Oct 03 2010

The performance of stock market is usually an important component in Macroeconometrics analysis. We usually use stock indices as indicator for stock market. Since stock indices are constructed in various ways, we should pay additional attention to each individual stock index.

The Construction of DJIA is as follows:

Thirty stocks are included in the index. Prices of the stocks are added together directly and then multiplied by an adjusting divisor. Each time, a stock pays a large sum of dividend or splits into multiply shares, the adjusting divisor is modified so as to ensure the index evolves smoothly. It worth noticing that the divisor is multiplied to all stock prices rather than a single one. Therefore, even if only one of the stock price jumps due to some reason, the divisor for all prices will be changed.

Shoven and Sialm wrote a paper about the flaws of the Dow Jones Industrial Average. According to their argument, there are 3 flaws of DJIA. Their major focus is whether these flaws induce large statistical error into DJIAs portrait of the stock market as a whole.

Firstly, stock prices are added together directly, or called an equally weighted summation of prices. It fails to capture quantity of the stock — as long as their stock prices are identical, two corporations, whatever their size may differ from each other, share the same weight in this index. To rectify this flaw, the authors considered a different weighting index — weight based on each stocks relative share of the stock market. And they found no significant improvement by doing this.

Secondly. There are thousands on stocks in the financial market, while only thirty of them are included in DJIA. Whether such a small component is a satisfying representative of the whole market? The two authors enlarged the index by including more stocks. The results tends to support the argument that thirty stocks are enough.

Thirdly, no dividend-correction procedures are considered in DJIA — in fact, few stock indices consider dividend correction. Suppose the index keep constant over time, while all gains are tunneled out of financial market as dividends. Could we say that to invest into the stock market results in positive returns? Also proved by Shoven and Sialm, ignoring dividend payments leads to a significant underestimate of stock returns, especially in the long run.

In conclusion, the equally weighted prices and only a small portion of stocks included are not fatal flaws with DJIA. But, is it still a proper indicator due to the ignorance of dividends? From my point of view, not exactly. What we care in macroeconometric analysis is that. whether it can explain and forecast other economy indicators and whether it can be explained and forecast by others satisfactorily. There is at least one condition under which ignoring dividend payments matters little — as long as the dividend are payed in a rather regular pattern, thus it will not cause explanatory or forecasting errors. Since Shoven and Sialm merely examined the statistical summary of DJIA with dividends, we may require further investigation on stability of the pattern of dividend payments. It is an issue for almost all stock indices.