MSF502 0130HW-CH3
xlsx
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School
Illinois Institute Of Technology *
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Course
502
Subject
Statistics
Date
Apr 3, 2024
Type
xlsx
Pages
12
Uploaded by BarristerInternet1945
Name: Tanvi Vikas Patil
I have used excel functions to calculate the formulas Question 25
A) Calculate and interpret the 25th, 50th and 75th percentiles (took only 10 company)
Company
P/E Ratio
Chevron corp (CVX)
7
Hewlwtt-Packard (HPQ)
8
Exxonmobil (XOM)
10
caterpillar (CAT)
11
Intel (INTC)
11
Boeing (BA)
12
Cisco System (CSCO)
12
American experess (AXP)
13
DuPont (DD)
13
3M (MMM)
14
General Electric (GE)
15
merck (MRK)
17
McDonald's (MCD)
17
Johnson & Johnson
17
Home Depot (HD)
19
coca-cola (KO)
20
Plizer (PFE)
21
Alcoa (AA)
24
Tesla, INC
42.11
AT&T (T)
49
Super micro computer, INC
51.82
Using the PERCENTILE.INC function we get the follwing data For 25th percentiles
12
For 50th percentiles
15
For 75th percentiles
20
Therefore, 25th, 50th and 75th percentile is 17, 19 and 49 respectively
B) Construct an boxplot
yes there are outliers The following distribution is not Symmetric and its positively skewness
This chart isn't available in your version of Excel.
Editing this shape or saving this workbook into a different file format will permanently break the chart.
Question 34
Year
Annual Return
1
17.3
2
19.6
3
6.8
4
8.2
A) calculate arithmetic mean return
12.975
Therefore the arithmetic mean return is 12.975 by using AVEGRAGE function.
The arithmetic mean of the data sets is the simple average of the datasets in which the data base are added and then the sum is divided by total number of datasets.
B) calculate geometric return
11.7261713181829
Thus the geometric mean of the return is 11.726 by using GEOMEAN function
The geometric mean is the central value of the set of data points which is found by multiplying the datasets and taking its root by the number of dataset
Question 65
Average return is 8 %
standard deviation is 12%
A)
z = (x - average return)/standard deviation
z = (20 - 8)/12
z = 1
thus, P(x > 12) = P(z > 1) = 0.1587 thus, 16%
B)
z = (-16 - 8)/12 = -2
P(x < -16) = P(z < -2)
0.0228
thus, 2.3%
Question 73
Year
Vanguard Group
Fidelity Investment
2007
56.17
-11.9
2008
52.57
20.95
2009
-17.55
2.76
2010
7.29
18.98
2011
-2.72
5.6
2012
16.57
-2.83
2013
59.66
-0.09
2014
33.22
21.72
2015
17.93
-0.87
2016
21.72
21.72
2017
-32.67
-1.56
2018
-31.9
-14.64
2019
58.89
31.34
2020
23.09
-11.22
2021
31.78
-11.49
2022
-12.72
18.69
2023
7.34
23.09
A) Calculate the sample covariance between the returns
89.5033529411765
Thus, 89.50 is the covariance by using COVARAINCE.S function
B) Calculate Interpret the correlation coefficient 0.199919771589507
Thus, 0.19 is the correlation coefficient by using CORREL function
Question 52
Year
Direxion Funds
Davis Funds
2006
31.91
-17.56
2007
18.33
-9.87
2008
59.45
14.46
2009
-11.37
31.98
2010
36.13
-11.32
2011
9.38
33.76
2012
18.76
11.95
2013
5.87
0.01
2014
-7.34
10.54
2015
11.78
-1.54
2016
25.89
18.38
2017
-11.56
-12.72
2018
14.63
-20.27
2019
24.87
-1.97
2020
-23.76
2.33
2021
-0.87
16.41
2022
34.87
18.69
2023
-23.45
21.72
A) which fund had the heigher average return?
For Direxion Fund:
Average annual return = sum of annual return/number of years 11.8622222222222
For Davis Fund:
Average annual return = sum of annual return/number of years 5.83222222222222
Thus, the Direxion fund had a higher average annual return
B) which fund was riskier over this time period
we have to calculate standard deviation to know which fund was riskier
Standard deviation of Direxion Fund
495.587524183007 variance
22.2617951698197
standard deviation
Standard deviation of Davis Fund
268.213512418301 variance
16.3772254188034
standard deviation
Thus, Direxion fund had a higher standard deviation, so this was riskier over this time period.
C) risk free rate is 3%. Which fund has the higher sharpe ratio?
sharpe ratio = (average annual return - risk free rate)/ standard devaition
For the Direxion Fund sharpe ratio is,
0.531503507779246
For the Davis Fund sharpe ratio is,
0.354286032819725
Direxion Fund has the higher sharpe ratio
The Sharpe ratio is a measure used to evaluate the return of an investment relative to its risk. A higher sharpe ratio indicates a better risk-adjusted return. In this case, the direxion fund has a higher ratio
Implying that it provide a better risk return compare to davis fund Therefore, sharpe ratio for Direxion Fund is 0.53
Therefore, sharpe ratio for Davis Fund is 0.35
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Question 44
Date
GOOG
TESLA
3/1/2019
58.665501
18.657333
4/1/2019
59.424
15.912667
5/1/2019
55.181499
12.344
6/1/2019
54.045502
14.897333
7/1/2019
60.834
16.107332
8/1/2019
59.404999
15.040667
9/1/2019
60.950001
16.058001
10/1/2019
63.005501
20.994667
11/1/2019
65.248001
21.996
12/1/2019
66.850998
27.888666
1/1/2020
71.711502
43.371334
2/1/2020
66.966499
44.532665
3/1/2020
58.140499
34.933334
4/1/2020
67.432999
52.125332
5/1/2020
71.445999
55.666668
6/1/2020
70.680496
71.987335
7/1/2020
74.148003
95.384003
8/1/2020
81.709
166.106674
9/1/2020
73.480003
143.003326
10/1/2020
81.050499
129.346664
11/1/2020
88.037003
189.199997
12/1/2020
87.594002
235.223328
1/1/2021
91.787003
264.51001
2/1/2021
101.843002
225.166672
3/1/2021
103.431503
222.643326
4/1/2021
120.505997
236.479996
5/1/2021
120.578003
208.406662
6/1/2021
125.316002
226.566666
7/1/2021
135.220993
229.066666
8/1/2021
145.462006
245.240005
9/1/2021
133.265503
258.493347
10/1/2021
148.270493
371.333344
11/1/2021
142.451996
381.58667
12/1/2021
144.679504
352.26001
1/1/2022
135.698502
312.23999
2/1/2022
134.891006
290.143341
3/1/2022
139.649506
359.200012
4/1/2022
114.966499
290.253326
5/1/2022
114.039001
252.753326
6/1/2022
109.372498
224.473328
7/1/2022
116.639999
297.149994
8/1/2022
109.150002
275.609985
9/1/2022
96.150002
265.25
10/1/2022
94.660004
227.539993
11/1/2022
101.449997
194.699997
12/1/2022
88.730003
123.18
1/1/2023
99.870003
173.220001
2/1/2023
90.300003
205.710007
3/1/2023
104
207.460007
4/1/2023
108.220001
164.309998
5/1/2023
123.370003
203.929993
6/1/2023
120.970001
261.769989
7/1/2023
133.110001
267.429993
8/1/2023
137.350006
258.079987
9/1/2023
131.850006
250.220001
10/1/2023
125.300003
200.839996
11/1/2023
133.919998
240.080002
12/1/2023
140.929993
248.479996
Mean
100.231130137931
180.285413137931
A) calculate the sample variance and sample standard deviation for each firm
variance for GOOG
876.25978087264
variance for TESLA
11734.9659090946
Standard deviation for GOOG
29.6016854397286
Standard deviation for TESLA
108.328047656618
B) which firms stock price had greater variability as measured by the standard deviation
C) Which stock price had the greater relative dispersion?
Calculate coefficient of variation for GOOG
0.295334247942659
Calculate coefficient of variation for TESLA
0.600869730784818
Tesla
had greater variability measured by standard deviation Thus, TESLA
had a great relative dispersion as compare to GOOG
Sure, let's create two datasets—one cross-sectional and one tim
Cross-Sectional Dataset:
This dataset represents information about different companies a
Company
Industry
Employees
Company A
Technology
500
1000
Company B
Finance
300
500
Company C
Healthcare
700
1200
Company D
400
800
Company E
Retail
200
300
In this cross-sectional dataset:
Qualitative variables: Company (categorical), Industry (catego
Quantitative variables: Revenue, Employees, Profit Margin.
Time Series Dataset:
This dataset represents the stock prices of a single company ove
Date
1/1/2023
50
2 Positive
2/1/2023
55
2.5 Neutral
3/1/2023
48
1.8 Negative
4/1/2023
60
3 Positive
Revenue (in millions)
Manufacturi
ng
Stock Price ($)
Trading Volume (millions)
News Sentiment (Positive/Negative)
5/1/2023
58
2.2 Neutral
In this time series dataset:
Qualitative variables: Date (temporal), News Sentiment (categ
Quantitative variables: Stock Price, Trading Volume.
Note: The "News Sentiment" variable is included to represent a q
Cross-Sectional Dataset:
Country
Region
GDP per Capita (USD)
Unemployment Rate (%)
USA
North America
65,298
5.8
Canada
North America
48,470
6.5
Germany
Europe
46,208
3.2
UK
Europe
42,330
4.5
Japan
Asia
40,850
2.4
South Korea
Asia
31,346
3.7
Brazil
South America
8,717
12.6
India
Asia
2,100
7.8
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Nigeria
Africa
2,230
8.1
Russia
Europe
10,230
5.8
Australia
Oceania
53,800
5.2
Mexico
North America
9,224
3.6
Saudi Arabia
Asia
20,028
5.7
South Africa
Africa
5,410
28.5
France
Europe
41,760
8.5
me series—related to economics or finance. For simplicity, I'll provide fictional d
at a specific point in time.
Profit Margin
15%
8%
20%
12%
5%
orical).
er a period of months.
gorical).
qualitative variable, with categories like Positive, Neutral, or Negative sentime
Human Development Index (HDI)
0.926
0.929
0.947
0.932
0.919
0.916
0.765
0.645
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0.539
0.824
0.944
0.779
0.857
0.709
0.901
datasets with a mix of qualitative and quantitative variables.
ent based on news related to the company during that month.
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