1. Beta Estimate of High Frequency Data
Angela Ryu
Economics 201FS
Honors Junior Workshop: Finance
Duke University
March 3, 2010

2. Data XOM (Exxon Mobile) GOOG (Google) WMT (Wal-Mart)
Dec – Jan (2264 days)
GOOG (Google)
Aug – Jan (1093 days)
WMT (Wal-Mart)
Apr – Jan (2921 days)
 FOR ALL 3 stocks

3. Motivation Multivariate Measures: Beta
Problem of balancing bias/precision
High frequency sampling: biased, due to microstructure noise
Low frequency sampling: imprecise
Theoretical approach requires more background knowledge
 approach empirically!

4. Preparation Interday returns are excluded
Beta calculated from: (for βX = Y, X,Y stock prices)
Sampling intervals: 1 to 20 minutes
Beta Calculation intervals: 1 to 50 days
Mean Squared Error calculated for each Beta interval
MSE of GOOG(X) vs. XOM(Y) , 30 days interval? = Average of Squared Errors of each days predicted by using β
i.e. ypre_day31 = βday1_30 * xact_day31 SEday31 = (ypre_day31 – yact_day31 )2 ypre_day32 = βday2_31 * xact_day32  SEday32 = (ypre_day32 – yact_day32 )2 …  MSE30 = avg(SEday31 , SEday32 , ... SEday1093 )

5. WMT vs. XOM (2 min.)

6. WMT vs. XOM (5 min.)

7. WMT vs. XOM (10 min.)

8. WMT vs. XOM (15 min.)

9. WMT vs. XOM (20 min.)

10. XOM vs. WMT (2 min.)

11. XOM vs. WMT (5 min.)

12. XOM vs. WMT (10 min.)

13. XOM vs. WMT (15 min.)

14. XOM vs. WMT (20 min.)

15. GOOG vs. WMT (2 min.)

16. GOOG vs. WMT (5 min.)

17. GOOG vs. WMT (10 min)

18. GOOG vs. WMT (15 min.)

19. GOOG vs. WMT (20 min.)

20. Results
5 – 15 days interval for Beta gave least MSE for many stock pairs, for most sampling intervals
As the sampling interval increased, MSE for shorter Beta intervals increased rapidly
For 20 min. sampling interval, there is less increase of MSE as increase in Beta interval compared to shorter sampling intervals

21. Analysis
Against our intuition: why would more information harm prediction of the price?
Possible interpretation
Given a sampling interval, after a certain range of “information” gather for Beta estimation, say 5 – 15 days, more information distorts the prediction
On the other hand, some short Beta intervals (e.g. 1 day, 2 days) for longer sampling intervals may be insufficient and result in high MSE

22. Questions & Further Steps
Theoretical evidence? Any relevant papers?
Is the estimator biased? Why?
What is the role of Microstructure noise?
Check calculations. Try with other stocks or possibly portfolios (industry/macroeconomic factors)
Use Realized Beta and compare the results
Andersen, Bollerslev, Diebold and Wu (2003)