Impact of Risk Free and Risky Asset on Portfolio Return

Impact of Risk Free and
Risky Asset on Portfolio
Return
Security Analysis & Portfolio Management
The report has analyzed for 10 stocks listed on Karachi
Stock Exchange and the data of 2 years from July1, 2013 to
June 30, 2015. The listed companies include 10 different
companies from the different industries and out of which 2
portfolios of the stocks have been crafted.
Atif Ahmed (9549)
Sheikh Waleed Ahmed (9768)
Sarah Haider (9559)
Nida Siddiqui (9575)
Muhammad Ateeq (9769)

2Impact of Risk Free and Risky Asset on Portfolio Return
1. Introduction to the Report:
The report has analysed for 10 stocks listed on Karachi Stock Exchange and the data of 2
years from July1, 2013 to June 30, 2015. The listed companies include 10 different companies
from the different industries and out of which 2 portfolios of the stocks have been crafted. The
assignment includes 2 portfolios, one with the inclusion of risky asset and the other portfolio is a
risk-free asset portfolio that includes T-Bills. A little description of the companies is given below:
Serial Number Companies
1 SNGP
2 ABOT
3 EFOODS
4 CPPL
5 INIL
6 KOHE
7 APL
8 PTC
9 AKZO
10 ABL
Table 1: List of Selected Companies
1.1.Sui Northern Gas Pipelines Limited (SNGP)
Sui Northern Gas Pipelines Limited was incorporated in as a private limited company
in 1963 and later renewed into a public limited company in 1964 under the Companies Act
1913. SNGP is listed in all the three stock exchanges of the country. As per the 3rd
quarterly
statement of March 31st
2013, company advocated a net profit of Rs. 1,014 Million. As on
December 18th
, 2015 the stock is traded at Rs. 26.46. The stock has shown a high volatility in
a period of month. As on November 23rd
, 2015 the stock was on Rs. 31.13 and now it has
dropped to Rs. 26.46.

1.2.Abbott Laboratories Pakistan Limited (ABOT)
Abbott laboratories Pakistan limited is a public limited company that became
functional on July 02, 1948. Its shares have been traded on all the three stock exchanges of
Pakistan. The gross profitability in the third quarter has shown an increase of 3%, since in the
last quarter the profitability was 37% which rose to 40% in the third quarter. At the moment
the stock is traded at Rs. 43.71.
1.3.Engro Foods (EFOODS)
Engro Corporation Limited is one of the largest conglomerates of Pakistan. It started
its operation in the year 1957as an Esso/Mobil joint venture. Engro Foods is one of the
business units of Engro Corporation Limited that was formed in the year 2005 as wholly
owned business unit and became operative in 2006. Engro Foods is now competing as major
player in the food industry in Pakistan. It operates to cater local needs with products
confirming to the global standards. As on December, 18th
2015, the stock is traded at Rs.
146.59.
1.4.Attock Petroleum Limited Pakistan (APL)
Attock Petroleum Limited is the 4th
oil marketing company of Pakistan that became
operative in the year 1998. It has managed to maintain its reputation across Pakistan and
abroad by providing quality petroleum products. As per the 1st
quarter ended on September
30th
, 2015, the company has shown a decrease in the net sales of 43% as compared to the net
sales last year of the same period. This advocated the global oil price crises that have
significantly influenced the overall performance of the company. As on December 18th
, 2015
the stock of APL Pakistan stands at Rs. 467.
1.5.Pakistan Telecommunication Limited (PTCL)
PTCL is the country’s leading telecommunication service provider. It was
incorporated in the year 1947. The major change in the history of PTCL took place was the
privatization of the company. The share holding of PTCL was reduced to only 62% when the

privatization program took place in 2006 during the tenure of the then prime minister Shaukat
Aziz. 26% of the total shares were sold to Etisalat Telecommunications and the remaining
12% were offered to the general public. As per the 3rd
quarterly financial report, an increase
of 14% has been administered. As on December 18th
, 2015 the stock price of PTCL is at Rs.
16.01.
1.6.AKZO Nobel Pakistan Limited
Akzo Nobel Pakistan Limited operates as a separate entity of paints in Pakistan. Akzo
Nobel was the parent company of ICI Pakistan limited but when Akzo Nobel withdrew its
shares from the company other than the paints business it was acquired by Younus Brothers.
The remaining businesses of ICI Pakistan limited was later got merged and now operate under
the name of Younus Brothers. As on June 2012, Akzo Nobel Pakistan Limited operates as an
independent and separate entity. As on December 18th
, 2015 the stock price of AKZO Nobel
is Rs.242.19.
1.7.Allied Bank Limited (ABL)
Allied bank is one of the oldest and the first Muslim bank of Pakistan which was
established before the independence of Pakistan. It was formed in the year 1942 under the
name of Australasia Bank and later in the year 1974 it was renamed as Allied Bank of
Pakistan. As on December 18th
, 2015 the stock stands at Rs. 94.99.
2. Methodology:
The analysis has been done using Microsoft excel. The returns for the selected stocks
have been calculated using the formula:
Return =
𝑂𝑝𝑒𝑛𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒 −𝐶𝑙𝑜𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒
𝐶𝑙𝑜𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒
The source for data collection is the website of KSE where daily prices of 10 stocks are
gathered. The closing values of KSE-100 index are grasped from the same website. Moving
forward, the techniques that are employed for analysis of the data includes descriptive analysis,

correlation and covariance analysis. The portfolio return and risk for both risky and risk free
portfolio is evaluated and compared with the return and risk of KSE-100 index. The beta co-
efficient is also estimated and compared for two portfolios.
3. Purpose:
The purpose of the study is to make portfolios of companies from the different and
unrelated industries in order to deviate and minimize the risk. For achieving this objective, 10
companies from different industries were taken and their risks, returns, correlations, covariance’s
were analysed.
4. Data Analysis:
The data analysis section follows different techniques and estimations for getting to
conclusion for the targeted portfolios.
Descriptive Statistics
SNGP ABOT EFOODS CPPL INIL KOHE APL PTC AKZO ABL (T-Bills )
KSE 100
Index
Mean 0.001 0.001 0.000 0.003 0.001 0.001 0.000 0.000 0.003 0.001 -0.001 0.001
Standard
Error
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.000
Median -0.002 0.000 -0.001 0.000 0.000 0.001 0.000 -0.001 0.001 0.000 0.000 0.001
Standard
Deviation
0.019 0.021 0.023 0.024 0.021 0.018 0.018 0.019 0.027 0.017 0.009 0.009
Sample
Variance
0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000
Kurtosis 0.801 0.311 0.005 -0.262 0.179 6.413 120.254 1.853 0.236 5.003 18.047 3.285
Skewness 0.489 0.125 0.224 0.212 0.204 -1.045 -7.663 -0.146 -0.042 -0.249 -0.728 -0.35
Range 0.101 0.115 0.100 0.100 0.100 0.159 0.331 0.143 0.172 0.167 0.115 0.090
Minimum -0.051 -0.066 -0.051 -0.051 -0.051 -0.111 -0.284 -0.094 -0.123 -0.12 -0.059 -0.046
Maximum 0.050 0.049 0.049 0.049 0.049 0.049 0.047 0.049 0.049 0.049 0.055 0.044
Sum 0.261 0.662 0.060 1.571 0.370 0.277 0.020 -0.078 1.650 0.349 -0.249 0.476
Count 492 492 492 492 492 492 492 492 492 492 492 492
Table 2: The descriptive statistics includes the mean, standard error, median, standard deviation, skewness and kurtosis,
etc.

4.1.Average Returns Graph
The average return graph above has shown the variation in the returns.The graph
depicts that least returns have been delivered by the t-bills, PTC and E-foods, whereas, the
highest returns have been shown by AKZO and CPPL during last three years.
4.2.Mean and Standard Deviation Analysis
The graph above reveals the mean returns and the standard devotion of the different
stocks. From the graph it can be analysed that mean return given by all the companies,
including KSE 100index and the t-bills is less than 0.005 during the last three years.
However, it can also be analysed that the standard deviation of the returns from their mean
values is very high, i.e. more than 0.25.
The graph has also shown that the average return of t-bills was less than 0, in the last
three year, the table of descriptive statistics have also shown that in the last three year the
average return give be t-bills was about -0.000506882, however, it has also been noticed that
the least deviation has also been shown by the t-bills in accordance with its nature of being a
risk free asset.
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
Average Returns
Average Returns

The co-efficient of variation represents the relative risk per unit of return. The table # 3 depicts that if
we take individual asset risk i.e. standard deviation into consideration than it can be observed that the
return is much less in proportion than the returns.
Co-efficient of Variation
KSE 100
Index
Mean 0.001 0.001 0.000 0.003 0.001 0.001 0.000 0.000 0.003 0.001 -0.001 0.001
Standard
Deviation
0.019 0.021 0.023 0.024 0.021 0.018 0.018 0.019 0.027 0.017 0.009 0.009
Co-efficient of
Variation
35.5 15.7 186.6 7.5 28.3 32.7 449.3 -120.0 8.1 24.2 -17.0 9.3
Table 3: For instance, Efoods and APL have 186.6 and 449.3 time the risk per unit of its stock returns respectively.
4.3.Kurtosis
The kurtosis analysis quantifies whether the shape of the data distribution matches the
Gaussian distribution. A Gaussian distribution has a kurtosis of 0.A flatter distribution has a
negative kurtosis. The kurtosis of a normal distribution is supposed to be 3.
However, in the above case, it has been observed that the data is not distributed
normally, since none of the assets have the kurtosis of 3. The reason, behind the uneven
distribution is that data for the stock prices and returns have been gathered from diversified
companies, therefore, the values of the returns varies widely.
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
Mean & Standard Deviation Analysis
Mean
Standard Deviation

4.4.Skewness
Skewness tells the symmetrical distribution of the data, if the data is symmetrical the
skewness appears to be zero. A symmetrical distribution with a long tail to the rig shows that
the data is positively skewed, in the same manner, asymmetrical distribution with a long tail
towards the left or the lower values shows that the data is negatively skewed. It can be
observed from the graph above, that none of the stocks have shown symmetrical distribution,
however, it can be analysed that the data of KOHE, APL, PTC, AKZO, ABL, T-Bills and
KSE 100 Index are negative skewed, whereas the returns for SNGP, ABOT, EFOODS,
CPPL, and INIL are positively skewed. However, the collected data is far away from ±0,
therefore, it can be stated that the returns are very far from symmetry.
-20
0
20
40
60
80
100
120
140
Kurtosis
Kurtosis
-10
-8
-6
-4
-2
0
2
Skewness
Skewness

4.5.Minimum and Maximum Analysis
The graph above has analysed the minimum and the maximum returns given by the
selected stocks. It can be analysed from the graph, that the maximum return delivered by all
the stocks are almost equal i.e. approximately 0.05. However, among all the stocks it has also
been analysed that the highest maximum return has been given the t-bills, which is exactly
0.05. On the other hand, it has also been observed that the minimum returns yielded by the
stocks have varied significantly, amount all the selected stock the lowest return is 0.28, given
by APL. On an average, the minim return yielded by the stocks is -0.0921.
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
Minimum & Maximum
Minimum
Maximum

4.6.Correlation Analysis
The correlation analysis reveals the direction of the data and the movement of the
data. It can be observed, from the table above, that KSE 100 index has a positive correlation
with all the stock returns except for T-bills.
KSE 100
Index
SNGP 1.00
ABOT 0.02 1.00
EFOODS 0.29 0.04 1.00
CPPL 0.11 0.00 0.25 1.00
INIL 0.20 0.05 0.18 0.21 1.00
KOHE 0.08 -0.03 0.12 0.15 0.06 1.00
APL 0.21 0.00 0.17 0.08 0.13 0.02 1.00
PTC 0.33 0.02 0.34 0.19 0.12 0.04 0.21 1.00
AKZO 0.21 0.00 0.30 0.25 0.17 0.12 0.21 0.23 1.00
ABL -0.03 0.02 -0.04 0.08 0.00 -0.03 -0.05 0.00 -0.01 1.00
(T-Bills ) -0.01 -0.09 -0.06 0.03 0.05 0.00 -0.04 -0.08 -0.03 0.02 1.00
KSE 100
Index
0.43 0.03 0.58 0.33 0.26 0.12 0.38 0.51 0.40 0.08 -0.05 1.00
Table 4: Therefore, it can be interpreted that with the increase in the returns of KSE 100, the returns of all
the selected companies will increase; however, the returns of t-bills will decrease.
4.6.1. Correlation Analysis with KSE-100 Index
The graph above has shown that the highest correlation with KSE 100 index
has been shown by E-foods, which is about 58%, secondly, PTC has also shown a
strong correlation with KSE 100 index which is about 51%. The remaining stocks
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Correlation Anlaysis (KSE100 INDEX)
KSE 100 Index

have also shown a positive yet moderate relationship with the returns of KSE 100
index. On the other hand ABT and ABL has shown weak correlation with KSE 100
index of about 2% and 8% respectively. Furthermore, it has also been analysed that
that with the increase in the KSE 100 stock return, the returns of T-bills will decline
by 4%.
4.6.2. Correlation Analysis with T-bills
On the other hand, it has also been observed that T-bills have shown a
negative relation with majority of the stocks, therefore, it can be interpreted that with
the increase in the returns of t-bills, the returns of most of the stocks will decline. On
the other hand, it has also been analysed that some of the stocks have shown positive
relationship with the t-bills returns, these stocks include CPPL, INIL, KOHE, and
ABL. Among the four stocks, INIL has shown the positive correlation i.e. about 5%,
however, it has also been analysed that the correlation is still very weak. On the other
hand, PTC and ABOT have shown the highest negative correlation i.e. about 7.5%
and 8.9%.
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
Correlation Anlaysis (T-Bills )
(T-Bills )

4.7.Portfolio Risk and Return Analysis
KSE 100
Index
Portfolio
(including risk
free asset)
Difference
Return 0.000968202 0.000903946 -0.006%
Risk 0.008975809 0.009208 0.023%
It can be analysed from the table that the return of the KSE 100 index and the
portfolio including the risk free assets is very low i.e. about 0.0009, on the country it can also
be observed that that the risk involved in KSE 100 index is 2.3% lower than the risk involved
in the portfolio investment. Therefore, it can be stated that both portfolio and the KSE 100
index yield same level of return with differentiated level of risk. The diversification of 10
assets equally weighted portfolio tends to make the portfolio returns very competitive in
comparison with KSE 100 index returns.
KSE 100
Index
Portfolio
(excluding risk
free asset)
Difference
Return 0.0009682 0.001045028 0.008%
Risk 0.0089758 0.009664 0.069%
The table above has shown the risk and the returns of the portfolio by including and
excluding the risk free assets. It can be stated that that the return of KSE 100 is 0.0009682,
whereas, the return of the portfolio is about 0.001045, whereas, the difference been the two
portfolios is about 0.008%, which is very minimal. Therefore, it can be stated that the returns
yield by the portfolio is very low, however, the return is 0.014% higher that returns of the
portfolio including risk free rate. On the other hand, the risk of KSE 100 index excluding has
also increased by 0.046%. The inclusion of risk free asset does reduce the risk by 0.046%.
5. Conclusion
A detailed analysis was attempted on the stock market returns gathering data for prices of
10 stocks of various companies along with the risk free asset returns i.e. T-bills. Returns and risk
for two portfolios were estimated and its results were compared to KSE-100 index returns. The
accumulated returns of each portfolio found to be very close in context to the KSE-100 index

return and risk. Even the inclusion of a risk free asset proved to reduce the percentage of risk
existed in the portfolio before its addition. The findings brought to the conclusion that
diversification can actually contribute in hedging the risk at substantial level.

6. Appendices
SNGP ABOT EFOODS CPPL INIL KOHE APL PTC AKZO ABL (T-Bills ) KSE 100 Index
Mean 0.000531 0.001345 0.000123 0.003193 0.000752 0.000562 0.000041 -0.000159 0.003353 0.000710 -0.000507 0.000968
Standard Deviation 0.018838 0.021136 0.022865 0.023965 0.021262 0.018366 0.018247 0.019099 0.027288 0.017203 0.008601 0.008976
SNGP 1
ABOT 0.016431 1
EFOODS 0.289564 0.043587 1
CPPL 0.110658 -0.001571 0.252833 1
INIL 0.199102 0.054195 0.176778 0.214725 1
KOHE 0.076793 -0.033053 0.119386 0.148405 0.062310 1
APL 0.212026 -0.001713 0.174338 0.082851 0.134248 0.016894 1
PTC 0.333884 0.015155 0.343688 0.192099 0.119193 0.040336 0.212745 1
AKZO 0.207651 -0.000001 0.298287 0.254826 0.170707 0.119615 0.210716 0.231889 1
ABL -0.025522 0.019589 -0.039551 0.082745 0.000321 -0.034966 -0.047306 -0.000786 -0.005174 1
(T-Bills ) -0.008041 -0.089952 -0.057386 0.026942 0.050537 0.002826 -0.040736 -0.075191 -0.026809 0.020086 1
KSE 100 Index 0.429294 0.026544 0.580150 0.327612 0.255536 0.123488 0.378341 0.514874 0.397336 0.081791 -0.049930 1
SNGP 0.000354878 6.54221E-06 0.000124723 4.99573E-05 7.9747E-05 2.65695E-05 7.28808E-05 0.000120128 0.000106744 -8.2707E-06 -1.3029E-06 7.25886E-05
ABOT 6.5422E-06 0.000446734 2.10645E-05 -7.95622E-07 2.43546E-05 -1.28308E-05 -6.60505E-07 6.11775E-06 -7.651E-10 7.1224E-06 -1.6352E-05 5.03574E-06
EFOODS 0.000124723 2.10645E-05 0.000522792 0.00013854 8.59395E-05 5.01352E-05 7.27345E-05 0.000150086 0.000186109 -1.5557E-05 -1.1285E-05 0.000119064
CPPL 4.99573E-05 -7.95622E-07 0.00013854 0.000574319 0.00010941 6.53203E-05 3.62292E-05 8.79252E-05 0.000166644 3.4112E-05 5.5532E-06 7.04709E-05
INIL 7.9747E-05 2.43546E-05 8.59395E-05 0.00010941 0.000452063 2.43324E-05 5.20824E-05 6.93204E-05 9.90419E-05 1.1754E-07 9.24153E-06 4.8767E-05
KOHE 2.65695E-05 -1.28308E-05 5.01352E-05 6.53203E-05 2.43324E-05 0.000337325 5.66172E-06 1.41491E-05 5.99484E-05 -5.5234E-06 4.4635E-07 2.03574E-05
APL 7.28808E-05 -6.60505E-07 7.27345E-05 3.62292E-05 5.20824E-05 5.66172E-06 0.000332941 7.41404E-05 0.000104918 -1.4849E-05 -6.393E-06 6.19642E-05
PTC 0.000120128 6.11775E-06 0.000150086 8.79252E-05 4.84018E-05 1.41491E-05 7.41404E-05 0.000364772 0.000120854 -1.2908E-07 -1.2351E-05 8.82643E-05
AKZO 0.000106744 -7.65098E-10 0.000186109 0.000166644 9.90419E-05 5.99484E-05 0.000104918 0.000120854 0.000744625 -2.4289E-06 -6.292E-06 9.73197E-05
ABL -8.2707E-06 7.12241E-06 -1.55566E-05 3.41124E-05 1.17543E-07 -1.10475E-05 -1.4849E-05 -2.5818E-07 -2.4289E-06 0.00029593 2.97185E-06 1.2629E-05
(T-Bills ) -1.30289E-06 -1.6352E-05 -1.12852E-05 5.5532E-06 9.24153E-06 4.4635E-07 -6.39296E-06 -1.2351E-05 -6.292E-06 2.9719E-06 7.39735E-05 -3.85453E-06
KSE 100 Index 7.25886E-05 5.03574E-06 0.000119064 7.04709E-05 4.8767E-05 2.03574E-05 6.19642E-05 8.82643E-05 9.73197E-05 1.2629E-05 -3.8545E-06 8.05651E-05

Equally
Weighted
Portfolio
Companies SNGP ABOT EFOODS CPPL INIL KOHE APL PTC AKZO ABL (T-Bills ) Total
Weights 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.09090909 0.090909091 1
0.0000848
Portolio Variance 0.000084782 Portolio S.D 0.009208
W*Covariance*W
OR
W^2*Covariance
Mean 0.000530516 0.001344823 0.000122533 0.00319338 0.00075218 0.000562278 4.06076E-05 -0.00015918 0.003352882 0.00071026 -0.00050688
Weights 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.090909091 0.09090909 0.090909091
Ind. Mean *
Weight
4.82287E-05 0.000122257 1.11394E-05 0.000290307 6.838E-05 5.11162E-05 3.6916E-06 -1.4471E-05 0.000304807 6.4569E-05 -4.608E-05
Portfolio Return 0.000903946
KSE 100 Index
Portfolio (inc.
risk free asset)
Difference
Return 0.000968202 0.000903946 -0.006%
Risk 0.008975809 0.009208 0.023%
Equally
Weighted
Portfolio
Companies SNGP ABOT EFOODS CPPL INIL KOHE APL PTC AKZO ABL Total
Weights 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 1.000000
Portolio Variance 0.000093390 Portolio S.D 0.009664
W*Covariance*W
OR
W^2*Covariance

SNGP ABOT EFOODS CPPL INIL KOHE APL PTC AKZO ABL
Mean 0.000530516 0.001344823 0.000122533 0.00319338 0.00075218 0.000562278 4.06076E-05 -0.00015918 0.003352882 0.00071026
Weights 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
Ind. Mean *
Weight
5.30516E-05 0.000134482 1.22533E-05 0.000319338 7.5218E-05 5.62278E-05 4.06076E-06 -1.5918E-05 0.000335288 7.1026E-05
Portfolio Return 0.001045028
KSE 100 Index
Portfolio (exc.
risk free asset)
Difference
Return 0.0000883 0.001045028 0.096%
Risk 0.0000973 0.009664 0.957%

Impact of Risk Free and Risky Asset on Portfolio Return

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