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

2. 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?

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

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

5. PG: Annualized RV

6. AVP: Annualized RV

7. CL: Annualized RV

8. Sector Annualized RV

9. 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.

10. PG: HAR-RV, one day

11. PG: HAR-RV, day, week

12. PG and Sector (HAR-RV,day)

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

14. Linear regression: First Pass
Regressing one-day and five-day PG lag terms on PG return:
Coefficients:
(Intercept) lag lag5
Regressing one-day and five-day PG lag terms and one-day and five-day sector lag terms on PG return:
(Intercept) lag lag sector sector5

15. 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