1. Calculating and Plotting MSE
Angela Ryu
Economics 201FS
Honors Junior Workshop: Finance
Duke University
March 24, 2010

2. Example XOM (Y) vs. WMT (X) Number of days: 1093 days
Sampling interval: 5 minutes
Beta Calculation days: 30 days

3. Preparation (1) - Setup
Get WMT, XOM log returns and denote Px, Py respectively.
Sample P by 5 minutes: 76 data for each day
Take out the overnight returns
Size (Px) = Size (Py) = 76 * 1093

4. Preparation (2) – Calculate Beta
Days – (1:30), (2:31), (3:32), … , (1064:1093)
Case (1:30):
Take first 76 * 30 data (1 to 76*30) from Px and Py and denote X1:30 and Y1:30 .
Calculate with (where Y = βX)
Take the mean and denote β1:30
Case (2:31):
Exclude the day 1 data (1 to 76) and add data on the day 31 (76*30+1 to 76*31). Get β2:31
Repeat to get β3:32, …, β1063:1092
Note: all betas are scalar

5. Preparation (2) – Calculate Beta
Case (1:30):
Case (2:31):
Day 1 (76 data)
Day 2 (76 data) …
Day 30 (76 data)
Day 31 (76 data)
Day 1092 (76 data)
Day 1093 (76 data)
Day 1 (76 data)
Day 2 (76 data) …
Day 30 (76 data)
Day 31 (76 data)
Day 1092 (76 data)
Day 1093 (76 data)

6. Preparation (3) – Calculate MSE
Calculate SE for each beta.
SE31 = (Y31 - β1:30 * X31 )2
SE32 = (Y32 – β2:31 * X32 )2 …
SE1093= (Y1093 – β1063:1092 * X1093 )2
Note: SEi is a vector of size 76 for all i = 31, … 1093
Take the average to get MSE30
MSE30 = avg [avg(SE1:30 ), …, avg(SE1064:1093)]
()2  Square each term in vector

7. Preparation (4) – change intervals & plot for each sampling interval
Sampling intervals: change from 1 min to 20 mins in prep. (1)
Beta Calculation intervals: change from 1 day to 50 days in prep (2)
Plot for each sampling interval
X axis: Beta Cal. Interval days (from 1 to 50)
Y axis: the value of MSE
In total, we get 20 plots

8. WMT(Y) vs. XOM(X) (5 min)