Fundamental weighted index

A value-weighted index has a built-in habit: whenever a stock becomes expensive, it becomes a bigger part of the index. The workbook states the criticism plainly — value weighting results in overweighting overvalued stocks and underweighting undervalued stocks.

A fundamental-weighted index breaks that link. Instead of weighting each company by what the market says it is worth, it weights by what the business actually produces — its sales, profits, book value, cash flows, dividends, net assets and the like.

If two companies have identical sales, they get identical weight, even if the market values one at twice the other. A price rise does not by itself increase a company's weight; only a change in the fundamental does.

The workbook notes these are also referred to as alternative indices.

Choosing the factor. The index designer first identifies the fundamental factor. It can be one factor or a combination; where several are used, the weight of each factor must also be set.

Setting weights (Table 8.1). Three companies, weighted by previous-year sales:

Measuring the move (Table 8.2). Prices go to Rs 170, Rs 1,500 and Rs 750 — changes of +70%, +25% and −11.76%:

(70% × 10%) + (25% × 50%) + (−11.76% × 40%)
= 7.00% + 12.50% − 4.70% = 14.80%

The index goes from 100 to 114.80.

Notice that price never entered the weights. Company B's share price is twelve times A's, but B's weight is five times A's because its sales are five times A's.

Factors and risk premia. The workbook closes the section with the link to Chapter 3: some factors of return are specific to individual securities, others are common to groups of securities, and the risk premium is the reward for exposure to these systematic risk factors.

Weight of company i = Fundamental of i ÷ Σ Fundamentals

Index return = Σ (Weight × Price return)

A benchmark-tracking portfolio of Rs 10 lakh follows the workbook's sales-weighted index from Table 8.1:

Rs 11,47,960 ÷ Rs 10,00,000 − 1 = 14.80%   → index 114.80

Now the rebalancing question. After the move, the portfolio holds A at 14.8% of value, B at 54.4% and C at 30.7%. But weights are set by sales, not price. If sales are unchanged at the next reset, the portfolio sells some A and B and buys C to get back to 10 / 50 / 40.

That is the fundamental index doing what it was designed to do: trimming the stocks whose prices ran ahead and adding to the one that fell, which is the opposite of what a value-weighted index does automatically.

Chapter 8, section 8.3 names fundamental weighting as one of the four schemes; section 8.3.4 (Fundamental weighted and factor-based Index) gives the rationale and the Table 8.1 / 8.2 worked example ending at 114.80. Expect the rationale question — which criticism of value weighting it answers — and a weighted-return calculation.

• It counters overweighting of overvalued stocks — the criticism of value weighting. It is not a fix for price-weighted indices.
• Weights come from fundamentals, not price or market cap. Company B's Rs 1,200 share price is irrelevant to its 50% weight.
• Also called "alternative indices" in the workbook.
• It can use one factor or several; with several, the factor weights must be set too.
• Index return is the weighted average of price returns using fundamental weights: 14.80% in the example, so the level is 114.80, not 14.80.
• Do not confuse with an equal-weighted index, which gives every stock the same weight regardless of fundamentals.