Dow Jones Distortion Index - additional details
The following provides additional details for my original post on the Dow Jones Distortion Index here.
Methodology details
The Dow Jones Distortion Index (“DJDI”) is defined as half of the sum of the absolute difference between each stock’s price-weighted contribution to the Dow Jones Industrial Average (“DJIA”) and its share of the DJIA total market cap. Let \(P_n\) equal the price of stock \(n\) and \(M_n\) equal the market capitalization of stock \(n\) on any given day. The DJDI is calculated as:
\[DJDI = \frac{1}{2}\sum_{n=1}^{N} |P^*_n - M^*_n|\]where \(P^*_n = \frac{P_n}{\sum_{i=1}^{N} P_i}\) is the share of the sum price of the DJIA components contributed by stock \(n\), \(M^*_n = \frac{M_n}{\sum_{i=1}^{N} M_i}\) is the share of the total market cap of the DJIA components contributed by stock \(n\), and \(N\) is the number of stocks comprising the DJIA (currently \(N = 30\)).
Real example: May 27, 2016
The following table illustrates how the DJDI is calculated, stock-by-stock, for May 27, 2016:
| Ticker | Market Cap (BN) | [M] Share of sum market cap | Price | [P] Share of sum price | Absolute difference (P - M) |
|---|---|---|---|---|---|
| AAPL | $549.66 | 10.21% | $100.35 | 3.85% | 6.37% |
| AXP | $62.31 | 1.16% | $65.52 | 2.51% | 1.35% |
| BA | $82.31 | 1.53% | $129.22 | 4.95% | 3.42% |
| CAT | $42.02 | 0.78% | $71.96 | 2.76% | 1.98% |
| CSCO | $145.46 | 2.70% | $28.92 | 1.11% | 1.59% |
| CVX | $192.28 | 3.57% | $102.02 | 3.91% | 0.34% |
| DD | $58.67 | 1.09% | $67.17 | 2.57% | 1.48% |
| DIS | $162.71 | 3.02% | $100.29 | 3.84% | 0.82% |
| GE | $276.97 | 5.15% | $30.12 | 1.15% | 3.99% |
| GS | $66.27 | 1.23% | $159.53 | 6.11% | 4.88% |
| HD | $166.62 | 3.10% | $133.94 | 5.13% | 2.04% |
| IBM | $146.72 | 2.73% | $152.84 | 5.86% | 3.13% |
| INTC | $149.07 | 2.77% | $31.57 | 1.21% | 1.56% |
| JNJ | $310.99 | 5.78% | $113.06 | 4.33% | 1.45% |
| JPM | $239.26 | 4.45% | $65.43 | 2.51% | 1.94% |
| KO | $193.73 | 3.60% | $44.78 | 1.72% | 1.88% |
| MCD | $108.20 | 2.01% | $123.25 | 4.72% | 2.71% |
| MMM | $102.43 | 1.90% | $168.89 | 6.47% | 4.57% |
| MRK | $156.34 | 2.91% | $56.48 | 2.16% | 0.74% |
| MSFT | $411.26 | 7.64% | $52.32 | 2.00% | 5.64% |
| NKE | $94.65 | 1.76% | $56.19 | 2.15% | 0.39% |
| PFE | $209.90 | 3.90% | $34.61 | 1.33% | 2.57% |
| PG | $216.75 | 4.03% | $81.43 | 3.12% | 0.91% |
| TRV | $33.39 | 0.62% | $114.18 | 4.37% | 3.75% |
| UNH | $127.41 | 2.37% | $134.00 | 5.13% | 2.77% |
| UTX | $84.32 | 1.57% | $100.76 | 3.86% | 2.29% |
| V | $189.96 | 3.53% | $79.66 | 3.05% | 0.48% |
| VZ | $206.34 | 3.83% | $50.62 | 1.94% | 1.89% |
| WMT | $222.07 | 4.13% | $70.75 | 2.71% | 1.42% |
| XOM | $373.24 | 6.94% | $90.01 | 3.45% | 3.49% |
| DJDI | 35.9% |