har-rv models including sector and market regressors
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HAR-RV Models Including Sector and Market Regressors
Sharon Lee
Spring 2009
HAR-RV Models• 1) The original:
• 2) Including sectors:
• 3) Including market:
• 4) Including market and sectors:
RVt, t+h = ß0 + ßD RVt + ßW RVt-5, t + ßMRVt-22, t +εt+1
RVt, t+h = ß0 + ßD RVt + ßW RVt-5, t + ßM RVt-22, t
+ ßSD RVsector, t + ßSW RVsector, t-5, t + ßSMRVsector, t-22, t + εt+1
RVt, t+h = ß0 + ßD RVt + ßW RVt-5, t + ßMRVt-22, t
+ ßSD RVsector, t + ßSW RVsector, t-5, t + ßSM RVsector, t-22, t
+ ßMD RVmkt, t + ßMW RVmkt, t-5, t + ßMM RVmkt, t-22, t + εt+1
RVt, t+h = ß0 + ßD RVt + ßW RVt-5, t + ßM RVt-22, t
+ ßMD RVmkt, t + ßMW RVmkt, t-5, t + ßMM RVmkt, t-22, t + εt+1
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
Dispersion
• Dt is the dispersion measure at time t• rit is the return of the ith company (or sector) • rwt 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) RVt, t+h = ß0 + ßD RVt + ßW RVt-5, t + ßM RVt-22, t
+ ßSD RVsector, t + ßSW RVsector, t-5, t + ßSM RVsector, t-22, t
+ ßMD RVmkt, t + ßMW RVmkt, t-5, t + ßSMRVmkt, t-22, t
+ ßdsD Dsector, t + ßdsW Dsector, t-5, t + ßdsM Dsector, t-22, t +
+ ßdmD Dmkt, t + ßdmW Dmkt, t-5, t + ßdmW Dmkt, t-22, t +εt+1
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)
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
Consumer GoodsAVP AVON PRODUCTS INC
CL COLGATE PALMOLIVE
CPB CAMPBELL SOUP CO
F FORD MOTOR CO
HNZ HEINZ H J CO
IP INTL PAPER *not in downloads
KFT KRAFT FOODS INC
KO COCA COLA CO THE
MO ALTRIA GROUP INC
PEP PEPSICO INC
PG PROCTER GAMBLE CO
PM PHILIP MORRIS INTL *less than 2000 observations
SLE SARA LEE CP
XRX XEROX CP
HAR-RV Model 5DAY WEEK MONTH
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) -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 ***
PG R-Squared
1) HAR-RV 31.8% 45.7% 48.6%
2) & Sector 33.0% 51.8% 54.2%
3) & Market 45.1% 52.0% 54.0%
4) Sector & Market 45.2% 52.7% 55.7%
5) & Dispersion 47.0% 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%
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%.
Health Care
ABT ABBOTT LABORATORIES
AMGN Amgen Inc.
BAX BAXTER INTL INC
BMY BRISTOL MYERS SQIBB
CI CIGNA CP *not in downloads
COV COVIDIEN LTD *less than 2000 observations
JNJ JOHNSON AND JOHNS DC
MDT MEDTRONIC INC
MRK MERCK CO INC
PFE PFIZER INC
UNH UNITEDHEALTH GROUP
WYE WYETH *less than 2000 observations
HAR-RV Model 5DAY WEEK MONTH
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 ***
JNJ R-squared
1) HAR-RV 38.1% 51.0% 47.1%
2) & Sector 52.8% 64.8% 54.8%
3) & Market 48.8% 59.1% 45.2%
4) Sector & Market 51.5% 64.1% 43.0%
5) & Dispersion 56.2% 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%
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%
FinancialAIG AMER INTL GROUP INC *not in downloads
ALL ALLSTATE CP
AXP AMER EXPRESS INC
BAC BK OF AMERICA CP
BK BANK OF NY MELLON CP
C CITIGROUP INC
COF CAPITAL ONE FINANCIA
GS GOLDMAN SACHS GRP
HIG HARTFORD FIN SVC *not in downloads
JPM JP MORGAN CHASE CO
MS MORGAN STANLEY *less than 2000 observations
NYX NYSE EURONEXT *less than 2000 observations
RF REGIONS FINANCIAL CP *less than 2000 observations
USB US BANCORP
WB WACHOVIA CP *not in downloads
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 ***
DAY WEEK MONTH
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 *
JPM R-Squared
1) HAR-RV 46.0% 47.0% 50.4%
2) & Sector 50.9% 53.3% 51.6%
3) & Market 59.9% 75.8% 60.1%
4) Sector & Market 60.0% 76.1% 57.7%
5) Dispersion 64.6% 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%
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%
Basic Materials
AA ALCOA INC
BHI BAKER HUGHES INTL
COP CONOCOPHILLIPS
CVX CHEVRON CORP
DD DU PONT E I DE NEM
DOW DOW CHEMICAL
EP EL PASO CORPORATION
HAL HALLIBURTON CO
NOV NATL OILWELL VARCO
OXY OCCIDENTAL PET
SLB SCHLUMBERGER LTD
WMB WILLIAMS COS
XOM EXXON MOBIL CP
DAY WEEK MONTH
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 ***
AA R-Squared
1) HAR-RV 49.7% 59.5% 52.5%
2) & Sector 55.9% 67.4% 53.9%
3) & Market 57.2% 69.1% 54.4%
4) Sector & Market 58.1% 71.5% 53.1%
5) Dispersion 59.0% 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%
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%
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
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
DAY WEEK MONTH
TGT R-Squared
1) HAR-RV 56.6% 67.0% 60.8%
2) & Sector 56.5% 67.1% 61.3%
3) & Market 54.3% 67.3% 57.9%
4) Sector & Market 54.3% 67.6% 58.5%
5) & Dispersion 54.5% 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%
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%
TechnologyCSCO Cisco Systems, Inc.
DELL Dell Inc.
EMC E M C CP
GOOG Google Inc. *less than 2000
HPQ HEWLETT PACKARD CO
IBM INTL BUSINESS MACH
INTC Intel Corporation
MSFT Microsoft Corporation
ORCL Oracle Corporation
QCOM QUALCOMM Incorporated
S SPRINT NXTEL CP *less than 2000
T AT&T INC.
TXN TEXAS INSTRUMENTS
TYC TYCO INTL LTD NEW
VZ VERIZON COMMUN
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 ***
DAY WEEK MONTH
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 ***
ORCL R-Squared
1) HAR-RV 31.8% 45.7% 48.6%
2) & Sector 45.3% 52.9% 57.1%
3) & Market 50.9% 60.7% 63.8%
4) Sector & Market 54.0% 60.9% 56.3%
5) & Dispersion 57.9% 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%
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%
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.
Betas
• Basic Materials: 1.19• Financial: 1.50• Service: 0.92
• Consumer Goods: 0.78• Health Care: 0.66• Technology: 1.1
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
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%.
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