Realized Beta: Market vs. Individual stocks Angela Ryu Economics 201FS 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 – Jan (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. y pre_day31 = β day1_30 * x act_day31  SE day31 = (y pre_day31 – y act_day31 ) 2 y pre_day32 = β day2_31 * x act_day32  SE day32 = (y pre_day32 – y act_day32 ) 2 …  MSE 30 = avg(SE day31, SE day32,... SE day1093 )

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?