## Tuesday, October 25, 2011

### Characteristics of Security Indexes

CFA Level 1 - Securities Markets

The Three Predominant Weighting Schemes
In constructing stock market series, there are three predominant weighting schemes used:

1.
Price weighted series
2. Market weighted series
3. Unweighted series

1. Price Weighted Series
A price weighted series is the average of the stocks" prices in the series. It is calculated by adding together each stock price and dividing the total by the number of stocks in the series.

Formula 12.1

Price weighted series
= Sum of stock prices
# of stocks

The main problem that occurs with the price weighted series is the effect a price change in a high-priced stock will have on the series, as well as the lack of effect a low-priced stock will have on the series.
Two well-known examples of a price weighted series are the Dow Jones Industrial Average and the Nikkei Dow Jones Stock Average.

2.Market Weighted Series
A market weighted series is the market value (stock price multiplied by shares outstanding) of each company in the series divided by a sum calculated in the base period. This amount is then multiplied by the base value.

Formula 12.2

Sum of current market values * beginning value
Sum of base market values

Similar to the price weighted series, the major problem with the market weighted series is the effect a market value change in a large market cap stock will have on the series, as well as the lack of effect a small market cap stock will have on the series.

Well-known examples of a market-weighted series are the S&P 500 Index Composite, the New York Stock Exchange Index and the Financial Times Actuaries Share Indexes.

3. Unweighted Series
An unweighted series is based on the average price movement of the stock prices in the index. In this series, all stocks, no matter what the price, have the same effect on the series. To calculate the unweighted series, take an arithmetic average or a geometric mean of the relative returns.

Formula 12.3
 Unweighted price series = (X1 + X2 + ... + Xn)1/n

The Value Line Composite Average and the Financial Times Ordinary Share Index are examples of unweighted series.

Predominant Weighting Schemes Bias: Source and Direction

-Price Weighted Series Bias
Recall that the denominator of the price weighted series is the number of stocks with the stock price as the numerator. The problem occurs when a stock dividend or stock repurchase takes place. The numerator is adjusted to reflect the new stock price and the denominator needs to be adjusted to reflect the stock change. These changes tend to put a downward bias on the series as larger firms split their stock.

-Market Weighted Series Bias
As mentioned previously, large market cap stocks have a greater effect on the market weighted series relative to small market cap stocks.   As such, swings in the value of the larger cap stocks will have a greater effect on the overall series.

-Unweighted series Bias
The calculation of an unweighted series can be done through an arithmetic or geometric average. But if a geometric average is used, there will be a downward bias relative to pricing as compared to the series calculation using the arithmetic average.

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