# Price-weighted Index

A price-weighted index is a stock market index in which the constituent securities are weighted in proportion to their stock price per share. Price movement of companies with higher stock price have greater influence on the overall movement of the index.

Dow Jones Industrial Average is a prominent example of price-weighted indices.

The main advantage of the price-weighted index is its simplicity. The disadvantage is that in event of a stock-split, adjustment must be made to the divisor.

## Calculation

The weight of each stock in a price-weighted index can be calculated by dividing its stock price per share by the sum of share prices of all the stocks in the index. The weight for stock i can be calculated by dividing its price Pi by sum of prices of all stocks:

$$ w_i=\frac{P_i}{P_1+P_2+P_3+...+P_n} $$

The index can be created by summing the stock prices of the constituent securities at some time t and then dividing it by a arbitrary number, called divisor.

$$ Index=\frac{P_1+P_2+P_3+...+P_n}{D} $$

Once a divisor is set, it canâ€™t be changed arbitrarily. However, in event of a stock-split, it must be changes such that the index value before and after the split remains the same. This is important for the sake of continuity of the index.

## Example

On 2 January 2018, you created a price-weighted index of the 5 technology companies that you like namely Apple, Google, Facebook, Tesla and Microsoft. The following table shows their stock prices on 2 January 2018 and 13 April 2017:

Company | Ticker | Stock Price as at 2 Jan 2018 | Stock Price as at 13 April 2018 |
---|---|---|---|

GOOGL | 1073.21 | 1,037.29 | |

FB | 181.42 | 163.87 | |

Apple | AAPL | 172.26 | 174.14 |

Tesla | TSLA | 320.53 | 294.08 |

Microsoft | MSFT | 85.95 | 93.58 |

The sum of all prices is 1,833.37 and there are 5 stocks. The easiest way to create an index is to divide the sum of all stock prices by 5 and you get a value of 366.674 (=$1,833.37/5). This is the starting value of your index. On 13 April 2018, your index value would be worked out as follows:

$$ Index\ (13\ April\ 2018)=\frac{Sum\ of\ Stock\ Prices}{Divisor}=\frac{1,762.96}{5}=352.592 $$

If you want to start off the index with a value of 100, you must set the divisor different from 5 at time 0 i.e. 2 January 2018. The divisor to get you time 0 index value of 100 would be:

$$ Divisor=\frac{1,833.37}{100}=18.337 $$

The divisor must stay the same unless there is a stock split. The index value on 13 April 2018 based on starting value of 100 would be:

$$ Index\ (13\ April\ 2018)=\frac{Sum\ of\ Stock\ Prices}{Divisor}=\frac{1,762.94}{18.337}=96.159 $$

The percentage movement in both cases is the same i.e. a drop of 3.84%. Comparing the index drop with the drop in individual stock prices, you can see that the stocks with index return is skewed towards the company with highest stock price i.e. Google.

Company | Ticker | Stock Price as at 2 Jan 2018 | Stock Price as at 13 April 2018 | Return |
---|---|---|---|---|

GOOGL | 1073.21 | 1,037.29 | -3.35% | |

FB | 181.42 | 163.87 | -9.67% | |

Apple | AAPL | 172.26 | 174.14 | 1.09% |

Tesla | TSLA | 320.53 | 294.08 | -8.25% |

Microsoft | MSFT | 85.95 | 93.58 | 8.88% |

This is because Google has a disproportionately higher weight in the index, i.e. 58.53% and 58.83% at 2 January 2018 and 13 April 2018 respectively.