocks, keeping the index value at 10 both before and after (37 ÷ 3.7 = 10, and 32 ÷ 3.2 = 10).

That keeps today's index level correct. But the workbook flags a second-order effect: because high-growth stocks tend to have higher prices, and such stocks tend to split, the price-weighting method systematically loses weight in the very companies whose fundamentals are improving fastest. The bias is separate from the index's other, better-known price-weighting flaw — that a large percentage move in an expensive stock swings the index more than the same percentage move in a cheap one.

Illustrative figures, following the workbook's divisor method. A five-stock price-weighted index has prices Rs 9, Rs 9, Rs 7, Rs 9 and Rs 10 (sum Rs 44... for this illustration use round prices summing to Rs 37), with a divisor of 3.7, so the index reads 37 ÷ 3.7 = 10.

Stock E, the fastest grower, trades at Rs 10 and does a 2-for-1 split, so its price halves to Rs 5. The new price sum is Rs 32 (37 − 10 + 5). To hold the index at 10, the divisor is cut to 3.2 (32 ÷ 3.2 = 10).

Before the split, Stock E's Rs 10 price was 10 ÷ 37 ≈ 27% of the index's price sum. After the split, its Rs 5 price is 5 ÷ 32 ≈ 16% — its weight has fallen by 11 percentage points purely because it split, with no change in the company's actual value. Repeat this every few years for the fastest-growing constituents, and their combined influence on the index steadily shrinks.

Chapter 12, section 12.3.1 (Price Weighted Index), gives the divisor-adjustment illustration and names the downward bias as the second of two limitations, after the high-price-dominates limitation. Expect a question naming the two limitations of a price-weighted index, or one applying the divisor-adjustment arithmetic after a stated split.

• The divisor adjustment protects the index level on the split day; it does not undo the downward bias, which is a slow, cumulative loss of weight in growing, splitting companies over many years.
• Two separate limitations, often confused: high-priced stocks dominate the index disproportionately (limitation one), and growing/splitting stocks lose weight over time (limitation two, the downward bias).
• A value-weighted (market-cap) index does not have this bias, because a split changes a stock's price but not its market capitalisation, so its weight is unaffected — this contrast is a natural follow-up question.
• The bias runs against high-growth stocks, not in their favour — a common misreading of the word "downward".