Stock Market Indices
Table of Contents
Here we'll take a look at price and value-weighted stock indices. Say our index covers two stocks (A and B) with the following number of shares outstanding.
| Stock | Shares Outstanding |
|---|---|
| A | 50 |
| B | 300 |
We'll consider the price of each stock over two days:
| Stock | Price Day 1 ($) | Price Day 2 ($) |
|---|---|---|
| A | 200 | 190 |
| B | 30 | 35 |
1 Price-Weighted Index (DJIA)
To construct a price-weighted index we can simply average the prices each day (sum them and here divide by 2). The only complication arises when a stock in the index splits. We don't want the split to affect the index value, so we adjust the divisor.
For example, say stock A splits on day 2. For the index value to stay the same, we have to make the divisor (d):
\[112.5=\frac{35 + 95}{d} \Rightarrow d = \frac{130}{112.5} = 1.1555\]
Obviously, in a price-weighted index
The stock with the highest price has the largest effect on the index.
This may be undesirable, depending on your use for the index, because a stock's price is not a meaningful value—a high price does not mean a large market cap.
A price weighted-index tracks:
The performance of a portfolio comprised of one share of each stock in the index.
| Day | Index Value |
|---|---|
| 1 | 115 |
| 2 | 112.5 |
| % Change | -0.021739130 |
2 Value-Weighted (S&P 500)
| Day | Market Cap A | Market Cap B | Total Market Cap | Index Value |
|---|---|---|---|---|
| 1 | 10000 | 9000 | 19000 | 100 |
| 2 | 9500 | 10500 | 20000 | 105.26316 |
| % Change | 0.0526316 |
3 Index Creation
\(100*\frac{P_1}{P_0}\frac{P_2}{P_1}\frac{P_3}{P_2}\frac{P_4}{P_3}\frac{P_5}{P_4} = 100\frac{P_5}{P_0}\)