1. HAR-RV Models Including Sector and Market Regressors Sharon Lee Spring 2009

2. Intuition On its own, the HAR-RV model (Corsi 2003) predicts an individual equity’s future variance based on its past variances. Because a stock’s returns are affected by factors outside of the company, the variance should likewise be impacted by outside factors. Thus, including sector and market variances into this model should improve its explanatory ability. A new model may provide insight on the relationship between different sectors and time horizons.

3. The Basic HAR-RV Model HAR-RV makes use of average realized variance over daily, weekly, and monthly periods. h=1 corresponds to daily periods, h=5 corresponds to weekly periods, h=22 corresponds to monthly periods These time horizons correspond to day-ahead, 5-day ahead, and month-ahead predictions of average realized variance.

4. HAR-RV Models 1) The original: 2) Including sectors: 3) Including market: 4) Including market and sectors: RV t, t+h = ß 0 + ß D RV t + ß W RV t-5, t + ß M RV t-22, t +ε t+1 RV t, t+h = ß 0 + ß D RV t + ß W RV t-5, t + ß M RV t-22, t + ß SD RV sector, t + ß SW RV sector, t-5, t + ß SM RV sector, t-22, t + ε t+1 RV t, t+h = ß 0 + ß D RV t + ß W RV t-5, t + ß M RV t-22, t + ß SD RV sector, t + ß SW RV sector, t-5, t + ß SM RV sector, t-22, t + ß MD RV mkt, t + ß MW RV mkt, t-5, t + ß MM RV mkt, t-22, t + ε t+1 RV t, t+h = ß 0 + ß D RV t + ß W RV t-5, t + ß M RV t-22, t + ß MD RV mkt, t + ß MW RV mkt, t-5, t + ß MM RV mkt, t-22, t + ε t+1

5. Dispersion To take into consideration the associations between companies within a sector, and the associations between sectors in the market, we use cross-sectional dispersion measures of the asset returns (Solnik and Roulet 2000) The dispersion measures can assess the existence of changing company and sector association through time Cross-sector Dispersion Cross-market Dispersion

6. Dispersion D t is the dispersion measure at time t r it is the return of the ith company (or sector) r wt is the sector (or market) return This measure is based on the idea that companies are more associated with each other if the dispersion in the sector is low, and that they are less associated if the dispersion is high. This is similar for sectors in relation to dispersion in the market. These dispersion measures are lagged as well so the fifth HAR-RV model 5) RV t, t+h = ß 0 + ß D RV t + ß W RV t-5, t + ß M RV t-22, t + ß SD RV sector, t + ß SW RV sector, t-5, t + ß SM RV sector, t-22, t + ß MD RV mkt, t + ß MW RV mkt, t-5, t + ß SM RV mkt, t-22, t + ß dsD D sector, t + ß dsW D sector, t-5, t + ß dsM D sector, t-22, t + + ß dmD D mkt, t + ß dmW D mkt, t-5, t + ß dmW D mkt, t-22, t +ε t+1

7. Sector Data Consumer Goods (12, n=2918) Healthcare (9, n=2842) Financial (10, n=2408) Technology (14, n=2117) Basic Materials (10, n=2264) Industrials (5, n=2921) Utilities (3, n=2036) Conglomerates (4, n=2921) Services (12, n=2223)

8. Sectors and Market Stocks with less than 2000 observations were removed Sector portfolios created are equally-weighted Market: 79 stocks, 9 sectors (S&P100) From 1997 to 2009 Sampling frequency set at 5-min interval Utilities, Industrials and Conglomerate sectors nixed from analysis because of small sample sizes

9. Consumer Goods AVPAVON PRODUCTS INC CLCOLGATE PALMOLIVE CPBCAMPBELL SOUP CO FFORD MOTOR CO HNZHEINZ H J CO IPINTL PAPER *not in downloads KFTKRAFT FOODS INC KOCOCA COLA CO THE MOALTRIA GROUP INC PEPPEPSICO INC PGPROCTER GAMBLE CO PMPHILIP MORRIS INTL *less than 2000 observations SLESARA LEE CP XRXXEROX CP

10. HAR-RV Model 5 DAYWEEKMONTH Estimate Std. Error t value Pr(>|t|) (Intercept) -5.668821 5.991513 -0.946 0.3442 x1 0.394106 0.026429 14.912 < 2e-16 *** x2 -0.064870 0.049777 -1.303 0.1926 x3 0.333467 0.066794 4.992 6.48e-07 *** x1sect -0.131304 0.103615 -1.267 0.2052 x2sect 0.461743 0.176587 2.615 0.0090 ** x3sect -0.111906 0.184744 -0.606 0.5448 x1mkt 0.804274 0.113852 7.064 2.22e-12 *** x2mkt -0.299371 0.189755 -1.578 0.1148 x3mkt -0.374517 0.177216 -2.113 0.0347 * DS1 0.008392 0.037606 0.223 0.8234 DS2 -0.173278 0.061795 -2.804 0.0051 ** DS3 0.082290 0.062992 1.306 0.1916 DM1 -0.429632 0.062330 -6.893 7.30e-12 *** DM2 0.142871 0.105039 1.360 0.1739 DM3 0.231421 0.138662 1.669 0.0953. --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Estimate Std. Error t value Pr(>|t|) (Intercept) 0.431868 4.244282 0.102 0.918963 x1 0.077317 0.018664 4.143 3.58e- 05 *** x2 0.012432 0.035151 0.354 0.723631 x3 0.424292 0.047169 8.995 < 2e- 16 *** x1sect -0.018569 0.073171 -0.254 0.799698 x2sect 0.457860 0.124704 3.672 0.000247 *** x3sect -0.015129 0.130487 -0.116 0.907711 x1mkt 0.768576 0.080401 9.559 < 2e- 16 *** x2mkt -0.208109 0.134008 -1.553 0.120591 x3mkt -0.550097 0.125224 -4.393 1.18e-05 *** DS1 -0.004693 0.026557 -0.177 0.859750 DS2 -0.187870 0.043639 -4.305 1.75e-05 *** DS3 0.046110 0.044487 1.036 0.300098 DM1 -0.354018 0.044016 -8.043 1.49e-15 *** DM2 0.019559 0.074179 0.264 0.792063 DM3 0.389381 0.097984 3.974 7.32e-05 *** Estimate Std. Error t value Pr(>|t|) (Intercept) 0.431868 4.244282 0.102 0.918963 x1 0.077317 0.018664 4.143 3.58e-05 *** x2 0.012432 0.035151 0.354 0.723631 x3 0.424292 0.047169 8.995 < 2e-16 *** x1sect -0.018569 0.073171 -0.254 0.799698 x2sect 0.457860 0.124704 3.672 0.000247 *** x3sect -0.015129 0.130487 -0.116 0.907711 x1mkt 0.768576 0.080401 9.559 < 2e-16 *** x2mkt -0.208109 0.134008 -1.553 0.120591 x3mkt -0.550097 0.125224 -4.393 1.18e-05 *** DS1 -0.004693 0.026557 -0.177 0.859750 DS2 -0.187870 0.043639 -4.305 1.75e-05 *** DS3 0.046110 0.044487 1.036 0.300098 DM1 -0.354018 0.044016 -8.043 1.49e-15 *** DM2 0.019559 0.074179 0.264 0.792063 DM3 0.389381 0.097984 3.974 7.32e-05 *** --- Estimate Std. Error t value Pr(>|t|) (Intercept) -2.461921 3.775546 - 0.652 0.514432 x1 0.009202 0.011752 0.783 0.433706 x2 -0.056825 0.019914 - 2.854 0.004369 ** x3 0.160791 0.018022 8.922 < 2e-16 *** x1sect 0.026321 0.054798 0.480 0.631051 x2sect 0.335828 0.091202 3.682 0.000237 *** x3sect 0.405796 0.096053 4.225 2.50e-05 *** x1mkt 0.523003 0.063199 8.275 2.32e-16 *** x2mkt -0.136334 0.105253 - 1.295 0.195369 x3mkt -0.406370 0.101164 - 4.017 6.12e-05 *** DS1 -0.016966 0.020265 - 0.837 0.402573 DS2 -0.071733 0.032436 - 2.212 0.027114 * DS3 -0.164660 0.033410 - 4.928 8.98e-07 *** DM1 -0.274160 0.034675 - 7.907 4.36e-15 *** DM2 0.020947 0.058241 0.360 0.719144 DM3 0.287687 0.079228 3.631 0.000289 *** Estimate Std. Error t value Pr(>|t|) (Intercept) -2.461921 3.775546 -0.652 0.514432 x1 0.009202 0.011752 0.783 0.433706 x2 -0.056825 0.019914 -2.854 0.004369 ** x3 0.160791 0.018022 8.922 < 2e-16 *** x1sect 0.026321 0.054798 0.480 0.631051 x2sect 0.335828 0.091202 3.682 0.000237 *** x3sect 0.405796 0.096053 4.225 2.50e-05 *** x1mkt 0.523003 0.063199 8.275 2.32e-16 *** x2mkt -0.136334 0.105253 -1.295 0.195369 x3mkt -0.406370 0.101164 -4.017 6.12e-05 *** DS1 -0.016966 0.020265 -0.837 0.402573 DS2 -0.071733 0.032436 -2.212 0.027114 * DS3 -0.164660 0.033410 -4.928 8.98e-07 *** DM1 -0.274160 0.034675 -7.907 4.36e-15 *** DM2 0.020947 0.058241 0.360 0.719144 DM3 0.287687 0.079228 3.631 0.000289 *** Estimate Std. Error t value Pr(>|t|) (Intercept) -2.461921 3.775546 -0.652 0.514432 x1 0.009202 0.011752 0.783 0.433706 x2 -0.056825 0.019914 -2.854 0.004369 ** x3 0.160791 0.018022 8.922 < 2e-16 *** x1sect 0.026321 0.054798 0.480 0.631051 x2sect 0.335828 0.091202 3.682 0.000237 *** x3sect 0.405796 0.096053 4.225 2.50e-05 *** x1mkt 0.523003 0.063199 8.275 2.32e-16 *** x2mkt -0.136334 0.105253 -1.295 0.195369 x3mkt -0.406370 0.101164 -4.017 6.12e-05 *** DS1 -0.016966 0.020265 -0.837 0.402573 DS2 -0.071733 0.032436 -2.212 0.027114 * DS3 -0.164660 0.033410 -4.928 8.98e-07 *** DM1 -0.274160 0.034675 -7.907 4.36e-15 *** DM2 0.020947 0.058241 0.360 0.719144 DM3 0.287687 0.079228 3.631 0.000289 ***

11. PG R-Squared 1) HAR-RV31.8%45.7%48.6% 2) & Sector33.0%51.8%54.2% 3) & Market45.1%52.0%54.0% 4) Sector & Market45.2%52.7%55.7% 5) & Dispersion47.0%56.0%58.4% % Increase from 1) to 4)41.8%15.4%14.7% from 1) to 5)47.6%22.6%20.2%

12. Consumer Goods Sector Across the time horizons, the number of significant regressors increases, so that the month horizon has the most significant regressors. The consistently significant regressors are individual monthly, market daily, and market dispersion daily at the ‘***’ level (p-value < 0.001) R-squared improvement is at least 20% over the original model. The model provides the best fit at monthly period with 58.4%.

13. Health Care ABTABBOTT LABORATORIES AMGNAmgen Inc. BAXBAXTER INTL INC BMYBRISTOL MYERS SQIBB CICIGNA CP *not in downloads COVCOVIDIEN LTD *less than 2000 observations JNJJOHNSON AND JOHNS DC MDTMEDTRONIC INC MRKMERCK CO INC PFEPFIZER INC UNHUNITEDHEALTH GROUP WYEWYETH *less than 2000 observations

14. HAR-RV Model 5 DAYWEEKMONTH Estimate Std. Error t value Pr(>|t|) (Intercept) -2.92944 4.17310 -0.702 0.482772 x1 0.02930 0.02761 1.061 0.288715 x2 -0.15856 0.06421 -2.469 0.013616 * x3 0.85875 0.07596 11.305 < 2e-16 *** x1sect 0.17362 0.08602 2.018 0.043673 * x2sect 0.87410 0.13716 6.373 2.29e-10 *** x3sect -0.64264 0.12604 -5.099 3.74e-07 *** x1mkt 0.70091 0.08325 8.420 < 2e-16 *** x2mkt -0.23031 0.12663 -1.819 0.069104. x3mkt -0.52753 0.10895 -4.842 1.39e-06 *** DS1 -0.13287 0.03623 -3.668 0.000251 *** DS2 -0.25022 0.05416 -4.620 4.09e-06 *** DS3 0.24199 0.06116 3.956 7.87e-05 *** DM1 -0.25514 0.04789 -5.328 1.11e-07 *** DM2 0.03128 0.07390 0.423 0.672189 DM3 0.20659 0.07852 2.631 0.008582 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Estimate Std. Error t value Pr(>|t|) (Intercept) 4.247711 2.665907 1.593 0.11124 x1 -0.096672 0.017587 -5.497 4.37e-08 *** x2 -0.113189 0.040921 -2.766 0.00573 ** x3 0.850005 0.048399 17.562 < 2e-16 *** x1sect 0.442137 0.054794 8.069 1.21e-15 *** x2sect 0.473604 0.087379 5.420 6.68e-08 *** x3sect -0.498579 0.080291 -6.210 6.44e-10 *** x1mkt 0.632535 0.053033 11.927 < 2e-16 *** x2mkt -0.130868 0.080670 -1.622 0.10491 x3mkt -0.552723 0.069407 -7.963 2.78e-15 *** DS1 -0.156420 0.023078 -6.778 1.60e-11 *** DS2 -0.172040 0.034508 -4.986 6.71e-07 *** DS3 0.195482 0.038963 5.017 5.71e-07 *** DM1 -0.257085 0.030507 -8.427 < 2e-16 *** DM2 -0.009152 0.047078 -0.194 0.84588 DM3 0.237069 0.050031 4.738 2.31e-06 *** Estimate Std. Error t value Pr(>|t|) (Intercept) 17.519935 2.972651 5.894 4.43e-09 *** x1 0.003237 0.009608 0.337 0.73620 x2 0.014025 0.016294 0.861 0.38949 x3 -0.026530 0.014525 -1.826 0.06793. x1sect 0.385953 0.054357 7.100 1.73e-12 *** x2sect 0.034534 0.081943 0.421 0.67348 x3sect 0.642814 0.073854 8.704 < 2e-16 *** x1mkt 0.282217 0.051687 5.460 5.36e-08 *** x2mkt 0.067268 0.078309 0.859 0.39044 x3mkt -0.574149 0.069935 -8.210 3.95e-16 *** DS1 -0.010795 0.022327 -0.483 0.62881 DS2 -0.097662 0.032926 -2.966 0.00305 ** DS3 -0.347715 0.037478 -9.278 < 2e-16 *** DM1 -0.134530 0.029947 -4.492 7.45e-06 *** DM2 -0.139187 0.047762 -2.914 0.00361 ** DM3 0.424213 0.051752 8.197 4.38e-16 ***

15. JNJ R-squared 1) HAR-RV38.1%51.0%47.1% 2) & Sector52.8%64.8%54.8% 3) & Market48.8%59.1%45.2% 4) Sector & Market51.5%64.1%43.0% 5) & Dispersion56.2%71.6%54.0% % Increase from 1) to 4)35.2%25.7%-8.6% from 1) to 5)47.5%40.3%14.8%

16. Health Care Sector Analysis Consistently significant (***) regressors are sector monthly, market daily, sector dispersion monthly, and market dispersion daily. Model 5 shows huge improvement over Model 4, indicating the impact of adding the dispersion regressors. As with the consumer sector, R-squared has the greatest improvement for Day and sequentially declines. Best fit at week: 71.6%

17. Financial AIGAMER INTL GROUP INC *not in downloads ALLALLSTATE CP AXPAMER EXPRESS INC BACBK OF AMERICA CP BKBANK OF NY MELLON CP CCITIGROUP INC COFCAPITAL ONE FINANCIA GSGOLDMAN SACHS GRP HIGHARTFORD FIN SVC *not in downloads JPMJP MORGAN CHASE CO MSMORGAN STANLEY *less than 2000 observations NYXNYSE EURONEXT *less than 2000 observations RFREGIONS FINANCIAL CP *less than 2000 observations USBUS BANCORP WBWACHOVIA CP *not in downloads

18. HAR-RV Model 5 Estimate Std. Error t value Pr(>|t|) (Intercept) -27.12117 9.88356 -2.744 0.006123 ** x1 0.25206 0.02389 10.550 < 2e-16 *** x2 -0.45280 0.05346 -8.469 < 2e-16 *** x3 0.86848 0.07878 11.024 < 2e-16 *** x1sect 0.21265 0.09915 2.145 0.032087 * x2sect 0.08625 0.13053 0.661 0.508822 x3sect -0.22066 0.12922 -1.708 0.087864. x1mkt -0.62583 0.17719 -3.532 0.000422 *** x2mkt 1.55059 0.26190 5.921 3.77e-09 *** x3mkt -1.02582 0.21014 -4.882 1.14e-06 *** DS1 0.16893 0.04520 3.737 0.000191 *** DS2 -0.07631 0.08090 -0.943 0.345673 DS3 -0.14676 0.07967 -1.842 0.065609. DM1 1.22572 0.09706 12.628 < 2e-16 *** DM2 0.03133 0.15158 0.207 0.836283 DM3 -0.33199 0.18858 -1.760 0.078477. Estimate Std. Error t value Pr(>|t|) (Intercept) 30.486082 6.643530 4.589 4.74e-06 *** x1 -0.014154 0.020737 -0.683 0.494961 x2 0.027425 0.035209 0.779 0.436117 x3 -0.285567 0.031279 -9.130 < 2e-16 *** x1sect 0.161485 0.058249 2.772 0.005618 ** x2sect 0.078116 0.077133 1.013 0.311309 x3sect -0.004973 0.078496 -0.063 0.949494 x1mkt 1.063230 0.106807 9.955 < 2e-16 *** x2mkt 0.419145 0.155931 2.688 0.007248 ** x3mkt -0.872064 0.126482 -6.895 7.23e-12 *** DS1 -0.083317 0.026400 -3.156 0.001624 ** DS2 -0.172977 0.045080 -3.837 0.000128 *** DS3 -0.035759 0.046895 -0.763 0.445840 DM1 -0.302821 0.059020 -5.131 3.17e-07 *** DM2 -0.261822 0.086211 -3.037 0.002421 ** DM3 1.431167 0.103365 13.846 < 2e-16 *** DAYWEEKMONTH Estimate Std. Error t value Pr(>|t|) (Intercept) -29.46307 6.36518 -4.629 3.91e-06 *** x1 -0.03734 0.01535 -2.433 0.015079 * x2 -0.18275 0.03435 -5.320 1.15e-07 *** x3 0.90456 0.05062 17.870 < 2e-16 *** x1sect 0.14178 0.06370 2.226 0.026136 * x2sect -0.39353 0.08386 -4.693 2.88e-06 *** x3sect 0.14785 0.08302 1.781 0.075077. x1mkt 1.14236 0.11384 10.035 < 2e-16 *** x2mkt 1.27692 0.16826 7.589 4.92e-14 *** x3mkt -2.04171 0.13502 -15.121 < 2e-16 *** DS1 0.21600 0.02904 7.438 1.51e-13 *** DS2 -0.13734 0.05197 -2.642 0.008295 ** DS3 -0.03545 0.05119 -0.693 0.488653 DM1 0.21972 0.06236 3.524 0.000435 *** DM2 -0.28212 0.09739 -2.897 0.003811 ** DM3 0.26038 0.12120 2.148 0.031809 *

19. JPM R-Squared 1) HAR-RV46.0%47.0%50.4% 2) & Sector50.9%53.3%51.6% 3) & Market59.9%75.8%60.1% 4) Sector & Market60.0%76.1%57.7% 5) Dispersion64.6%76.8%65.0% % Increase from 1) to 4)30.5%61.7%14.5% from 1) to 5)40.6%63.4%29.0%

20. Financial Sector Analysis Sector lagged regressors provide little explanation for stock RV prediction, while market regressors are highly significant for all three time horizons. Model 5 shows greatest improvement over Model 4 for day and month, suggesting that dispersion factors provide insight for these time periods. Week predictions are the best by far at about 60% R-squared, with dispersion not increasing Model 4 by much. This may be related to the idea that low dispersion suggests high association between firms. Best fit at week: 76.8%

21. Basic Materials AAALCOA INC BHIBAKER HUGHES INTL COPCONOCOPHILLIPS CVXCHEVRON CORP DDDU PONT E I DE NEM DOWDOW CHEMICAL EPEL PASO CORPORATION HALHALLIBURTON CO NOVNATL OILWELL VARCO OXYOCCIDENTAL PET SLBSCHLUMBERGER LTD WMBWILLIAMS COS XOMEXXON MOBIL CP

22. DAYWEEKMONTH HAR-RV Model 5 Estimate Std. Error t value Pr(>|t|) (Intercept) 19.344265 6.731693 2.874 0.004101 ** x1 0.160447 0.027560 5.822 6.77e-09 *** x2 0.406660 0.054805 7.420 1.72e-13 *** x3 0.256999 0.054630 4.704 2.72e-06 *** x1sect -0.386410 0.077164 -5.008 5.99e-07 *** x2sect 0.039763 0.131470 0.302 0.762341 x3sect -0.001394 0.133235 -0.010 0.991655 x1mkt 0.996710 0.105546 9.443 < 2e-16 *** x2mkt -0.124989 0.160847 -0.777 0.437209 x3mkt -0.457759 0.134014 -3.416 0.000649 *** DS1 0.118592 0.026343 4.502 7.12e-06 *** DS2 -0.013515 0.044160 -0.306 0.759600 DS3 0.015063 0.045295 0.333 0.739506 DM1 -0.296402 0.069184 -4.284 1.92e-05 *** DM2 -0.074268 0.118483 -0.627 0.530846 DM3 0.254366 0.137842 1.845 0.065135. Estimate Std. Error t value Pr(>|t|) (Intercept) 26.82651 4.63563 5.787 8.30e-09 *** x1 0.11837 0.01896 6.243 5.22e-10 *** x2 0.39475 0.03770 10.471 < 2e-16 *** x3 0.24273 0.03758 6.459 1.32e-10 *** x1sect -0.31022 0.05309 -5.844 5.94e-09 *** x2sect -0.16859 0.09044 -1.864 0.0625. x3sect 0.14812 0.09168 1.616 0.1063 x1mkt 0.88565 0.07261 12.198 < 2e-16 *** x2mkt 0.13017 0.11065 1.176 0.2396 x3mkt -0.60956 0.09225 -6.608 5.00e-11 *** DS1 0.07630 0.01812 4.210 2.66e-05 *** DS2 0.07503 0.03038 2.470 0.0136 * DS3 -0.04593 0.03117 -1.473 0.1408 DM1 -0.19196 0.04759 -4.033 5.70e-05 *** DM2 -0.33406 0.08152 -4.098 4.33e-05 *** DM3 0.48937 0.09489 5.157 2.75e-07 *** Estimate Std. Error t value Pr(>|t|) (Intercept) 106.038764 5.496804 19.291 < 2e-16 *** x1 -0.015672 0.015911 -0.985 0.324737 x2 0.000692 0.026971 0.026 0.979532 x3 -0.220623 0.023951 -9.211 < 2e-16 *** x1sect -0.188366 0.059270 -3.178 0.001506 ** x2sect -0.192202 0.099994 -1.922 0.054733. x3sect 0.067771 0.101085 0.670 0.502655 x1mkt 0.720473 0.083041 8.676 < 2e-16 *** x2mkt 0.452872 0.125324 3.614 0.000309 *** x3mkt -0.277201 0.101049 -2.743 0.006139 ** DS1 0.045053 0.020326 2.216 0.026772 * DS2 0.067004 0.033761 1.985 0.047319 * DS3 -0.029537 0.034628 -0.853 0.393774 DM1 -0.249903 0.054263 -4.605 4.38e-06 *** DM2 -0.255263 0.093335 -2.735 0.006296 ** DM3 0.551759 0.110386 4.998 6.29e-07 ***

23. AA R-Squared 1) HAR-RV49.7%59.5%52.5% 2) & Sector55.9%67.4%53.9% 3) & Market57.2%69.1%54.4% 4) Sector & Market58.1%71.5%53.1% 5) Dispersion59.0%72.7%53.6% % Increase from 1) to 4)16.9%20.1%1.0% from 1) to 5)18.7%22.2%2.0%

24. Basic Material Sector Analysis Market dispersion factors for all time periods are significant for week and month though not day. All market regressors are significant (***) at month period. With the exception of sector daily, sector variables are not very significant. Minimal improvement (~2%) with addition of dispersion factors. Possibly indicates high association among basic material companies. As with the financial sector, the greatest improvement is for the week horizon. Best fit at week: 72.7%

25. Services UNITED PARCEL SVCUPS *less than 2000 observations TIME WARNER INCTWX TARGET CPTGT NORFOLK SO CPNSC MCDONALDS CPMCD *less than 2000 observations MASTERCARD INCMA HOME DEPOT INCHD FEDEX CORPFDX WALT DISNEY-DISNEY CDIS CVS CAREMARK CPCVS Comcast CorporationCMCSA *not found CBS CORP CL BCBS BURLINGTN N SANTE FEBNI Amazon.comAMZN

26. HAR-RV Model 5 Estimate Std. Error t value Pr(>|t|) (Intercept) 21.280362 8.030378 2.650 0.00811 ** x1 0.284466 0.027052 10.516 < 2e-16 *** x2 0.438019 0.045309 9.667 < 2e-16 *** x3 0.167756 0.042236 3.972 7.38e-05 *** x1sect -0.273345 0.114679 -2.384 0.01724 * x2sect -0.118440 0.193588 -0.612 0.54073 x3sect 0.604447 0.216633 2.790 0.00532 ** x1mkt 0.308769 0.154093 2.004 0.04523 * x2mkt -0.008657 0.245205 -0.035 0.97184 x3mkt -0.528738 0.234660 -2.253 0.02435 * DS1 0.088531 0.037254 2.376 0.01757 * DS2 0.001858 0.061003 0.030 0.97570 DS3 -0.157546 0.070292 -2.241 0.02512 * DM1 -0.112489 0.079658 -1.412 0.15806 DM2 0.031875 0.123515 0.258 0.79638 DM3 0.217832 0.167563 1.300 0.19375 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Estimate Std. Error t value Pr(>|t|) (Intercept) 35.243043 5.641928 6.247 5.11e-10 *** x1 0.147074 0.018967 7.754 1.41e-14 *** x2 0.525518 0.031782 16.535 < 2e-16 *** x3 0.144680 0.029642 4.881 1.14e-06 *** x1sect -0.255385 0.080407 -3.176 0.001515 ** x2sect -0.055337 0.135733 -0.408 0.683547 x3sect 0.740726 0.151886 4.877 1.16e-06 *** x1mkt 0.223631 0.108038 2.070 0.038588 * x2mkt -0.005849 0.171920 -0.034 0.972865 x3mkt -0.667437 0.164543 -4.056 5.18e-05 *** DS1 0.072341 0.026120 2.770 0.005665 ** DS2 -0.020105 0.042773 -0.470 0.638374 DS3 -0.175981 0.049284 -3.571 0.000364 *** DM1 -0.098418 0.055850 -1.762 0.078191. DM2 0.066854 0.086599 0.772 0.440211 DM3 0.270198 0.117517 2.299 0.021595 * Estimate Std. Error t value Pr(>|t|) (Intercept) 66.35107 5.67834 11.685 < 2e-16 *** x1 0.10857 0.01897 5.723 1.20e-08 *** x2 0.29138 0.03180 9.162 < 2e-16 *** x3 0.25158 0.02964 8.489 < 2e-16 *** x1sect -0.08895 0.08025 -1.108 0.267839 x2sect 0.15460 0.13566 1.140 0.254589 x3sect 0.78895 0.15246 5.175 2.51e-07 *** x1mkt 0.13161 0.10785 1.220 0.222510 x2mkt -0.42089 0.17183 -2.449 0.014396 * x3mkt -0.55136 0.16576 -3.326 0.000897 *** DS1 0.01851 0.02607 0.710 0.477676 DS2 -0.05770 0.04274 -1.350 0.177127 DS3 -0.21040 0.04949 -4.251 2.23e-05 *** DM1 -0.01260 0.05576 -0.226 0.821241 DM2 0.24626 0.08651 2.847 0.004464 ** DM3 0.14059 0.11884 1.183 0.236930 DAYWEEKMONTH

27. TGT R-Squared 1) HAR-RV56.6%67.0%60.8% 2) & Sector56.5%67.1%61.3% 3) & Market54.3%67.3%57.9% 4) Sector & Market54.3%67.6%58.5% 5) & Dispersion54.5%67.9%59.7% % Increase from 1) to 4)-3.9%0.9%-3.9% from 1) to 5)-3.7%1.3%-1.9%

28. Service Sector Analysis This sector is puzzling. Beyond the original HAR-RV with just the lagged single stock regressors, the models adding in sector, market and dispersion factors seem irrelevant. It seems that information about the company provides the best prediction. Best fit at week: 67.9%

29. Technology CSCOCisco Systems, Inc. DELLDell Inc. EMCE M C CP GOOGGoogle Inc.*less than 2000 HPQHEWLETT PACKARD CO IBMINTL BUSINESS MACH INTCIntel Corporation MSFTMicrosoft Corporation ORCLOracle Corporation QCOMQUALCOMM Incorporated SSPRINT NXTEL CP*less than 2000 TAT&T INC. TXNTEXAS INSTRUMENTS TYCTYCO INTL LTD NEW VZVERIZON COMMUN

30. HAR-RV Model 5 Estimate Std. Error t value Pr(>|t|) (Intercept) -20.74525 16.25461 -1.276 0.202009 x1 0.02284 0.03273 0.698 0.485391 x2 0.23284 0.06713 3.468 0.000535 *** x3 0.27872 0.08610 3.237 0.001227 ** x1sect 2.94851 0.19047 15.481 < 2e-16 *** x2sect -1.28543 0.29955 -4.291 1.86e-05 *** x3sect -0.36711 0.25813 -1.422 0.155125 x1mkt -1.64572 0.29885 -5.507 4.12e-08 *** x2mkt 0.80982 0.38034 2.129 0.033358 * x3mkt 0.86772 0.29445 2.947 0.003246 ** DS1 -0.85278 0.06930 -12.306 < 2e-16 *** DS2 0.60159 0.10188 5.905 4.13e-09 *** DS3 -0.27855 0.11432 -2.437 0.014909 * DM1 0.43375 0.16381 2.648 0.008164 ** DM2 -0.50889 0.23329 -2.181 0.029273 * DM3 -0.50279 0.28606 -1.758 0.078967. --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Estimate Std. Error t value Pr(>|t|) (Intercept) 2.091085 12.008482 0.174 0.861778 x1 0.021742 0.038362 0.567 0.570948 x2 0.034968 0.064964 0.538 0.590453 x3 -0.022573 0.058794 -0.384 0.701072 x1sect 0.828424 0.095137 8.708 < 2e-16 *** x2sect 0.238942 0.138957 1.720 0.085672. x3sect 0.794076 0.110575 7.181 9.73e-13 *** x1mkt -0.713990 0.194905 -3.663 0.000256 *** x2mkt 0.145834 0.236586 0.616 0.537694 x3mkt 0.871173 0.184270 4.728 2.43e-06 *** DS1 -0.171392 0.039995 -4.285 1.91e-05 *** DS2 0.074856 0.060565 1.236 0.216616 DS3 -0.218809 0.073409 -2.981 0.002911 ** DM1 0.005754 0.108096 0.053 0.957555 DM2 -0.323446 0.152192 -2.125 0.033689 * DM3 -1.401441 0.186236 -7.525 7.95e-14 *** DAYWEEKMONTH Estimate Std. Error t value Pr(>|t|) (Intercept) -0.24128 11.93089 -0.020 0.983868 x1 -0.04553 0.02395 -1.901 0.057451. x2 0.16445 0.04913 3.347 0.000831 *** x3 0.39949 0.06302 6.339 2.85e-10 *** x1sect 1.72184 0.13939 12.353 < 2e-16 *** x2sect -0.26788 0.21922 -1.222 0.221867 x3sect -0.37558 0.18893 -1.988 0.046961 * x1mkt -1.40876 0.21870 -6.441 1.48e-10 *** x2mkt 0.58890 0.27834 2.116 0.034490 * x3mkt 1.07252 0.21551 4.977 7.03e-07 *** DS1 -0.38600 0.05072 -7.611 4.16e-14 *** DS2 0.23874 0.07456 3.202 0.001386 ** DS3 -0.27406 0.08366 -3.276 0.001071 ** DM1 0.28255 0.11988 2.357 0.018522 * DM2 -0.48111 0.17073 -2.818 0.004880 ** DM3 -0.71433 0.20947 -3.410 0.000662 ***

31. ORCL R-Squared 1) HAR-RV31.8%45.7%48.6% 2) & Sector45.3%52.9%57.1% 3) & Market50.9%60.7%63.8% 4) Sector & Market54.0%60.9%56.3% 5) & Dispersion57.9%66.3%63.6% % Increase from 1) to 4)69.6%33.2%15.9% from 1) to 5)81.9%45.2%30.9%

32. Tech Sector Analysis The inclusion of dispersion factors are helpful in this sector. Across all time horizons the improvement is considerable. As with consumer and health care, the greatest improvement is for the day time period. Best fit at week: 66.3%

33. Sector Generalizations The improvement in models show that including dispersion increases the fit of the consumer, health care and technology sectors, with the most improvement in day and then progressively less improvement. Financial, basic materials and service sectors show greatest improvement in the week period, but to a far less degree than the other three sectors for all time horizons.

34. Betas Basic Materials: 1.19 Financial: 1.50 Service: 0.92 Consumer Goods: 0.78 Health Care: 0.66 Technology: 1.1

35. Value-weighted Portfolios? Intuitively, value-weighted portfolios should be more appropriate Instead, of using equal-weighted portfolios for sector stocks and for the market, I ran the HAR- RV Model 5 with value-weighted portfolios The market caps were used for each stock to calculate the new portfolios Results: –Overall, using the value-weighted portfolios show adjusted R- squared values with minimal change compared to equally- weighted. –The fit is slightly worsened for almost all sectors and time horizons. Problem: Market caps are recent

36. Conclusions Riskier and more volatile sectors tend to benefit most from additional regressors in the week period, and dispersion measures are only slightly beneficial. For sectors with less risk, dispersion considerably helps the predictions. Also, the model improvements are greatest for the day period. For all sectors, with the exception of consumer, the best fit was in the week period with an average R-squared of 68.6%.