Economics 690
Tauchen
Fall 2015
1.1
Scaling Returns
The convention is to use geometric returns expressed as a percent. Thus if P i are the 5-min price observations, then we compute the returns as r i
= 100
× log ( P i
)
− log ( P i
−
1
)
1.2
Scaling Variance
The variance measures are in units of variance per day. The daily realized variance is
RV =
1 r i
2
The variance measures are convenient mathematically but very hard for the user to interpret.
Thus we will always report, unless told otherwise, the annualized versions. For the case of the realized variance this would be
Annualized Realized Variance: =
√
252
×
RV
The units are now in percent standard deviations per year.
2.1
Default Matlab Graphics are Unacceptable
The default graphic for Matlab is optimized for viewing on the screen, but it is terrible for reporting results in papers and presentations. Below is a pretty bad plot of BAC 2007–2014.
A plot of the returns is equally bad. Some better graphics follow.

60
50
40
30
20
10
0
0000 0050 0100 0150 0200 0250 0300 0350 0400 0450
10
5
0
−5
−10
−15
−20
0000 0050 0100 0150 0200 0250 0300 0350 0400 0450
Some more effective plots of Bank of America are as follows:
2

Bank of America (BAC), 5−Min Returns
10
5
0
−5
−10
−15
−20
2007 2008 2009 2010 2011 2012 2013
Figure 1: Bank of America, 2007–2014
2014 2015
3

40
30
20
10
60
50
0
2007 2008 2009 2010 2011 2012 2013
Figure 2: Bank of America, 2007–2014
2014 2015
4

50
45
40
25
20
15
35
30
10
2008−01 2008−04 2008−07 2008−10
Figure 3: Bank of America, 2008
2009−01
5

Bank of America (BAC) 2008 09 16
30
29.5
29
28.5
28
27.5
27
26.5
26
25.5
09:00 10:00 11:00 12:00 13:00 14:00
Figure 4: Bank of America, September 9, 2009
15:00 16:00
6

Annualized Realized Volatility
200
150
100
50
0
Jan 03, 2007 Oct 19, 2007 Aug 11, 2008 Jun 01, 2009 Mar 17, 2010
Figure 5: Realized Variance (Annualized) XOM 2007-2010
Dec 30, 2010
7

Annualized Bipower Variation
200
150
100
50
0
Jan 03, 2007 Oct 19, 2007 Aug 11, 2008 Jun 01, 2009 Mar 17, 2010
Figure 6: Bipower Variation (Annualized) XOM 2007-2010
Dec 30, 2010
8