Realized Beta: Market vs. Individual stocks

Angela Ryu

Economics 201FSHonors 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: (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 )

Continuing from previous work

• Last presentation: MSE of ind. stock vs. ind. stock was plotted and 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 are 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?