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HAR-RV with Sector Variance Sharon Lee March 18, 2009.

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1 HAR-RV with Sector Variance Sharon Lee March 18, 2009

2 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?

3 Background Mathematics Realized Variance, where rt,j is the log-return Sector Realized Variance: Average of equally-weighted same sector stocks in S&P100

4 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.

5 Sectors Consumer Goods Healthcare Financial Technology –Stocks with less than 2000 observations were removed

6 Consumer Goods Sector 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

7 PG, Day

8 PG, Week

9 PG, Month

10 PG and Sector: Annualized RV

11 PG, Sector, Day

12 PG, Sector, Week

13 PG, Sector, Month

14 PG Regression PG Day EstimateStd. Errort-value Intercept 17.3194.2474.078 *** day 0.2550.02211.823 *** week 0.2260.0415.575 *** month 0.3690.0428.778 *** PG Week EstimateStd. Errort-value Intercept 23.8732.7678.629 *** day 0.1190.0148.459 *** week 0.2050.0267.769 *** month 0.4700.02717.113 *** PG Month EstimateStd. Errort-value Intercept 36.5692.21516.509 *** day 0.0540.0114.834 *** week 0.1740.0218.192 *** month 0.4640.02220.705 *** ***.001**.01*.05'.' 0.1' ' 1

15 PG and Sector Regression PG, Sector Day EstimateStd. Errort-value Intercept 8.8854.2562.087* day 0.2120.0268.276*** week -0.2400.059-4.084*** month 0.4650.0875.371*** daysect 0.0680.0461.476 wksect 0.8320.0899.349*** mosect -0.5220.093-5.596*** PG, Sector Week EstimateStd. Errort-value Intercept 14.3262.4955.742*** day 0.0570.0153.820*** week -0.4020.034-11.687*** month 0.6900.05113.599*** daysect 0.1060.0273.923*** wksect 1.0800.05220.708*** mosect -0.7740.055-14.147*** PG, Sector Month EstimateStd. Errort-value Intercept 29.7442.09014.234*** day -0.0060.013-0.489** week -0.1840.029-6.375*** month 0.5260.04212.407*** daysect 0.1340.0235.929*** wksect 0.6210.04414.070*** mosect -0.4350.047-9.356*** ***.001**.01*.05'.' 0.1' ' 1

16 Healthcare 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

17 JNJ, Day

18 JNJ, Week

19 JNJ, Month

20 JNJ and Sector: Annualized RV

21 JNJ, Sector, Day

22 JNJ, Sector, Week

23 JNJ, Sector, Month

24 JNJ Regression JNJ Day EstimateStd. Errort-value Intercept 13.6323.0554.462 *** day 0.1900.0228.492 *** week 0.4420.03911.349 *** month 0.2260.0386.019 *** JNJ Week EstimateStd. Errort-value Intercept 19.4892.0969.299 *** day 0.1570.01510.219 *** week 0.3190.02711.910 *** month 0.3220.02612.421 *** JNJ Month EstimateStd. Errort-value Intercept 31.4731.82317.266 *** day 0.0750.0135.612 *** week 0.1900.0238.141 *** month 0.4150.02317.839 ***

25 JNJ and Sector Regression JNJ, Sector Day EstimateStd. Errort-value Intercept 0.2352.7020.087 day 0.2660.02212.274*** week -0.0940.042-2.221*** month 0.5850.05410.845*** daysect -0.0070.021-0.331 wksect 0.6430.04414.771*** mosect -0.4960.048-10.406*** JNJ, Sector Week EstimateStd. Errort-value Intercept 4.5131.9022.372* day 0.1290.0158.432*** week -0.0880.030-2.967** month 0.6410.03816.857*** daysect 0.1720.01511.798*** wksect 0.4290.03114.007*** mosect -0.4460.034-13.270*** JNJ, Sector Month EstimateStd. Errort-value Intercept 18.5111.81710.187*** day 0.0590.0154.086** week -0.0210.029-0.730 month 0.5090.03713.758*** daysect 0.1010.0147.249*** wksect 0.2320.0297.886*** mosect -0.1920.033-5.859***

26 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

27 JPM, Day

28 JPM, Week

29 JPM, Month

30 JPM and Sector: Annualized RV

31 JPM, Sector, Day

32 JPM, Sector, Week

33 JPM, Sector, Month

34 JPM Regression JPM Day EstimateStd. Errort-value Intercept 33.8319.5163.555 *** day 0.4690.02122.713 *** week 0.1380.0344.068 *** month 0.2620.0347.685 *** JPM Week EstimateStd. Errort-value Intercept 58.0507.5067.734 *** day 0.2040.01612.550 *** week 0.2440.0279.074 *** month 0.3270.02712.083 *** JPM Month EstimateStd. Errort-value Intercept 66.8426.04911.050 *** day 0.1090.0138.465 *** week 0.0000.022-0.020 *** month 0.6680.02526.767 ***

35 JPM and Sector Regression JPM, Sector Day EstimateStd. Errort-value Intercept -4.6707.623-0.613 day 0.4340.02318.888*** week -0.0260.039-0.670 month 0.3530.0507.123*** daysect 0.3270.0555.935*** wksect 0.3730.0904.154*** mosect -0.4410.086-5.128*** JPM, Sector Week EstimateStd. Errort-value Intercept 4.2025.9860.702 day 0.1500.0188.339*** week -0.0080.031-0.245 month 0.4760.03912.237*** daysect 0.5520.04312.746*** wksect 0.2370.0703.363*** mosect -0.4350.067-6.451*** JPM, Sector Month EstimateStd. Errort-value Intercept 38.8784.8338.040*** day 0.0300.0152.030* week -0.0060.025-0.238 month 0.5070.03215.967*** daysect 0.3140.0358.993*** wksect 0.3690.0576.451*** mosect -0.4230.055-7.624***

36 Technology CSCOCisco Systems, Inc.Technology DELLDell Inc.Technology EMCE M C CPTechnology GOOGGoogle Inc.Technology *less than 2000 HPQHEWLETT PACKARD COTechnology IBMINTL BUSINESS MACHTechnology INTCIntel CorporationTechnology MSFTMicrosoft CorporationTechnology ORCLOracle CorporationTechnology QCOMQUALCOMM IncorporatedTechnology SSPRINT NXTEL CPTechnology *less than 2000 TAT&T INC.Technology TXNTEXAS INSTRUMENTSTechnology TYCTYCO INTL LTD NEWTechnology VZVERIZON COMMUNTechnology

37 ORCL, Day

38 ORCL, Week

39 ORCL, Month

40 ORCL, Sector, Day

41 ORCL, Sector, Week

42 ORCL, Sector, Month

43 ORCL Regression ORCL Day EstimateStd. Errort-value Intercept 17.3194.2474.078 *** day 0.2550.02211.823 *** week 0.2260.0415.575 *** month 0.3690.0428.778 *** ORCL Week EstimateStd. Errort-value Intercept 23.8742.7678.630 *** day 0.1190.0148.459 *** week 0.2050.0267.769 *** month 0.4700.02717.113 *** ORCL Month EstimateStd. Errort-value Intercept 36.5712.21516.509 *** day 0.0540.0114.834 *** week 0.1740.0218.192 *** month 0.4640.02220.704 ***

44 ORCL and Sector Regression ORCL, Sector Day EstimateStd. Errort-value Intercept 2.3655.1090.463 day 0.4460.02418.482*** week -0.0040.042-0.107 month 0.3550.0487.337*** daysect -0.0420.028-1.493 wksect 0.2450.0425.835*** mosect -0.1280.034-3.729*** ORCL, Sector Week EstimateStd. Errort-value Intercept 5.7723.6991.560 day 0.1320.0177.583*** week 0.1020.0303.379*** month 0.4660.03513.320*** daysect 0.0780.0203.849*** wksect 0.1970.0306.490*** mosect -0.1720.025-6.937*** ORCL, Sector Month EstimateStd. Errort-value Intercept 22.8052.9067.848*** day 0.0440.0143.222** week 0.0810.0233.442*** month 0.4890.02717.926*** daysect 0.0850.0165.337*** wksect 0.1710.0247.255*** mosect -0.1720.019-8.900***

45 Comparison Across Regressions Adjusted R-squared DaySector WeekSector MonthSector PG (Consumer)0.31840.360613%0.45690.587028%0.48580.572918% JNJ (Healthcare)0.38070.528439%0.51000.648227%0.47060.547516% JPM (Financial)0.45950.509211%0.47040.532513%0.50390.51602% ORCL (Technology)0.31840.452942%0.45690.528716%0.48580.570617% -Adding sector variance increases fit for each regression -The Financial sector shows least improvement -Healthcare and Technology sectors show large improvements for day prediction

46 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?

47 Next Steps… Add Basic Materials, Industrial, Services, and Utilities Sectors Investigate betas

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