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Beneath the Calm Waters: A Study of the Dow Index

Explore the relationship between Dow Jones Industrial Average component stock prices and index movements to understand the impact of the set divisor on index valuation. Analyze the daily stock prices and index values to uncover patterns and biases. The study covers data from November 1999 to November 2002, providing insights into the dynamics of the DJIA and its individual components.

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Beneath the Calm Waters: A Study of the Dow Index

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  1. Beneath the Calm Waters: A Study of the Dow Index Group 5 members Project Choice: Hyo Joon You Data Retrieval: Stephen Meronk Statistical Analysis: Christopher Ross Powerpoint Presentation: Anthony Mak Executive Summary: Joseph Singh Technical Appendix: Alejandro Vicente DJIA

  2. Brief info about the Dow • A measure of entire U.S. market, covering all major industries • Maintained and reviewed by the editors of WSJ. Stocks selected for reputation, growth, popularity, representation of its industry • Dow Jones Index currently consisting of 30 components (individual companies) DJIA

  3. DJIA Calculation • DJIA = sum of component stock prices divided by a divisor where It = Dow index value at time t, dt = divisor value at time t, and P(i,t) = price of component i at time t. DJIA

  4. Introduction • What: Is there a relationship between the Dow Jones set divisor and DJIA? • Why: If there is, then the index is biased in that the divisor, which is determined by WSJ, can be set in such a way as to keep the DJIA levels relatively constant when prices of the components are in fact changing. An unbiased divisor should only reflect splits and dividends. • How: Analyze daily prices of stocks and find the relationship between changes in DJIA and divisor. DJIA

  5. Data • Closing index values and prices at each operating day from November 1st, 1999 to November 22nd, 2002 DJIA

  6. DJIA

  7. Exploratory Analysis • Is there a relationship between the change in the number of shares held for each individual stock versus the change in price? %#shares = (1)*%S(1) + ((2)*%S(2) + . . . + ((30)*%S(30) + C

  8. Call: lm(formula = shares ~ MMM + AA + T + AXP + CAT + C + KO + DD + EK + XOM + GE + GM + HPQ + HD + HON + INTC + IBM + IP + JPM + JNJ + MCD + MRK + MSFT + MO + PG + SBC + BA + DIS + UTX + WMT + 0, data = P) Residuals: Min 1Q Median 3Q Max -1.39436 -0.24627 -0.02073 0.24519 1.94281 Coefficients: Estimate Std. Error t value Pr(>|t|) MMM 0.013522 0.003633 3.722 0.000213 *** AA 0.015499 0.003079 5.034 6.04e-07 *** T -0.132302 0.003210 -41.212 < 2e-16 *** AXP 0.018347 0.004150 4.421 1.13e-05 *** CAT -0.025740 0.005441 -4.731 2.68e-06 *** C 0.029800 0.003885 7.670 5.43e-14 *** KO 0.001976 0.004308 0.459 0.646631 DD -0.043242 0.005971 -7.242 1.12e-12 *** EK -0.001057 0.002805 -0.377 0.706283 XOM 0.016022 0.005169 3.100 0.002009 ** GE 0.019873 0.003558 5.586 3.27e-08 *** GM 0.007839 0.002964 2.644 0.008357 ** HPQ 0.002107 0.002697 0.781 0.435052 HD -0.000881 0.003317 -0.266 0.790606 HON -0.017194 0.002937 -5.855 7.17e-09 *** INTC -0.004738 0.001846 -2.567 0.010463 * IBM 0.003808 0.003136 1.214 0.225104 Exploratory Analysis

  9. Exploratory Analysis IP 0.039177 0.006189 6.331 4.24e-10 *** JPM -0.019003 0.003597 -5.284 1.67e-07 *** JNJ -0.007824 0.004463 -1.753 0.080017 . MCD 0.001297 0.004616 0.281 0.778833 MRK -0.011812 0.003347 -3.529 0.000443 *** MSFT -0.019897 0.002943 -6.761 2.79e-11 *** MO 0.007771 0.001474 5.271 1.78e-07 *** PG -0.039595 0.004155 -9.529 < 2e-16 *** SBC 0.013263 0.003583 3.702 0.000230 *** BA 0.014151 0.002902 4.876 1.33e-06 *** DIS -0.004581 0.002725 -1.681 0.093097 . UTX -0.009107 0.003467 -2.627 0.008804 ** WMT 0.008481 0.003889 2.181 0.029519 * --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 0.4177 on 738 degrees of freedom Multiple R-Squared: 0.9987, Adjusted R-squared: 0.9986 F-statistic: 1.875e+04 on 30 and 738 DF, p-value: < 2.2e-16

  10. Exploratory Analysis

  11. Exploratory Analysis DJIA

  12. Linear Regression Graph DJIA

  13. Statistical Analysis Formulas: %DJIA = *%#shares + C %DJIA = -0.74%#shares + 3.04 Call: lm(formula = DJI ~ shares, data = P) Residuals: Min 1Q Median 3Q Max -26.069 -2.791 1.497 5.453 12.928 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.04238 0.65735 4.628 4.33e-06 *** shares -0.74398 0.05811 -12.802 < 2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 7.527 on 766 degrees of freedom Multiple R-Squared: 0.1763, Adjusted R-squared: 0.1752 F-statistic: 163.9 on 1 and 766 DF, p-value: < 2.2e-16 DJIA

  14. Conclusions • There is a statistically significant relationship between the divisor values and the movements of DJIA across time. • Effort to inflate index value above fair valuation? DJIA

  15. Questions? DJIA

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