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Beneath the Calm Waters: A Study of the Dow Index

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.

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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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