Free Samples
ECOM2001 Quantitative Techniques For Business
.cms-body-content table{width:100%!important;} #subhidecontent{ position: relative;
overflow-x: auto;
width: 100%;}
ECOM2001 Quantitative Techniques For Business
0 Download8 Pages / 1,960 Words
Course Code: ECOM2001
University: Curtin University
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: Australia
Questions:
1. Under the assumption that the returns of each asset are drawn from an independently and identically distributed normal distribution, are the expected returns statistically different fromzero for each asset? State clearly the null and alternative hypothesis in each case.
2. Assume the returns of each asset are independent from each other, are the mean returns statistically different from each other? 3. Calculate the correlation matrix of the returns
Answer:
This prices of AAPL asset between July 2008 and July 2009, after which the price rose up at a relatively low rate where and later decrease gently on Dec 2014. The recession and recovery are registered between Sep 2017 and 22010. Due to the regular pattern of recoveries and recession o the price, the series is said to display an upward trend which associated with seasonality, which is the main source of the fluctuation of prices of AAPL asset. The upwards trend, reveals the AAPL asset is performing well in the stock market as no extremely low prices that have been registered between July 2008 and July 2018.
it’s clear that the prices of HQP started at a higher level almost at the same but a slightly higher level. This trend has been accompanied by a series of recessions and recoveries. The recessions have been registered in July 2009, April 2012 and September 2016. The recoveries were registered at the between 2010 and 1011, 2015 and 2016, and 2017 and 2018. This pattern reveals that the prices of HQP asset are fluctuating across the years. The pattern is also irregular thus there no stability of prices, even though the HQP asset begins selling at higher prices and ends at higher prices.
These prices of INTC are fluctuation ate very low as revealed by gentle falls and rises. Though there’s no regular pattern of prices movements displayed, the prices of INTC are stable. There are few but minor falls of prices. Also, the prices of INTC start at a low level and end at a higher level, this suggests an upward trend of prices.
These prices of INTC are fluctuation ate very low as revealed by gentle falls and rises. Though there’s no regular pattern of prices movements displayed, the prices of INTC are stable. There are few but minor falls of prices. Also, the prices of INTC start at a low level and end at a higher level, this suggests an upward trend of prices.
he price s of MSFT between July 2008 and December 2013, were low but increasing at a relatively low rate. The graph shows an upward trend between 2014 and 2018. , implying that the prices of MSFT are stable. Moreover, the graphs reveal that the fluctuation rate of price is very low
Task 2
Computation of the returns of the four assets was done using the formula:
The computation was done in Microsoft Excel and the results are recorded in the file named Task2 computation of return.
Interpretation of Kurtosis
According to Petters, Arlie &Xiaoying Dong (2016), the kurtosis of the normally distributed variable is 3. The Kurtosis of AAPL, HQP, INTC, and MSFT are greater than 3, implying that the returns of the four assets are not normally distributed.
Hypothesis test: Are the average returns of the four assets significantly different from 0 at 0.05 significant levels? Assumption: assets are from independently and identically normal distribution.
The z-test for a single sample mean was employed. The hypotheses to be tested are:
Rejection region:
If
The following are the tables showing the results of the tests for the four returns series.
AAPL Asset
z-Test: One-Sample for Mean
AAPL
Mean
0.0857
Known Variance
3.53
Hypothesis test: Are the average returns of the four assets significantly different from 0 at 0.05 significant levels? Assumption: assets are from independently and identically normal distribution.
The z-test for a single sample mean was employed. The hypotheses to be tested are:
Rejection region:
If
The following are the tables showing the results of the tests for the four returns series.
AAPL Asset
z-Test: One-Sample for Mean
AAPL
Mean
0.0857
Known Variance
3.53
Observations
2518
Hypothesized Mean Difference
0
z
2.2814
P(Z<=z) one-tail
0.0113
z Critical one-tail
1.6449
P(Z<=z) two-tail
0.0225
z Critical two-tail
1.9600
From table z-statistic (two-tailed) is 2.2814, which is greater than the z-critical, 1.96, implying that the null hypothesis ( will be rejected. This suggests that the average returns of AAPL are significantly different from 0. This has also been supported by P-value, 0.0225 which is less than 0.05 significant levels, which also allows the rejection of .
HQP Asset
z-Test: One-Sample for Mean
HQP
Mean
0.006
Known Variance
4.53
Observations
2518
Hypothesized Mean Difference
0
z
0.145
P(Z<=z) one-tail
0.442
z Critical one-tail
1.645
P(Z<=z) two-tail
0.885
z Critical two-tail
1.960
From table z-statistic (two-tailed) is 0.145, which is less than the z-critical, 1.96, implying that null hypothesis ( will not be rejected. This reveals that the average return of HQP is not significantly different from 0.
INTC Asset
z-Test: one Sample for Mean
INTC
Mean
0.0313
Known Variance
3.2
Observations
2518
Hypothesized Mean Difference
0
z
0.8751
P(Z<=z) one-tail
0.1908
z Critical one-tail
1.6449
P(Z<=z) two-tail
0.3815
z Critical two-tail
1.9600
From the above table z-statistic (two-tailed) is 0.8751, which is less than the z-critical, 1.96, implying that the null hypothesis ( will not be rejected. This reveals that the average return of INTC is not significantly different from 0.
MSFT Asset
z-Test: One-Sample for Mean
MSFT
Mean
0.0572
Known Variance
2.96
Observations
2518
Hypothesized Mean Difference
0
z
1.6615
P(Z<=z) one-tail
0.0483
z Critical one-tail
1.6449
P(Z<=z) two-tail
0.0966
z Critical two-tail
1.9600
From the above table z-statistic (two-tailed) is 1.662, which is less than the z-critical, 1.96, implying that the null hypothesis ( will not be rejected. This reveals that the average return of MSFT is not significantly different from 0.
Hypothesis Test: Are the mean returns significantly different from each other at 0.05 significant levels? Assumption: assets are independent of each other. The hypotheses to be tested are
Rejection region:
If or
To determine this, one way ANOVA test was conducted.
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
AAPL
2518
215.853
0.086
3.532
HQP
2518
15.527
0.006
4.530
INTC
2518
78.858
0.031
3.199
MSFT
2518
144.049
0.057
2.956
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
8.8197443
3
2.9399
0.8271
0.4787
2.6058
Within Groups
35785.925
10068
3.5544
Total
35794.745
10071
From the table above, the F-statistics (0.8271) is less than F-critical (2.6058). Also, the p-value is greater than 0.05. These results suggest that the null hypothesis will be accepted. Therefore, the mean returns of the four assets are not significantly different from each other.
Task 6
Correlation Matrix of the Returns
The following table shows the correlation between different pairs of the four assets.
AAPL
HQP
INTC
MSFT
AAPL
1
HQP
0.4069
1
INTC
0.5024
0.5266
1
MSFT
0.4780
0.4749
0.6312
1
All the correlations between returns of different assets are positive. This reveals that returns of different assets are positively correlated.
Task 7
The four assets are not independent as the correlation between different pairs of assets are not 0. This has been clearly revealed in task 6 above.
Hypothesis Test: Are the mean returns significantly different from each other at 0.05 significant levels? Assumption: assets are independent of each other. The hypotheses to be tested are
The Paired t-test as conducted on different pairs of the four return series. Results are shown in the table below
t-Test: Paired Two Sample for Means
AAPL
HQP
Mean
0.085724153
0.006166509
Variance
3.53180602
4.530370335
Observations
2518
2518
Pearson Correlation
0.406902996
Hypothesized Mean Difference
0
df
2517
t Stat
1.820860402
P(T<=t) one-tail
0.034373379
t Critical one-tail
1.645459242
P(T<=t) two-tail
0.068746758
t Critical two-tail
1.96090693
t- Statistic=1.821, which is less than critical-t(1.96), this implies that the mean difference 0 between AAPL and HQP
t-Test: Paired Two Sample for Means
AAPL
INTC
Mean
0.085724153
0.03131784
Variance
3.53180602
3.199130054
Observations
2518
2518
Pearson Correlation
0.502435483
Hypothesized Mean Difference
0
df
2517
t Stat
1.490894465
P(T<=t) one-tail
0.068057255
t Critical one-tail
1.645459242
P(T<=t) two-tail
0.13611451
t Critical two-tail
1.96090693
The t-statistics is 1.49, which is less than the critical-t (1.96), suggesting that the mean difference between APPL and INTC is 0.
t-Test: Paired Two Sample for Means
AAPL
MSFT
Mean
0.085724153
0.057207522
Variance
3.53180602
2.956383348
Observations
2518
2518
Pearson Correlation
0.477990101
Hypothesized Mean Difference
0
df
2517
t Stat
0.776144947
P(T<=t) one-tail
0.218868165
t Critical one-tail
1.645459242
P(T<=t) two-tail
0.437736331
t Critical two-tail
1.96090693
The t-statistic is 0.776 which is less than critical t(1.96), implying that the mean difference between the APPL and MSFT is 0
t-Test: Paired Two Sample for Means
HQP
INTC
Mean
0.006166509
0.03131784
Variance
4.530370335
3.199130054
Observations
2518
2518
Pearson Correlation
0.526587893
Hypothesized Mean Difference
0
df
2517
t Stat
-0.654355571
P(T<=t) one-tail
0.256471267
t Critical one-tail
1.645459242
P(T<=t) two-tail
0.512942535
t Critical two-tail
1.96090693
The t-statistic is 0.654, which is less than the critical t(1.96), implying that the mean difference between HQP and INTC.
t-Test: Paired Two Sample for Means
HQP
MSFT
Mean
0.006166509
0.057207522
Variance
4.530370335
2.956383348
Observations
2518
2518
Pearson Correlation
0.474940557
Hypothesized Mean Difference
0
df
2517
t Stat
-1.278939683
P(T<=t) one-tail
0.100518098
t Critical one-tail
1.645459242
P(T<=t) two-tail
0.201036196
t Critical two-tail
1.96090693
The t-statistics is -1.279, which is absolutely less than the critical t( 1.96), suggesting that the mean difference between the HQP and MSFT is 0.
t-Test: Paired Two Sample for Means
INTC
MSFT
Mean
0.03131784
0.057207522
Variance
3.199130054
2.956383348
Observations
2518
2518
Pearson Correlation
0.631248664
Hypothesized Mean Difference
0
df
2517
t Stat
-0.861721004
P(T<=t) one-tail
0.194461575
t Critical one-tail
1.645459242
P(T<=t) two-tail
0.38892315
t Critical two-tail
1.96090693
The t-statistics is 0.862, which is less than the critical t (1.96), implying the mean difference between INTC and MSFT is 0.
Decision:
Since the t-statistics in all the six pairs is less than the critical t, the average returns in among the four assets are not t significantly different from each other.
The result, in this case, concurs with the results in Task 5 above that is no significant difference between the mean returns of the four assets.
Optimization in the portfolio
The assets that will be chosen are APPL and MSFT. The two assets are optimal weights are 0.78 and 0.22 respectively. The optimal portfolio returns are 0.08.
Method applied to obtain the result
The average returns of the four assets were computation
Asset
Mean
Variance
Std Dev
AAPL
0.09
3.53
1.879
HQP
0.01
4.53
2.128
INTC
0.03
3.20
1.789
MSFT
0.06
2.96
1.719
The covariance matrix of the returns of the four assets
Covariance matrix
AAPL
HQP
INTC
MSFT
AAPL
3.530403397
1.62698538
1.68819326
1.5439214
HQP
1.626985381
4.52857114
2.0039236
1.73745663
INTC
1.688193258
2.0039236
3.19785955
1.94054753
MSFT
1.543921401
1.73745663
1.94054753
2.95520925
Inference of working weight: choose the equal weight of 0.25
Computation the portfolio means from the average returns of individual assets and inferred weight. Returns matrix is multiplied by the weight vector.
Computation of the portfolio standard deviation from the covariance matrix and the inferred weights
Determination of the objection function using the Sharp ratio
Sharpe ratio is given by
These results were factored in the excel solver to obtain optimal values as shown in the figure below
Notes
Constraint sum of Weights of the portfolio assets
Changing variables were the weights
Sharpe ratio was the objective function
The following are the optimal results obtained
weight
AAPL
0.78
HQP
0.00
INTC
0.00
MSFT
0.22
sum
1
Mean of portfolio
0.08
Variance
2.829
std dev
1.682
Rf=1.50%
Sharpe ratio
0.0032
Test for Normality of the four price series.
The test was done using a kurtosis level (3) of a normally distributed variable.
AAPL
HQP
INTC
MSFT
Kurtosis
-0.644
-0.825
0.623
0.881
Skewness
0.395
-0.006
0.889
1.252
From the table, it's clear that no kurtosis value that is equal to 3 or approximately 3, therefore, four prices series are not normally distributed.
References
Petters, Arlie O., and Xiaoying Dong. An Introduction to Mathematical Finance with Applications. Springer New York:, 2016.
Free Membership to World's Largest Sample Bank
To View this & another 50000+ free samples. Please put
your valid email id.
E-mail
Yes, alert me for offers and important updates
Submit
Download Sample Now
Earn back the money you have spent on the downloaded sample by uploading a unique assignment/study material/research material you have. After we assess the authenticity of the uploaded content, you will get 100% money back in your wallet within 7 days.
UploadUnique Document
DocumentUnder Evaluation
Get Moneyinto Your Wallet
Total 8 pages
PAY 5 USD TO DOWNLOAD
*The content must not be available online or in our existing Database to qualify as
unique.
Cite This Work
To export a reference to this article please select a referencing stye below:
APA
MLA
Harvard
OSCOLA
Vancouver
My Assignment Help. (2021). Quantitative Techniques For Business. Retrieved from https://myassignmenthelp.com/free-samples/ecom2001-quantitative-techniques-for-business/regular-pattern.html.
"Quantitative Techniques For Business." My Assignment Help, 2021, https://myassignmenthelp.com/free-samples/ecom2001-quantitative-techniques-for-business/regular-pattern.html.
My Assignment Help (2021) Quantitative Techniques For Business [Online]. Available from: https://myassignmenthelp.com/free-samples/ecom2001-quantitative-techniques-for-business/regular-pattern.html[Accessed 18 December 2021].
My Assignment Help. 'Quantitative Techniques For Business' (My Assignment Help, 2021)
My Assignment Help. Quantitative Techniques For Business [Internet]. My Assignment Help. 2021 [cited 18 December 2021]. Available from: https://myassignmenthelp.com/free-samples/ecom2001-quantitative-techniques-for-business/regular-pattern.html.
×
.close{position: absolute;right: 5px;z-index: 999;opacity: 1;color: #ff8b00;}
×
Thank you for your interest
The respective sample has been mail to your register email id
×
CONGRATS!
$20 Credited
successfully in your wallet.
* $5 to be used on order value more than $50. Valid for
only 1
month.
Account created successfully!
We have sent login details on your registered email.
User:
Password:
Planning to buy homework online but not sure whom to select. Well, you will not find a better homework help website than Myassignmenthelp.com globally. The reason is that we are committed to ease out the pressure on students and help them enjoy life a little more. We started providing homework help for the same reason and ensure that quality solutions are provided every time. We provide homework writer on all subjects from school to Grad levels. The solutions are multiple checked for rendering error-free and made grammatically and factually sound.
Latest Management Samples
div#loaddata .card img {max-width: 100%;
}
MPM755 Building Success In Commerce
Download :
0 | Pages :
9
Course Code: MPM755
University: Deakin University
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: Australia
Answers:
Introduction
The process of developing a successful business entity requires a multidimensional analysis of several factors that relate to the internal and external environment in commerce. The areas covered in this current unit are essential in transforming the business perspective regarding the key commerce factors such as ethics, technology, culture, entrepreneurship, leadership, culture, and globalization (Nzelibe, 1996; Barza, 2…
Read
More
SNM660 Evidence Based Practice
Download :
0 | Pages :
8
Course Code: SNM660
University: The University Of Sheffield
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: United Kingdom
Answers:
Critical reflection on the objective, design, methodology and outcome of the research undertaken Assessment-I
Smoking and tobacco addiction is one of the few among the most basic general restorative issues, particularly to developed nations such as the UK. It has been represented that among all risk segments smoking is the fourth driving purpose behind infections and other several ailments like asthma, breathing and problems in the l…
Read
More
Tags:
Australia Maidstone Management Business management with marketing University of New South Wales Masters in Business Administration
BSBHRM513 Manage Workforce Planning
Download :
0 | Pages :
20
Course Code: BSBHRM513
University: Tafe NSW
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: Australia
Answer:
Task 1
1.0 Data on staff turnover and demographics
That includes the staffing information of JKL industries for the fiscal year of 2014-15, it can be said that the company is having problems related to employee turnover. For the role of Senior Manager in Sydney, the organization needs 4 managers; however, one manager is exiting. It will make one empty position which might hurt the decision making process. On the other hand, In Brisba…
Read
More
MKT2031 Issues In Small Business And Entrepreneurship
Download :
0 | Pages :
5
Course Code: MKT2031
University: University Of Northampton
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: United Kingdom
Answer:
Entrepreneurial ventures
Entrepreneurship is the capacity and willingness to develop, manage, and put in order operations of any business venture with an intention to make profits despite the risks that may be involved in such venture. Small and large businesses have a vital role to play in the overall performance of the economy. It is, therefore, necessary to consider the difference between entrepreneurial ventures, individual, and c…
Read
More
Tags:
Turkey Istanbul Management University of Employee Masters in Business Administration
MN506 System Management
Download :
0 | Pages :
7
Course Code: MN506
University: Melbourne Institute Of Technology
MyAssignmentHelp.com is not sponsored or endorsed by this college or university
Country: Australia
Answer:
Introduction
An operating system (OS) is defined as a system software that is installed in the systems for the management of the hardware along with the other software resources. Every computer system and mobile device requires an operating system for functioning and execution of operations. There is a great use of mobile devices such as tablets and Smartphones that has increased. One of the widely used and implemented operating syste…
Read
More
Tags:
Australia Cheltenham Computer Science Litigation and Dispute Management University of New South Wales Information Technology
Next