1. Assignment:
InvestmentAnalysis & portfolio management
Submitted To:
Mr. Abrar Hussain
Submitted By:
Ayesha Bibi (12007)
Tahira Ayub (BB12015)
Fazeela Mushtaq (BB12020)
Farwa Yousaf (BB12027)
Zubaida Abaiadullah (BB12061)
University of Punjab, Gujranwala Campus
Gujranwala

2. Table of Contents
Introduction.......................................................................................................................................3
Minimum Variance Portfolio ...............................................................................................................5
Beta of the Portfolio: ..........................................................................................................................6
Combination of Risky and Riskless portfolio .........................................................................................7
Ratios................................................................................................................................................8
Sharp Ratio=...................................................................................................................................8
CV=................................................................................................................................................8
Treynors Measure=.........................................................................................................................8
JenksonAlpha=...............................................................................................................................8
Appraisal Ratio=..............................................................................................................................8

3. Introduction
We are risk averse investors. We seek professional answers to our financial problems. We seek
answers from our advisors, including tax and wealth strategists, stockbrokers, bankers, and real
estate brokers. When seek the proper market knowledge that helps us to invest our money in
good company or in buying of shares of financially stable companies. We want a guarantee of
our money before investing in any company. We prefer to invest in those companies that provide
high return and low risk. We prefer to invest in those companies that provide normal return with
low risk, as compared to those companies that provide high return and high risk.
First of all we search the KSE website to thoroughly to understands the pattern of prices of
different shares of of companies. Then we observe the sectors of KSE.We choose top 17 sectors
of KSE i.e AUTOMOBILE ASSEMBLER, AUTOMOBILE PARTS & ACCESSORIES,
CABLE & ELECTRICAL GOODS, CEMENT, CHEMICAL, CLOSE - END MUTUAL FUND,
COMMERCIAL BANKS, ENGINEERING, FERTILIZER, FOOD & PERSONAL CARE
PRODUCTS, GLASS & CERAMICS, INSURANCE, INV. BANKS / INV. COS. /
SECURITIES COS, JUTE etc.We choose almost 30 companies for making portfolio of
minimum variance, maximum variance portfolio , risk free, and risky asset combined portfolio.
The name of companies we choose from these sectors are Millat Tractors Limited, Thal
Limited, Pak Elektron Limited, Cherat Cement Company Limited, Fauji Cement
Company Limited, Indus Motor Company Limited, Kohat Cement Limited, Lucky Cement
Limited, I.C.I. Pakistan Limited, Pakistan State Oil Company Limited, Shell Pakistan
Limited, Packages Limited,colgate,Bata Pakistan Ltd,Noon Pakistan Ltd,Bank of
Punjab,KE Ltd, Jahangir Siddiqui Company Limited,Fauji fertilizer, Pakistan Tobacco
Company Limited,Honda altas cars, Hub power company Ltd,Oil and gas development
company Ltd, National Bank of Pakistan,
We take the daily data of these companies for 5 years from 2010-2014.And by analysis of this
data we select 28 companies on the basis of their returns.The companies that we select are Millat
Tractors Limited, Thal Limited, Pak Elektron Limited, Cherat Cement Company Limited, Fauji
Cement Company Limited, Indus Motor Company Limited, Kohat Cement Limited, Lucky
Cement Limited, I.C.I. Pakistan Limited, Pakistan State Oil Company Limited, , Packages

4. Limited, colgate, Bata Pakistan Ltd, Noon Pakistan Ltd, Bank of Punjab, KE Ltd, Jahangir
Siddiqui Company Limited , Pakistan Tobacco Company Limited, Honda altas cars,Hub power
company .
We compute Arithmetic mean, Geometric mean, variances, standard deviation and covariance’s
of that companies data. Our benchmark rate is KSE 100.

5. Minimum Variance Portfolio
We select 20 best companies out of 30 with maximum returns and minimum variance.
We shuffle all these companies with different weights and see their different pattern of
variance, return and standard deviation. All the companies give maximum return and
minimum variance.
Return of the Portfolio:
0.00114472
Variance of the portfolio:
0.48
Standard deviation:
0.69
weights R V STD
INDU 0.05 0.0008316 0.0011766 0.0343015
ICI 0.09 0.0014555 0.5786014 0.7606585
LUCK 0.02 0.0001375 0.0017225 0.0415036
PSO 0.07 0.0012051 0.0003312 0.0181979
PKGS 0.06 0.0008907 0.000627 0.0250395
THALL 0.03 0.0003949 0.0006781 0.0260394
MTL 0.02 0.0001147 0.0003366 0.0183459
FFC 0.06 0.0009848 0.0002783 0.0166824
HCAR 0.07 0.0017815 0.0023842 0.0488281
SCBPL 0.04 0.0007629 0.0018808 0.0433678
OGDC 0.03 0.000464 0.000207 0.0143864
HUBC 0.04 0.000684 0.0004726 0.0217398
BOP 0.02 0.0001022 0.0010552 0.0324832
KEL 0.05 0.0009304 0.0015591 0.039485
JSCL 0.04 0.0006005 0.0025671 0.0506663
KOHC 0.11 0.0024933 0.0009994 0.0316135
PAKT 0.08 0.0017304 0.0020114 0.0448482
NOPK 0.03 0.000127 0.0015948 0.0399353
BATA 0.05 0.0009795 0.0011668 0.0341586
PAEL 0.04 0.0005949 0.001521 0.0390003

6. Beta of the Portfolio:
Beta of portfolio=0.122097
COM Beta weights
INDU -0.02983 0.01
ICI -0.08145 0.01
LUCK 0.56611 0.12
PSO 0.158031 0.1
PKGS -0.02321 0.02
THALL 0.046381 0.04
MTL -0.04267 0.03
FFC 0.020116 0.05
HCAR 0.023881 0.03
SCBPL 0.010499 0.04
OGDC -0.01308 0.01
HUBC -0.0262 0.01
BOP 0.101798 0.1
KEL -0.1087 0.01
JSCL 0.19613 0.05
KOHC 0.025345 0.08
PAKT 0.076852 0.13
NOPK 0.051884 0.1
BATA -0.10193 0.02
PAEL 0.088639 0.04
1

7. Combination of Risky and Riskless portfolio
We make a combination portfolio of risky and riskless assets. Riskless assets are given as T-
Bills issued by the government of Pakistan. 85% was invested in risky asset and 15% was
invested in riskless assets. The maximum return 0.0178 is given by the combination of the
portfolio. Variance is 0.0063 and SD is 7.96%
weights R V STD
INDU 0.04 0.000832 0.001177 0.034301
ICI 0.08 0.001455 0.578601 0.760659
LUCK 0.02 0.000138 0.001723 0.041504
PSO 0.06 0.001205 0.000331 0.018198
PKGS 0.07 0.000891 0.000627 0.025039
THALL 0.03 0.000395 0.000678 0.026039
MTL 0.02 0.000115 0.000337 0.018346
FFC 0.05 0.000985 0.000278 0.016682
HCAR 0.08 0.001782 0.002384 0.048828
SCBPL 0.02 0.000763 0.001881 0.043368
OGDC 0.01 0.000464 0.000207 0.014386
HUBC 0.02 0.000684 0.000473 0.02174
BOP 0.02 0.000102 0.001055 0.032483
KEL 0.02 0.00093 0.001559 0.039485
JSCL 0.03 0.0006 0.002567 0.050666
KOHC 0.13 0.002493 0.000999 0.031614
PAKT 0.07 0.00173 0.002011 0.044848
NOPK 0.03 0.000127 0.001595 0.039935
BATA 0.03 0.00098 0.001167 0.034159
PAEL 0.02 0.000595 0.001521 0.039
t-bills 0.15 0.111721 0.000262 0.016177
Risky and riskless portfolio
Return of Portfolio variance of portfolio Standard Deviation
0.0178 0.0063 7.96%

8. Ratios
Sharp Ratio= 0.0094-0.00178/0.003848
1.98
Thisratio showsthe selectedcompaniesare givingexcessreturnatperunitof risk.
CV= 0.003848/0.0008633
4.45 per unit
It shows4.45 at per unitof risk.
Treynors Measure=
0.0094-0.000178/0.12209
0.062
It showsexcessreturnof 0.062 per unitof systematicrisk.
Jenkson
Alpha= 0.0078
It showsthe overreturncalculatedbyCAPM.
Appraisal Ratio= 0.068
It shows the unsystematic risk which can be controlled by the Company.