beta estimate of high frequency data
DESCRIPTION
Beta Estimate of High Frequency Data. Angela Ryu Economics 201FS Honors Junior Workshop: Finance Duke University March 3, 2010. Data. XOM (Exxon Mobile) Dec 1 1999 – Jan 7 2009 (2264 days) GOOG (Google) Aug 20 2004 – Jan 7 2009 (1093 days) WMT (Wal-Mart) - PowerPoint PPT PresentationTRANSCRIPT
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Beta Estimate of High Frequency Data
Angela Ryu
Economics 201FSHonors Junior Workshop: Finance
Duke University
March 3, 2010
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Data
• XOM (Exxon Mobile) – Dec 1 1999 – Jan 7 2009 (2264 days)
• GOOG (Google)– Aug 20 2004 – Jan 7 2009 (1093 days)
• WMT (Wal-Mart)– Apr 9 1997 – Jan 7 2009 (2921 days)
FOR ALL 3 stocks
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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!
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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 )
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WMT vs. XOM (2 min.)
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WMT vs. XOM (5 min.)
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WMT vs. XOM (10 min.)
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WMT vs. XOM (15 min.)
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WMT vs. XOM (20 min.)
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XOM vs. WMT (2 min.)
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XOM vs. WMT (5 min.)
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XOM vs. WMT (10 min.)
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XOM vs. WMT (15 min.)
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XOM vs. WMT (20 min.)
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GOOG vs. WMT (2 min.)
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GOOG vs. WMT (5 min.)
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GOOG vs. WMT (10 min)
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GOOG vs. WMT (15 min.)
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GOOG vs. WMT (20 min.)
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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
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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
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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)