# 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:

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%