# 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% |