Realized Beta Market vs Individual stocks Angela Ryu

Realized Beta: Market vs. Individual stocks Angela Ryu Economics 201 FS Honors Junior Workshop: Finance Duke University March 17, 2010

Data • S&P 500 • TGT, XOM, WMT, IBM, MSFT, AAPL, JPM, GS, C (9 stocks) • Aug 20 2004 – Jan 7 2009 (1093 days)

Preparation • Overnight returns are excluded • Beta calculated from: prices) (for βX = Y, X, Y stock • 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_day 31 = βday 1_30 * xact_day 31 SEday 31 = (ypre_day 31 – yact_day 31 )2 ypre_day 32 = βday 2_31 * xact_day 32 SEday 32 = (ypre_day 32 – yact_day 32 )2 … MSE 30 = avg(SEday 31 , SEday 32 , . . . SEday 1093 )

Continuing from previous work • Last presentation: MSE of ind. stock vs. ind. stock was plotted analyzed • Now, plot MSE of S&P 500 vs. ind. stock and see how it changes as the sampling interval (1 to 20 minutes) and Beta calculation interval (1 to 50 days) changes.

SPY vs. JPM (2 min. ) Almost linearly increasing

SPY vs. JPM (5 min. )

SPY vs. JPM (10 min. ) Sudden increase in small (1 – 3 days) Beta Cal. interval

SPY vs. JPM (15 min. )

SPY vs. JPM (20 min. ) At longer sampling int. (18 ~ 20 min), slope decreases: that is, an additional day in Beta calculation does not increase MSE as much as for the case for shorter (2 – 10 min) sampling int.

Comparing 9 stocks (5 min) TGT WMT XOM GS C JPM AAPL MSFT IBM

Comparing 9 stocks (20 min)

Results • Alike ind. stock vs. ind. stock case, 3 results were found – As the sampling interval increased, MSE spiked up for very short Beta calculation interval (1 – 3 days) – As the sampling interval increased, Slope of MSE flattened. – For relatively long sampling intervals (10 – 20 min) MSE was smallest at 5 – 15 day Beta Calculation interval • MSE plots of 9 stocks are very similar to each other

Questions & Further Steps • What would be possible explanations? If there any, how should its validity be checked? • Would results from even shorter sampling intervals (1 sec, 30 sec, etc. ) show similar results? Any microstructure noise factor?