HAR-RV with Sector Variance

Sharon Lee

March 18, 2009

Intuition

• The returns of an individual equity should be correlated with returns from its sector

• Using the predictive model HAR-RV, how does incorporating sector realized volatility affect the predicted values for an equity?

Background Mathematics

Realized Variance, where rt,j is the log-return

Sector Realized Variance: Average of equally-weighted same sector stocks in S&P100

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.

Sectors

• Consumer Goods

• Healthcare

• Financial

• Technology

– Stocks with less than 2000 observations were removed

Consumer Goods Sector

AVP 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

PG and Sector: Annualized RV

PG, Sector, Day

PG, Sector, Week

PG, Sector, Month

PG RegressionPG Day

  Estimate Std. Error t-value  

Intercept 17.319 4.247 4.078 ***

day 0.255 0.022 11.823 ***

week 0.226 0.041 5.575 ***

month 0.369 0.042 8.778 ***

PG Week

  Estimate Std. Error t-value  

Intercept 23.873 2.767 8.629 ***

day 0.119 0.014 8.459 ***

week 0.205 0.026 7.769 ***

month 0.470 0.027 17.113 ***

PG Month

  Estimate Std. Error t-value  

Intercept 36.569 2.215 16.509 ***

day 0.054 0.011 4.834 ***

week 0.174 0.021 8.192 ***

month 0.464 0.022 20.705 ***

*** .001 **.01 * .05 '.' 0.1 ' ' 1

PG and Sector RegressionPG, Sector Day

  Estimate Std. Error t-value  

Intercept 8.885 4.256 2.087 *

day 0.212 0.026 8.276 ***

week -0.240 0.059 -4.084 ***

month 0.465 0.087 5.371 ***

daysect 0.068 0.046 1.476  

wksect 0.832 0.089 9.349 ***

mosect -0.522 0.093 -5.596 ***

PG, Sector Week

  Estimate Std. Error t-value  

Intercept 14.326 2.495 5.742 ***

day 0.057 0.015 3.820 ***

week -0.402 0.034 -11.687 ***

month 0.690 0.051 13.599 ***

daysect 0.106 0.027 3.923 ***

wksect 1.080 0.052 20.708 ***

mosect -0.774 0.055 -14.147 ***

PG, Sector Month

  Estimate Std. Error t-value  

Intercept 29.744 2.090 14.234 ***

day -0.006 0.013 -0.489 ** 

week -0.184 0.029 -6.375 ***

month 0.526 0.042 12.407 ***

daysect 0.134 0.023 5.929 ***

wksect 0.621 0.044 14.070 ***

mosect -0.435 0.047 -9.356 ***

*** .001 **.01 * .05 '.' 0.1 ' ' 1

HealthcareABT 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

JNJ and Sector: Annualized RV

JNJ, Sector, Day

JNJ, Sector, Week

JNJ, Sector, Month

JNJ RegressionJNJ Day

  Estimate Std. Error t-value  

Intercept 13.632 3.055 4.462 ***

day 0.190 0.022 8.492 ***

week 0.442 0.039 11.349 ***

month 0.226 0.038 6.019 ***

JNJ Week

  Estimate Std. Error t-value  

Intercept 19.489 2.096 9.299 ***

day 0.157 0.015 10.219 ***

week 0.319 0.027 11.910 ***

month 0.322 0.026 12.421 ***

JNJ Month

  Estimate Std. Error t-value  

Intercept 31.473 1.823 17.266 ***

day 0.075 0.013 5.612 ***

week 0.190 0.023 8.141 ***

month 0.415 0.023 17.839 ***

JNJ and Sector RegressionJNJ, Sector Day

  Estimate Std. Error t-value  

Intercept 0.235 2.702 0.087  

day 0.266 0.022 12.274 ***

week -0.094 0.042 -2.221 ***

month 0.585 0.054 10.845 ***

daysect -0.007 0.021 -0.331  

wksect 0.643 0.044 14.771 ***

mosect -0.496 0.048 -10.406 ***

JNJ, Sector Week

  Estimate Std. Error t-value  

Intercept 4.513 1.902 2.372 *

day 0.129 0.015 8.432 ***

week -0.088 0.030 -2.967 **

month 0.641 0.038 16.857 ***

daysect 0.172 0.015 11.798 ***

wksect 0.429 0.031 14.007 ***

mosect -0.446 0.034 -13.270 ***

JNJ, Sector Month

  Estimate Std. Error t-value  

Intercept 18.511 1.817 10.187 ***

day 0.059 0.015 4.086 **

week -0.021 0.029 -0.730  

month 0.509 0.037 13.758 ***

daysect 0.101 0.014 7.249 ***

wksect 0.232 0.029 7.886 ***

mosect -0.192 0.033 -5.859 ***

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

JPM and Sector: Annualized RV

JPM, Sector, Day

JPM, Sector, Week

JPM, Sector, Month

JPM RegressionJPM Day

  Estimate Std. Error t-value  

Intercept 33.831 9.516 3.555 ***

day 0.469 0.021 22.713 ***

week 0.138 0.034 4.068 ***

month 0.262 0.034 7.685 ***

JPM Week

  Estimate Std. Error t-value  

Intercept 58.050 7.506 7.734 ***

day 0.204 0.016 12.550 ***

week 0.244 0.027 9.074 ***

month 0.327 0.027 12.083 ***

JPM Month

  Estimate Std. Error t-value  

Intercept 66.842 6.049 11.050 ***

day 0.109 0.013 8.465 ***

week 0.000 0.022 -0.020 ***

month 0.668 0.025 26.767 ***

JPM and Sector RegressionJPM, Sector Day

  Estimate Std. Error t-value  

Intercept -4.670 7.623 -0.613  

day 0.434 0.023 18.888 ***

week -0.026 0.039 -0.670  

month 0.353 0.050 7.123 ***

daysect 0.327 0.055 5.935 ***

wksect 0.373 0.090 4.154 ***

mosect -0.441 0.086 -5.128 ***

JPM, Sector Week

  Estimate Std. Error t-value  

Intercept 4.202 5.986 0.702  

day 0.150 0.018 8.339 ***

week -0.008 0.031 -0.245  

month 0.476 0.039 12.237 ***

daysect 0.552 0.043 12.746 ***

wksect 0.237 0.070 3.363 ***

mosect -0.435 0.067 -6.451 ***

JPM, Sector Month

  Estimate Std. Error t-value  

Intercept 38.878 4.833 8.040 ***

day 0.030 0.015 2.030 *

week -0.006 0.025 -0.238  

month 0.507 0.032 15.967 ***

daysect 0.314 0.035 8.993 ***

wksect 0.369 0.057 6.451 ***

mosect -0.423 0.055 -7.624 ***

TechnologyCSCO Cisco Systems, Inc. Technology

DELL Dell Inc. Technology

EMC E M C CP Technology

GOOG Google Inc. Technology *less than 2000

HPQ HEWLETT PACKARD CO Technology

IBM INTL BUSINESS MACH Technology

INTC Intel Corporation Technology

MSFT Microsoft Corporation Technology

ORCL Oracle Corporation Technology

QCOM QUALCOMM Incorporated Technology

S SPRINT NXTEL CP Technology *less than 2000

T AT&T INC. Technology

TXN TEXAS INSTRUMENTS Technology

TYC TYCO INTL LTD NEW Technology

VZ VERIZON COMMUN Technology

ORCL, Sector, Day

ORCL, Sector, Week

ORCL, Sector, Month

ORCL RegressionORCL Day

  Estimate Std. Error t-value  

Intercept 17.319 4.247 4.078 ***

day 0.255 0.022 11.823 ***

week 0.226 0.041 5.575 ***

month 0.369 0.042 8.778 ***

ORCL Week

  Estimate Std. Error t-value  

Intercept 23.874 2.767 8.630 ***

day 0.119 0.014 8.459 ***

week 0.205 0.026 7.769 ***

month 0.470 0.027 17.113 ***

ORCL Month

  Estimate Std. Error t-value  

Intercept 36.571 2.215 16.509 ***

day 0.054 0.011 4.834 ***

week 0.174 0.021 8.192 ***

month 0.464 0.022 20.704 ***

ORCL and Sector RegressionORCL, Sector Day

  Estimate Std. Error t-value  

Intercept 2.365 5.109 0.463  

day 0.446 0.024 18.482 ***

week -0.004 0.042 -0.107  

month 0.355 0.048 7.337 ***

daysect -0.042 0.028 -1.493  

wksect 0.245 0.042 5.835 ***

mosect -0.128 0.034 -3.729 ***

ORCL, Sector Week

  Estimate Std. Error t-value  

Intercept 5.772 3.699 1.560  

day 0.132 0.017 7.583 ***

week 0.102 0.030 3.379 ***

month 0.466 0.035 13.320 ***

daysect 0.078 0.020 3.849 ***

wksect 0.197 0.030 6.490 ***

mosect -0.172 0.025 -6.937 ***

ORCL, Sector Month

  Estimate Std. Error t-value  

Intercept 22.805 2.906 7.848 ***

day 0.044 0.014 3.222 **

week 0.081 0.023 3.442 ***

month 0.489 0.027 17.926 ***

daysect 0.085 0.016 5.337 ***

wksect 0.171 0.024 7.255 ***

mosect -0.172 0.019 -8.900 ***

Comparison Across RegressionsAdjusted R-squared

  Day Sector   Week Sector   Month Sector  

PG (Consumer) 0.3184 0.3606 13% 0.4569 0.5870 28% 0.4858 0.5729 18%

JNJ (Healthcare) 0.3807 0.5284 39% 0.5100 0.6482 27% 0.4706 0.5475 16%

JPM (Financial) 0.4595 0.5092 11% 0.4704 0.5325 13% 0.5039 0.5160 2%

ORCL (Technology) 0.3184 0.4529 42% 0.4569 0.5287 16% 0.4858 0.5706 17%

- Adding sector variance increases fit for each regression- The Financial sector shows least improvement- Healthcare and Technology sectors show large improvements for

day prediction

New Questions

• Since the R-squared analyses show that sector variance affects individual stocks in different degrees, what can be said about investor behavior for particular sectors across each time horizon? – Do the risk factor (beta) for sectors have any

correlation with results?

Next Steps…

• Add Basic Materials, Industrial, Services, and Utilities Sectors

• Investigate betas