HAR-RV with Sector Variance Sharon Lee February 18, 2009

Starting Point Intuitively, 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?

Consumer Goods Sector Proctor & Gamble Co. (PG) Avon Products, Inc. (AVP) Colgate-Palmolive Co. (CL)

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

PG: Annualized RV

AVP: Annualized RV

CL: Annualized RV

Sector Annualized RV

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.

PG: HAR-RV, one day

PG: HAR-RV, day, week

PG and Sector (HAR-RV,day)

PG and Sector (HAR-RV, 5-day)

Linear regression: First Pass Regressing one-day and five-day PG lag terms on PG return: Coefficients: (Intercept) lag1 lag5 2.1459 0.4549 0.3180 Regressing one-day and five-day PG lag terms and one-day and five-day sector lag terms on PG return: (Intercept) lag1 lag5 sector1 sector5 0.89684 0.08773 0.11054 0.49368 0.13244

What’s Next Figure out how to run regressions with t-tests for significance Investigate R-squared values Incorporate more stocks and sectors Consider additional regressors