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Calculating and Plotting MSEPowerPoint Presentation

Calculating and Plotting MSE

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### Calculating and Plotting MSE

Angela Ryu

Economics 201FS

Honors Junior Workshop: Finance

Duke University

March 24, 2010

Example

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

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

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

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

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

WMT(Y) vs. XOM(X) (5 min) sampling interval

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