Quantitative Techniques for Business: Stock Portfolio Analysis

This assignment focuses on applying quantitative techniques to analyze stock data. It begins with graphical representations of stock prices and returns, followed by the calculation of returns and descriptive statistics, including kurtosis, to assess the normality of the return distributions. The assignment then delves into hypothesis testing, examining the daily returns of Apple, Hewlett Packard, Intel, and Microsoft stocks. Various hypotheses are tested, and conclusions are drawn based on p-values and significance levels. Further analysis includes comparing mean returns between stocks using two-sample t-tests and constructing a correlation matrix to assess dependencies. Finally, the assignment culminates in portfolio optimization, selecting the best stocks based on risk-return characteristics and determining optimal portfolio weights to maximize return per unit risk. The conclusion acknowledges the limitations of assuming normal distribution for stock prices due to their dependence on past values and investor sentiment.

Quantitative Techniques For Business
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Question 1
The price of the various stocks is graphically indicated below.

The returns of the various stocks are graphically represented below.

It is evident that for all the four stocks, from the late 2008 there has been a drastic fall in the
stock price which has continued for almost whole of 2009 before the stocks have shown some
sign of recovery. This is attributed to the global financial crisis which was at its peak during
the time.
Question 2
The computation of the returns has been carried out using the given formula and the values
are indicated in excel. The respective plots of these are illustrated below.

Question 3
The respective histogram for each return series is as highlighted below.

The relevant descriptive statistics are highlighted below.
The kurtosis for the various given asset return is not equal to three which represents that
neither of these return distribution would be normally distributed. This is because the kurtosis
for normal distribution should be equal to 3. Since the respective kurtosis values are greater
than 3 in all the cases, hence the tails would be slender in comparison to a normal
distribution.
Question 4
The respective hypotheses are highlighted below.
H0: μApple = 0
H1: μApple ≠ 0

Owing to unknown population standard deviation, t statistic would be used for hypothesis
testing. The result of the same is outlined below.
Assuming a significance level of 0.05 or 5%, it is apparent that the p value is 0.0002 which
implies rejection of H0 and H1 acceptance. Hence, it can be concluded that daily returns on
Apple stock are different from zero.
The respective hypotheses are highlighted below.
H0: μHPQ = 0
H1: μHPQ ≠ 0
Owing to unknown population standard deviation, t statistic would be used for hypothesis
testing. The result of the same is outlined below.
Assuming a significance level of 0.05 or 5%, it is apparent that the p value is 0.9379 which
implies non-rejection of H0 and H1 acceptance. Hence, it can be concluded that daily returns
on Hewlett Packard stock are not statistically different from zero.
The respective hypotheses are highlighted below.

H0: μINTC = 0
H1: μINTC ≠ 0
Owing to unknown population standard deviation, t statistic would be used for hypothesis
testing. The result of the same is outlined below.
Assuming a significance level of 0.05 or 5%, it is apparent that the p value is 0.5914 which
implies non-rejection of H0 and H1 acceptance. Hence, it can be concluded that daily returns
on Intel Corporation stock are not statistically different from zero.
The respective hypotheses are highlighted below.
H0: μMSFT = 0
H1: μMSFT ≠ 0
Owing to unknown population standard deviation, t statistic would be used for hypothesis
testing. The result of the same is outlined below.
Assuming a significance level of 0.05 or 5%, it is apparent that the p value is 0.3284 which
implies non-rejection of H0 and H1 acceptance. Hence, it can be concluded that daily returns
on Microsoft stock are not statistically different from zero.

Question 5
The requisite hypotheses are stated below.
H0: μAPL= μHPQ
H1: μAPL≠ μHPQ
The requisite test to be conducted is two sample independent t test which is as highlighted
below.
The relevant p value derived has come out as 0.1029. Since this is greater than the
significance level, hence the available statistical evidence is not sufficient for rejection of null
hypothesis. Thus, it would be fair to conclude that there is no significant statistical difference
between the mean returns of the two stocks.
H0: μAPL= μINTC
H1: μAPL≠ μINTC
The requisite test to be conducted is two sample independent t test which is as highlighted
below.

The relevant p value derived has come out as 0.0170. Since this is lesser than the significance
level, hence the available statistical evidence is sufficient for rejection of null hypothesis.
Thus, it would be fair to conclude that there is significant statistical difference between the
mean returns of the two stocks.
H0: μAPL= μMSFT
H1: μAPL≠ μMSFT
The requisite test to be conducted is two sample independent t test which is as highlighted
below.
The relevant p value derived has come out as 0.0170. Since this is lesser than the significance
level, hence the available statistical evidence is sufficient for rejection of null hypothesis.