har-rv models including sector and market regressors

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


(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 ***

---


(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


(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


(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 ***


(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


(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 .


(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


(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.


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


(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 .


(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 ***


(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


(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


(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 *


(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.


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


(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


(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


(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.


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%.

har-rv models including sector and market regressors

Documents