# Homework about Financial Risk Management

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### Question Description

Go to Yahoo Finance and download historical data for SPY ETF over the last two years, starting from 2017 to today. Compute the daily return using the adjusted close price column. This should result in a new time series (column).

Using the daily returns of the SPY ETF, calibrate a Geometric Brownian Motion process. Report the corresponding mu and sigma.

Given the calibrated model, simulate the SPY price path over the next three months, i.e. 256/4=64 trading days. Provide a couple of plots to demonstrate this.

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mikewinter3
School: Cornell University

Attached.

1

Geometric Brownian motion Process for SPY ETF Stock Price

Student name:
Institutional affiliation:

2
Geometric Brownian motion Process for SPY ETF Stock Price
The attached word document and excel file addresses the question “Homework about Financial
Risk Management” by answering the following:
Go to Yahoo Finance and download historical data for SPY ETF over the last two years, starting
from 2017 to today. Compute the daily return using the adjusted close price column. This should
result in a new time series (column).
Using the daily returns of the SPY ETF, calibrate a Geometric Brownian Motion process. Report
the corresponding mu and sigma.
Given the calibrated model, simulate the SPY price path over the next three months, i.e. 256/4=64
trading days. Provide a couple of plots to demonstrate this.

1

Geometric Brownian motion Process for SPY ETF Stock Price

Student name:
Institutional affiliation:

2

Geometric Brownian motion

Geometric Brownian motion Process for SPY ETF Stock Price
See the attached excel file for the data I downloaded from Yahoo Finance.
Using the daily returns of the SPY ETF, calibrate a Geometric Brownian Motion process. Report
the corresponding mu and sigma.
See the attached excel file the daily returns of the SPY ETF and calibrated Geometric Brownian
motion process:
Mean (mu)
Std deviation( sigma)

-0.03912%
0.008507644

See the excel file for the simulated SPY price path over the next three months, that is between 6 th
February 2017 to 8th May 2017 ( a total of 64 trading days). The following graphs demonstrate the
simulation:

3

Geometric Brownian motion

4

Geometric Brownian motion
References
Jenkins, M. S. (1992 ). The geometry of stock market profits : a guide to professional trading for
a living. Greenville, SC : Traders Press.
Lawrence, K. D., Klimberg, R. K., & Lawrence, S. M. (2009). Fundamentals of forecasting
using Excel. New York, N.Y.: Industrial Press.

Date
2/6/2017
2/7/2017
2/8/2017
2/9/2017
2/10/2017
2/13/2017
2/14/2017
2/15/2017
2/16/2017
2/17/2017
2/21/2017
2/22/2017
2/23/2017
2/24/2017
2/27/2017
2/28/2017
3/1/2017
3/2/2017
3/3/2017
3/6/2017
3/7/2017
3/8/2017
3/9/2017
3/10/2017
3/13/2017
3/14/2017
3/15/2017
3/16/2017
3/17/2017
3/20/2017
3/21/2017
3/22/2017
3/23/2017
3/24/2017
3/27/2017
3/28/2017
3/29/2017
3/30/2017
3/31/2017
4/3/2017
4/4/2017
4/5/2017
4/6/2017
4/7/2017
4/10/2017
4/11/2017

Open
High
Low
Close
228,87
229,33
228,54
228,93 220,3782 57790100
-0,00436%
229,38
229,66
228,72
228,94 220,3878 57931200
-0,13088%
228,94
229,39
228,31
229,24 220,6766 51566200
-0,58974%
229,24
230,95
229,24
230,6 221,9857 65955200
-0,39309%
231
231,77
230,62
231,51 222,8618 66015900
-0,54130%
232,08
233,07
232,05
232,77 224,0747 55182100
-0,39794%
232,56
233,71
232,16
233,7
224,97 67794500
-0,51933%
233,45
235,14
233,39
234,92 226,1444 86785800
0,08520%
234,95
235,16
233,85
234,72 225,9519 84722400
-0,15738%
233,95
235,09
233,93
235,09 226,308 77204100
-0,59199%
235,52
236,69
235,51
236,49 227,6557 88946100
0,08887%
236,02
236,54
235,83
236,28 227,4536 62115200
-0,06767%
236,88
236,9
235,56
236,44 227,6076 74615900
-0,12673%
235,46
236,79
235,41
236,74 227,8964 82381600
-0,15604%
236,64
237,31
236,35
237,11 228,2526 56515400
0,27065%
236,67
236,95
236,02
236,47 227,6365 96961900
-1,38043%
238,39
240,32
238,37
239,78 230,8228 1,49E+08
0,63372%
239,56
239,57
238,21
238,27 229,3693 70246000
-0,06291%
238,17
238,61
237,73
238,42 229,5136 81974300
0,29867%
237,5
238,12
237,01
237,71 228,8302 55391500
0,29960%
237,36
237,77
236,76
237 228,1467 65103700
0,18599%
237,34
237,64
236,4
236,56 227,7231 78168800
-0,12666%
236,7
237,24
235,74
236,86 228,0119 90683900
-0,34920%
237,97
238,02
236,59
237,69 228,8109 81991700
-0,05046%
237,62
237,86
237,24
237,81 228,9265 57256800
0,38414%
237,18
237,24
236,19
236,9 228,0504 59880800
-0,85793%
237,56
239,44
237,29
238,95 230,0239 96081800
0,19709%
239,11
239,2
238,1
238,48 229,5714 78344000
0,17592%
237,75
237,97
237,03
237,03 229,1682 89002100
0,10981%
237,03
237,36
236,32
236,77 228,9169 52537000
1,30065%
237,47
237,61
233,58
233,73 225,9777 1,32E+08
-0,23476%
233,77
234,61
233,05
234,28 226,5094 97569200
0,10682%
234,28
235,34
233,6
234,03 226,2677
1E+08
0,07270%
234,38
235,04
232,96
233,86 226,1034 1,13E+08
0,10273%
231,93
233,92
231,61
233,62 225,8713 87454500
-0,72242%
233,27
235,81
233,14
235,32 227,515 93483900
-0,09341%
234,99
235,81
234,73
235,54 227,7277 61950400
-0,31740%
235,47
236,52
235,27
236,29 228,4528 56737900
0,23331%
235,9
236,51
235,68
235,74 227,921 73733100
0,17421%
235,8
236,03
233,91
235,33 227,5246 85546500
-0,06369%
235
235,58
234,56
235,48 227,6696 56466200
0,29815%
236,26
237,39
234,54
234,78 226,9929 1,09E+08
-0,28033%
234,94
236,04
234,43
235,44 227,631 69135800
0,10205%
235,15
236
234,64
235,2 227,3989 74412300
-0,05950%
235,36
236,26
234,73
235,34 227,5343 67615300
0,11913%
234,9
235,18
233,34
235,06 227,2636 88045300
0,44011%

4/12/2017
4/13/2017
4/17/2017
4/18/2017
4/19/2017
4/20/2017
4/21/2017
4/24/2017
4/25/2017
4/26/2017
4/27/2017
4/28/2017
5/1/2017
5/2/2017
5/3/2017
5/4/2017
5/5/2017
5/8/2017
5/9/2017
5/10/2017
5/11/2017
5/12/2017
5/15/2017
5/16/2017
5/17/2017
5/18/2017
5/19/2017
5/22/2017
5/23/2017
5/24/2017
5/25/2017
5/26/2017
5/30/2017
5/31/2017
6/1/2017
6/2/2017
6/5/2017
6/6/2017
6/7/2017
6/8/2017
6/9/2017
6/12/2017
6/13/2017
6/14/2017
6/15/2017
6/16/2017
6/19/2017

234,74
233,64
233,11
233,72
234,52
234,15
235,25
237,18
237,91
238,51
238,77
238,9
238,68
238,84
238,77
238,83
239,19
239,75
239,96
239,39
239,35
239,09
239,47
240,64
240,08
235,73
237,33
238,9
239,95
240,32
241,2
241,54
241,34
241,84
241,97
243,42
243,97
243,34
243,6
243,77
244,09
243,13
243,98
244,86
242,68
242,77
243,59

234,96
234,49
234,57
234,49
234,95
235,85
235,31
237,41
238,95
239,53
238,95
238,93
239,17
238,98
238,88
238,92
239,72
239,92
240,19
239,87
239,57
239,43
240,44
240,67
240,08
237,75
239,08
239,71
240,24
240,73
242,08
241,9
241,79
241,88
243,38
244,35
244,3
243,98
243,92
244,33
245,01
243,42
244,61
244,87
243,91
242,83
244,73

233,77
232,51
232,88
233,08
233,18
233,78
234,13
234,56
237,81
238,35
237,98
237,93
238,2
238,3
237,7
237,78
238,68
239,17
239,04
239,15
238,13
238,67
239,45
239,63
235,75
235,43
237,27
238,82
239,51
239,93
240,96
241,45
241,16
240,64
241,64
243,08
243,76
243,12
242,83
243,17
241,95
242,38
243,58
243,29
242,36
241,63
243,48

234,03
232,51
234,57
233,87
233,44
235,34
234,59
237,17
238,55
238,4
238,6
238,08
238,68
238,77
238,48
238,76
239,7
239,66
239,44
239,87
239,38
238,98
240,3
240,08
235,82
236,77
238,31
239,52
240,05
240,61
241,76
241,71
241,5
241,44
243,36
244,17
243,99
243,21
243,66
243,78
243,41
243,36
244,55
244,24
243,77
242,64
244,66

226,2677
224,7982
226,7899
226,113
225,6973
227,5343
226,8092
229,3036
230,6378
230,4928
230,6862
230,1834
230,7635
230,8505
230,5701
230,8409
231,7497
231,711
231,4983
231,914
231,4403
231,0536
232,3298
232,1171
227,9984
228,9169
230,4058
231,5757
232,0881
232,6295
233,7413
233,693
233,49
233,432
235,2883
236,0714
235,8974
235,1433
235,5784
235,6944
235,3366
235,2883
236,4388
236,1391
235,6847
235,7362
237,6987

81864400
92880400
68405400
83225800
68699900
92572200
...

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Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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