Module 2 · Equity

Security Market Indexes

EN: Index construction, weighting methods, and rebalancing.
VN: Cấu trúc index, các phương pháp gán trọng số, tái cân bằng.

1. Index Weighting Methods Core

\[ \text{Price-weighted}: w_i = \frac{P_i}{\sum P_i} \] \[ \text{Equal-weighted}: w_i = \frac{1}{N} \] \[ \text{Mkt-cap weighted}: w_i = \frac{P_i \cdot Q_i}{\sum P_i Q_i} \] \[ \text{Float-adjusted MCAP}: w_i = \frac{P_i \cdot \text{Float}_i}{\sum P_i \cdot \text{Float}_i} \] \[ \text{Fundamental-weighted}: w_i \propto \text{Fundamental}_i \text{ (sales, BV, CF, dividends)} \]

Examples

Price DJIA, Nikkei.
Mkt-cap S&P 500, MSCI.
Equal S&P 500 EWI.

Practice problem

3 stocks: prices $20/$50/$80, shares outstanding 100/40/25 (millions). Compute weight of stock 1 in price-weighted vs mkt-cap-weighted index.

Show solution

Price-weighted: 20/(20+50+80) = 20/150 ≈ 13.3%

Mkt cap: 20×100=2000, 50×40=2000, 80×25=2000 → 2000/6000

Price-weighted ≈ 13.3%; Mkt-cap = 33.3% (equal here by coincidence)

2. Bias by Method Concept

Price-weighted Bias toward high-priced stocks; arbitrary (stock splits change weights).
Mkt-cap Bias toward large/overvalued stocks (momentum-tilted).
Equal Bias toward small-cap and value; requires frequent rebalancing.
Fundamental Tilts toward value; lower turnover than equal-weight.

3. Return on a Price-Weighted Index Core

\[ \text{Index} = \frac{\sum P_i}{\text{Divisor}} \]

Divisor adjusted for stock splits, additions/deletions to keep index level continuous.

Practice problem

3-stock price-weighted index, divisor 3. Initial prices $20, $40, $60 → final prices $25, $42, $58. Compute return.

Show solution

Initial sum 120, final sum 125

Return = 125/120 − 1

≈ 4.17%

Practice problem Practice

Practice problem

A 3-stock price-weighted index has prices $20, $40, $60 (sum = $120). Stock #2 doubles to $80. Compute new index level if divisor stays at 3.

Show solution

New sum = 20 + 80 + 60 = 160

Index = 160 / 3

≈ 53.33 (was 40)