individual and portfolio analysis of 10 securities

7/30/2019 Individual and Portfolio Analysis of 10 securities

1/31

Rm Rm - Rm' Rm - Rm' ^ 2

2011 11347.66 -0.05612828 -0.18489 0.034184041

2010 12022.46 0.28076728 0.152006 0.0231059142009 9386.92 0.60049514 0.471734 0.222533112

2008 5865.01 -0.583366958 -0.71213 0.507126208

2007 14077.16 0.402037747 0.273277 0.074680188

2006 10040.5 0.050634064 -0.07813 0.006103816

2005 9556.61 0.536827801 0.408067 0.166518526

2004 6218.4 0.39064317 0.261882 0.068582278

2003 4471.6 0.655283722 0.526523 0.277226192

2002 2701.41 1.121981682 0.993221 0.986487351

2001 1273.06 -0.155566169 -0.28433 0.080841931

2000 1507.59

Total 3.243609201 1.827238 2.447389556

Market Data

We are taking the 'KSE-100 Index' as proxy of market.


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0

2000

4000

6000

8000

10000

12000

14000

16000

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Market Index

Market Index

0

2000

4000

6000

8000

10000

12000

14000

16000

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Market Return Trend

Market Return

-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Market Index & Return Trend

KSE 100 Index

KSE 100 Index Return


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Mean Return

(Rm')=

Variance=

= 0.489477911

Standard Deviation=

0.69962698

9.28%

3%

0.128760986

SQRT (Variance)

E(R - R') ^ 2 / n

=

This is the arithmetic average of daily returns of market of the past 5 years. We are using this mean as the

expected future returns from this security because this is the best estimate that we can make from

historical data.

Risk Free Rate of Return (As

on short term T-Bills) =

Market Risk Premium

(Assumed)=


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Return R - R' (R - R')(Rm - Rm') R - R' ^ 2

2011 34.2 -0.085805934 -0.26273 0.04857533 0.069025271

2010 37.41 0.203667954 0.026747 0.004065755 0.0007154172009 31.08 1.20581973 1.028899 0.485366825 1.058633265

2008 14.09 -0.538032787 -0.71495 0.509138339 0.511158453

2007 30.5 0.105072464 -0.07185 -0.019634447 0.005162166

2006 27.6 0.15 -0.02692 0.00210323 0.000724723

2005 24 -0.252336449 -0.42926 -0.175165588 0.184261679

2004 32.1 -0.165149545 -0.34207 -0.089582096 0.117012036

2003 38.45 -0.041147132 -0.21807 -0.114817659 0.047553569

2002 40.1 1.587096774 1.410176 1.400616086 1.988596629

2001 15.5 -0.223057644 -0.39998 0.113724697 0.159982656

2000 19.95

Total 1.946127431 0 2.164390472 4.142825863

Hub Power


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0

5

10

15

20

25

30

35

40

45

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Share Price Trend

Share Price

-1

-0.5

0

0.5

1

1.5

2

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Return Trend

Return

-5

0

5

10

15

20

25

30

35

40

45

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Share Price & Return Trend

Share Price

Return


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Mean Return

(R') = 0.176920676

Variance= E(R - R') ^ 2 / n

= 0.376620533

SQRT (Variance)

= 0.613694169

Coefficient of

Variation= Standard Deviation / Mean Return

= 3.468753254

Beta=

= 0.401984984

Covariance

with market=

= 0.19676277

RRR using

CAPM= Rf + (Rp)B

= 10.48%

The required rate of return is the same as the risk free rate of return. This is because the beta is 0.

Standard Deviation=

Cov-i,m / Var-m

E [ (Ri-Ri') * (Rm-Rm') ] / n

This is the arithmetic average of daily returns from this security of the past 5 years. We are using this

mean as the expected future returns from this security because this is the best estimate that we can make

from historical data.

This is the risk of the security.

This is the risk per unit of return of this security. An individual security among many securities is selected

on this basis. The lower the Coefficient of Variance is, the lower is the risk per unit of return.

The beta of this security is between 0 and 1. This meas that the risk of the security is less than the risk of

the market and the security movement is in the same direction as of the market.


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2011 5,565.80 0.276509861 0.059183 -0.01094224 0.003502588

2010 4,360.17 0.895726087 0.678399 0.103120902 0.460225062009 2,300.00 0.272327973 0.055001 0.025945747 0.003025086

2008 1,807.71 -0.207162124 -0.42449 0.302290704 0.180191179

2007 2,280.05 0.140025 -0.0773 -0.021124893 0.005975629

2006 2,000.00 0.126760563 -0.09057 0.007075692 0.008202314

2005 1,775.00 0.203389831 -0.01394 -0.005687375 0.00019425

2004 1,475.00 0.018646409 -0.19868 -0.052030958 0.039474054

2003 1,448.00 0.196694215 -0.02063 -0.010863732 0.00042572

2002 1,210.00 0.592105263 0.374778 0.372237336 0.140458602

2001 760 -0.124423963 -0.34175 0.097169134 0.116793852

2000 868

Total 2.390599115 0 0.807190317 0.958468335

Unilever


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0.00

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

6,000.00

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Share Price Trend

Share Price"

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Return Trend

Return

-1,000.00

0.00

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

6,000.00

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001


Share Price

Return


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Mean Return

(R') = 0.217327192


= 0.087133485

SQRT (Variance)

= 0.295183816

Coefficient of

Variation=Standard Deviation / Mean Return= 1.35824612

Beta=

= 0.149916751

Covariance

with market=

= 0.073380938

RRR using

CAPM= Rf + (Rp)B

= 9.73%

The required rate of return is the same as the risk free rate of return. This is because the is 0.

Standard Deviation=

Cov-i,m / Var-m

E [ (Ri-Ri') * (Rm-Rm') ] / n










10/31


2011 3,597.11 0.514661917 0.129585 -0.023958878 0.016792276

2010 2,374.86 0.906048348 0.520971 0.079190939 0.2714112462009 1,245.96 -0.065646794 -0.45072 -0.212621762 0.203151852

2008 1,333.50 -0.259166667 -0.64424 0.458783849 0.415049778

2007 1,800.00 0.8 0.414923 0.11338884 0.172161176

2006 1,000.00 0.298701299 -0.08638 0.00674826 0.007460745

2005 770 0.480911626 0.095835 0.03910697 0.009184294

2004 519.95 0.382845745 -0.00223 -0.000584301 4.97807E-06

2003 376 0.720823799 0.335747 0.176778374 0.112725978

2002 218.5 0.456666667 0.07159 0.071104434 0.005125094

2001 150 0 -0.38508 0.10948782 0.148284222

2000 150

Total 4.235845939 -5.6E-16 0.817424545 1.361351638

Nestle Pakistan


11/31

0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

3,000.00

3,500.00

4,000.00

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Share Price Trend

Share Price

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Return Trend

Return

-500.00

0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

3,000.00

3,500.00

4,000.00

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001


Share Price

Return


12/31

Mean Return

(R') = 0.385076904


= 0.12375924

SQRT (Variance)

= 0.351794315

Coefficient of


Beta=

= 0.151817519

Covariance

with market=

= 0.074311322

RRR using

CAPM= Rf + (Rp)B

= 9.73%

The required rate of return is the same as the risk free rate of return. This is because the is very near to 0.

Standard Deviation=

Cov-i,m / Var-m

E [ (Ri-Ri') * (Rm-Rm') ] / n










13/31


2011 818.4 0.18754988 -0.3302 0.061050831 0.109033452

2010 689.15 -0.296067416 -0.81382 -0.123705676 0.6623020712009 979 0.310575636 -0.20718 -0.097732175 0.042922053

2008 747 0.538778453 0.021026 -0.014973512 0.000442111

2007 485.45 2.595925926 2.078174 0.567916635 4.318806792

2006 135 0.5 -0.01775 0.001386911 0.000315134

2005 90 0.267605634 -0.25015 -0.102076438 0.062573213

2004 71 0.392156863 -0.1256 -0.032891134 0.015774143

2003 51 0.616481775 0.09873 0.051983462 0.009747565

2002 31.55 0.37173913 -0.14601 -0.145023022 0.021319763

2001 23 0.210526316 -0.30723 0.08735261 0.094387632

2000 19

Total 5.695272197 0 0.25328849 5.337623929

Bata


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0

200

400

600

800

1000

1200

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Share Price Trend

Share Price

-0.5

0

0.5

1

1.5

2

2.5

3

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Return Trend

Return

-200

0

200

400

600

800

1000

1200

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001


Share Price

Return


15/31

Mean Return

(R') = 0.517752018


= 0.485238539

SQRT (Variance)

= 0.696590654

Coefficient of


Beta=

= 0.047042422

Covariance

with market=

= 0.023026226

RRR using

CAPM= Rf + (Rp)B

= 9.42%


Standard Deviation=

Cov-i,m / Var-m

E [ (Ri-Ri') * (Rm-Rm') ] / n










16/31


2011 2,513.28 0.191201354 -0.10207 0.018871684 0.010418325

2010 2,109.87 0.420787879 0.127516 0.019383285 0.0162604142009 1,485.00 -0.376422471 -0.66969 -0.315917542 0.448490082

2008 2,381.42 0.056062084 -0.23721 0.168923489 0.056268331

2007 2,255.00 1.505555556 1.212284 0.331289047 1.469632509

2006 900 0.285714286 -0.00756 0.000590426 5.71122E-05

2005 700 0.129032258 -0.16424 -0.067020605 0.026974545

2004 620 0.24 -0.05327 -0.01395087 0.002837858

2003 500 0.612903226 0.319632 0.168293344 0.102164408

2002 310 0.033333333 -0.25994 -0.258176017 0.067567877

2001 300 0.127819549 -0.16545 0.047042497 0.027374365

2000 266

Total 3.225987053 0 0.099328737 2.228045826

Rafhan Maize Products


17/31

0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

3,000.00

3,500.00

4,000.00

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Share Price Trend

Share Price

-0.5

0

0.5

1

1.5

2

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

Return Trend

Return

-500

0

500

1000

1500

2000

2500

3000

2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001


ReturnShare Price


18/31

Mean Return

(R') = 0.29327155


= 0.202549621

SQRT (Variance)

= 0.450055131

Coefficient of


Beta=

= 0.018447993

Covariance

with market=

= 0.009029885

RRR using

CAPM= Rf + (Rp)B

= 9.33%


Standard Deviation=

Cov-i,m / Var-m

E [ (Ri-Ri') * (Rm-Rm') ] / n










19/31

Summary of Individual Securities

Mean Return Standard Deviation Coefficient of Variance Beta RRR

Hub Power 0.176920676 0.613694169 3.468753254 0.401984984 10.48%

Unilever 0.217327192 0.295183816 1.35824612 0.149916751 9.73%

Nestle 0.385076904 0.351794315 0.913568982 0.151817519 9.73%

Bata 0.517752018 0.696590654 1.345413692 0.047042422 9.42%

Rafhan Maize 0.29327155 0.450055131 1.534602078 0.018447993 9.33%

Best Security Bata Unilever Nestle Rafhan Maize

Because it has

the highest

mean return

Because it has the

lowest Standard

Deviation

Because it has the lowest

Coefficient of Variation

Because it has

the lowest risk

as compared

to the market

0

0.5

1

1.5

2

2.5

3

3.5

4

Hub Power Unilever Nestle Bata Rafhan Maize

Mean Return

Standard Deviation

Coefficient of Variance

Beta

RRR


20/31

0.5

0.5

= 19.71%

19.71%

Variance=

= 0.505089445

Standard Deviation= SQRT (Variance)

= 0.710696451

71.07%

Covariance=

= 0.101300906

( R1 - R1' ) ( R2 - R2' )

Total 0 0

Correlation=

=

0.559202097

Portfolio 1: Hub Power & Unilever

The correlation of Hub Power & Unilever is approximately 0.6. This means that these two securities are

moderately correlated, they move moderately in the same direction.

( R1 - R1' ) * (R2 - R2')

(W1 * R1) + (W1 * R2)Expected Return (ER)=

1.114309969

The risk of the portfolio as a whole is =

Weight of Hub Power=

Weight of Unilever=

The portfolio return of Hub Power & Nestle is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n

Covariance / (SD 1 * SD 2)


21/31

0.5

0.5

= 28.10%

28.10%

Variance=

= 0.486864442


= 0.697756721

69.78%

Covariance=

= 0.0082404

( R1 - R1' ) ( R2 - R2' )

Total 0 -5.55112E-16

Correlation=

=

0.03816871

Portfolio 2: Hub Power & Nestle

The correlation of Hub Power & Unilever is approximately 0.04 This means that these two securities

are slightly correlated, they move slightly in the same direction.

( R1 - R1' ) * (R2 - R2')


0.090644401



Weight of Nestle=

The portfolio return of Hub Power & Nestle is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



22/31

0.5

0.5

= 34.73%

34.73%

Variance=

= 0.643039829


= 0.801897642

80.19%

Covariance=

= -0.024205166

( R1 - R1' ) ( R2 - R2' )

Total 0 0

Correlation=

=

-0.056621115

Portfolio 3: Hub Power & Bata

The correlation of Hub Power & Unilever is approximately -0.06. This means that these two securities

are slightly negatively correlated, they move slightly in the opposite direction.

( R1 - R1' ) * (R2 - R2')


-0.266256821



Weight of Bata=

The portfolio return of Hub Power & Bata is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



23/31

0.5

0.5

= 23.51%

23.51%

Variance=

= 0.492898156


= 0.702067059

70.21%

Covariance=

= -0.077952988

( R1 - R1' ) ( R2 - R2' )

Total 0 0

Correlation=

=

-0.282237717

Portfolio 4: Hub Power & Rafhan Maize


have low negative correlation, they move weakly in the opposite direction.

( R1 - R1' ) * (R2 - R2')


-0.857482865



Weight of Rafhan Maize=

The portfolio return of Hub Power & Rafhan is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



24/31

0.5

0.5

= 30.12%

30.12%

Variance=

= 0.356949937


= 0.597452874

59.75%

Covariance=

= 0.066921743

( R1 - R1' ) ( R2 - R2' )

Total 0 -5.55112E-16

Correlation=

=

0.768037032

Portfolio 5: Unilever & Nestle


highly correlated, they move strongly in the same direction.

( R1 - R1' ) * (R2 - R2')


0.736139176


Weight of Unilever=

Weight of Nestle=

The portfolio return of Unilver & Nestle is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



25/31

0.5

0.5

= 36.75%

36.75%

Variance=

= 0.465236257


= 0.682082295

68.21%

Covariance=

= -0.061301956

( R1 - R1' ) ( R2 - R2' )

Total 0 0

Correlation=

=

-0.298128949

Portfolio 6: Unilever & Bata


have low negative correlation, they move weakly in the opposite direction.

( R1 - R1' ) * (R2 - R2')


-0.67432152


Weight of Unilever=

Weight of Bata=

The portfolio return of Unilever & Bata is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



26/31

0.5

0.5

= 25.53%

25.53%

Variance=

= 0.373378563


= 0.611047104

61.10%

Covariance=

= 0.00151818

( R1 - R1' ) ( R2 - R2' )

Total 0 0

Correlation=

=

0.01142786

The correlation of Hub Power & Unilever is approximately 0.01. This means that these two have a low

correlation, they move weakly in the same direction.

Portfolio 7: Unilever & Rafhan Maize

( R1 - R1' ) * (R2 - R2')


0.016699976


Weight of Unilever=


The portfolio return of Unilever & Rafhan Maize is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



27/31

0.5

0.5

= 45.14%

45.14%

Variance=

= 0.551201172


= 0.742429237

74.24%

Covariance=

= 0.054017376

( R1 - R1' ) ( R2 - R2' )

Total -5.55112E-16 0

Correlation=

=

0.220428134

Portfolio 8: Nestle & Bata

The correlation of Hub Power & Unilever is approximately 0.2. This means that these two securities

have low correlation, they move weakly in the same direction.

( R1 - R1' ) * (R2 - R2')


0.594191136


Weight of Nestle=

Weight of Bata=

The portfolio return of Nestle & Bata is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



28/31

0.5

0.5

= 33.92%

33.92%

Variance=

= 0.453121442


= 0.673142958

67.31%

Covariance=

= 0.10439344

( R1 - R1' ) ( R2 - R2' )

Total -5.55112E-16 0

Correlation=

=

0.659354043

Portfolio 9: Nestle & Rafhan Maize


highly correlated, they move strongly in the same direction.

( R1 - R1' ) * (R2 - R2')


1.148327835


Weight of Nestle=


The portfolio return of Nestle & Rafhan Maize is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



29/31

0.5

0.5

= 40.55%

40.55%

Variance=

= 0.698380797


= 0.835691807

83.57%

Covariance=

= 0.250115809

( R1 - R1' ) ( R2 - R2' )

Total 0 0

Correlation=

=

0.79780689

Portfolio 10: Bata & Rafhan Maize

The correlation of Hub Power & Unilever is approximately 0.8. This means that these two securities

are highly correlated, they move strongly in the same direction.

( R1 - R1' ) * (R2 - R2')


2.7512739


Weight of Bata=


The portfolio return of Bata & Rafhan Maize is=

[(W1*SD1)+(W2*SD2)+2(W1*W2*COV)]

E [ (R1-R1') * (R2-R2') ] / n



30/31

Portfolio 3= Hub Power & BataPortfolio 4= Hub Power & Rafhan Maize

Portfolio 5= Unilever & Nestle

Portfolio 6= Unilever & Bata

Portfolio 7= Unilever & Rafhan Maize

Portfolio 8= Nestle & Bata

Portfolio 9= Nestle & Rafhan Maize

Portfolio 10= Bata & Rafhan Maize

Return Risk

19.71% 71.07%

28.10% 69.78%

34.73% 80.19%

23.51% 70.21%

30.12% 59.75%

36.75% 68.21%

25.53% 61.10%

45.14% 74.24%

33.92% 67.31%

40.55% 83.57%

Summary of Portfolio Analysis

Portfolio 1= Hub Power & Unilever

Portfolio 2= Hub Power & Nestle

All securities in each portfolio carry equal weight.

Portfolio

Portfolio 10= Bata & Rafhan Maize

Portfolio 1= Hub Power & Unilever

Portfolio 3= Hub Power & Bata

Portfolio 2= Hub Power & Nestle

Portfolio 4= Hub Power & Rafhan Maize

Portfolio 5= Unilever & Nestle

Portfolio 6= Unilever & Bata

Portfolio 7= Unilever & Rafhan Maize

Portfolio 8= Nestle & Bata

Portfolio 9= Nestle & Rafhan Maize

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

Return

Risk

Portfolio Analysis


31/31

Decision:-

The basic purpose of portfolio is to diversify the risk. So we take decision on the basis of risk or standard

deviation of portfolio. The risk of portfolio 5 of Unilever & Nestle is less as compared to other portfolios

which is 59.75%. So being investor we choose the portfolio of Unilever & Nestle.

individual and portfolio analysis of 10 securities

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