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Indices With a Weight Problem

The nation's tabloids are more than eager to discuss the weight problems of Keira Knightley and Kirstie Alley, but do they discuss the problems and opportunities created by different indices' disparate weighting schemes?

The answer, sadly, is no.

Yet some very real trading opportunities are created by nothing more than the way indices are constructed.

The S&P 500 Index, the default benchmark for many institutions, is capitalization-weighted.

Each stock's weight in the index is based on its price multiplied by the number of shares outstanding, divided by the total market capitalization of all stocks in the index.

The Dow Jones Industrial Average, in contrast, is a price-weighted index. It is calculated by summing the prices of the 30 stocks in the index and dividing by a divisor, now .12493117, that reflects the impact of splits and stock dividends.

The more expensive a stock is, the greater its weight in the Dow Industrial Average.

The relative weights of the 30 Dow stocks in both indices are presented in the chart below.


Comparative Weights in Dow Industrials and S&P 500
Click here for larger image.
Source: Bloomberg

What is the impact of the different weighting schemes? The stocks with the highest and lowest prices in the Dow are Boeing (BA) and Intel (INTC), which closed on Friday at $79.99 and $18.56, respectively. If both stocks rise by $1 a share, they have an equal impact on the Dow. However, Intel accounts for 0.9426% of the S&P 500 and Boeing 0.5584%, meaning its impact will be 1.69 times as large.

If one of the Dow stocks has a big move higher or lower, as 3M (MMM) did Friday or Altria (MO) Thursday, the disparate impact on the indices is noticeable. The $7.29 drop in 3M accounted for 58.4 points of the Dow's loss of 134.63 points, or 43.38% of the index's move. On the same day, 3M accounted for 0.607 points of the S&P 500's 8.60 point loss, or 7.06%.

The Embedded Option

The systematic impact of differential weighting over time should lead to a higher actual volatility for the Dow, and it does. Its standard deviation of returns since August 1974 has been 1.021725 times as great as that of the S&P 500; we will use this number in a trade illustration below. And even though the indices track each other remarkably well over long periods of time, considering their significant differences, they should not be viewed as substitutes for one another on a daily basis. If they were, we should expect both the regression coefficient and the r-squared to be far closer to one than the .855 and .7639 shown.


Indices Are Not Substitutes
Click here for larger image.
Source: Bloomberg

If the S&P 500's historic volatility is systematically lower than the Dow's historic volatility, can we capture this by owning a Dow strangle --­ long an out-of-the-money (OTM) call option and an OTM put option -- against a short S&P 500 straddle, short both the at-the-money (ATM) call and put options?
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