market portfolio

Table of Contents1.Introduction32.Market Portfolio: KSE-100 Index32.1.KSE-100 Index Portfolio Calculation32.1.1.Realized Percentage Return32.1.2.Risk Calculation (Variance)32.1.3.Standard Deviation42.1.4.Standard Deviation for 9 weeks42.1.5.Beta Calculation (Using Calculator)43.Active Portfolio43.1. Active Portfolio Calculations53.1.1. Realized Percentage Return53.1.2. Risk Calculation (Variance)53.1.3. Standard Deviation63.1.4. Standard Deviation for 9 weeks63.1.5. Beta Calculation (Using Calculator)64.Levered Portfolio64.1.Levered Portfolio Calculations74.1.1.Realized Percentage Return74.1.2. Risk Calculation (Variance)74.1.3. Standard Deviation74.1.4. Standard Deviation for 9 weeks84.1.5. Beta Calculation (Using Calculator)85.Passive Portfolio85.1.Passive Portfolio Calculations85.1.1.Realized Percentage Return85.1.2.Risk Calculation (Variance)85.1.3.Standard Deviation95.1.4.Standard Deviation for 9 weeks95.1.5.Beta Calculation (Using Calculator)96.Sharpes Index106.1.Market Portfolio (KSE-100 Index)106.2.Active Portfolio106.3.Passive Portfolio106.4.Levered Portfolio117.Tryenors Index117.1.Market Portfolio (KSE-100 Index)117.2.Active Portfolio127.3.Passive Portfolio127.4.Levered Portfolio128.Differential CML138.1.Market Portfolio138.2.Active Portfolio148.3.Passive Portfolio148.4.Levered Portfolio149.Differential SML159.1. Market Portfolio159.2. Active Portfolio159.3. Passive Portfolio169.4. Levered Portfolio16

1. IntroductionAs part of the term project of the course Investment Portfolio Analysis, we operated four portfolios by the name of Active, Passive, Levered and Market. We initially invested PKR 100 million in each of the portfolio. We did a lot of buying and selling of stocks from Karachi Stock Exchange during the allotted duration of 9 weeks. The report contains all the calculations for the individual portfolios.2. Market Portfolio: KSE-100 Index2.1. KSE-100 Index Portfolio Calculation2.1.1. Realized Percentage ReturnRealized Rm = (W9 W0) / W0Realized Rm = (PKR 92,051,774.76 PKR 100,000,000.00) / PKR 100,000,000.00Rm = -7.95%2.1.2. Risk Calculation (Variance)Total Risk of Stock i = (VARi) = ( Rit Average Ri)2/ nReturns on KSE-100 Index

WeekReturnReturn-Avg.( Ri Average Ri)2

11.332.245.02

20.611.522.31

3-0.310.600.37

4-2.24-1.331.76

50.391.301.68

6-2.10-1.191.42

7-1.06-0.150.02

8-1.23-0.320.11

9-3.53-2.626.84

( Rit Average Ri)219.52

(VARi) = ( Rit Average Ri)2/ n

(VARi) = 19.52/9 = 2.168%2.1.3. Standard Deviation SD Market= VAR MarketSD Market= 2.168 = 1.47%2.1.4. Standard Deviation for 9 weeks

SD for 9 week = SD Market x 9 = 4.42%

2.1.5. Beta Calculation (Using Calculator)m = 13. Active Portfolio This was the portfolio, where active trading was done, many shares of different companies were bought and sold. The name of the companies, whose shares trading were done are listed below.Company NameSymbol

Ghani GlassGHGL

Fatima Fertilizer LimitedFATIMA

Bank of PunjabBOP

Berger PaintsBERG

Century Paper & Board Mills LimitedCEPB

Engro Foods LimitedEFOODS

Kot Addu Power Company LimitedKAPCO

DESCON CHEMICAL LTDDCH

Engro Fertilizers LimitedEFERT

Bolan Casting LimitedBCL

Lalpir Power LimitedLPL

Pakistan Petroleum LimitedPPL

Pakistan Cables LimitedPCAL

Byco Petroleum Pakistan LimitedBYCO

The main rationale behind buying these stocks was that these all are big companies at the KSE. They all have competitive managements. Their historical earnings and dividends have been impressive the upside potential of the companies was very high.

3.1. Active Portfolio Calculations 3.1.1. Realized Percentage Return Realized RA = (W9 W0) / W0Realized RA = (PKR 107,932,823.01 PKR 100,000,000.00) / PKR 100,000,000.00Ra = 7.93%3.1.2. Risk Calculation (Variance)Total Risk of Stock i = (VARi) = ( Rit Average Ri)2/ nActive Portfolio


110.619.6693.32

2-1.26-2.214.87

3-3.44-4.3919.26

4-4.79-5.7432.99

53.082.134.55

65.174.2217.80

70.69-0.260.07

8-1.79-2.747.53

90.27-0.680.46



(VARi) = 180.84/ 9 = 20.09%3.1.3. Standard Deviation SD A= VAR ASD A= 20.09= 4.48%3.1.4. Standard Deviation for 9 weeksSD for 9 week = SD A X 9 = 13.45%

3.1.5. Beta Calculation (Using Calculator)A = 1.214. Levered PortfolioThis was the portfolio, in which additional loan of PKR 50 million was taken apart from the PKR 100 million to do investments in the stocks. In this portfolio, weekly interest cost was also incurred. The name of the stocks bought in this portfolio is given below.

Company NameSymbol

Muslim Commercial Bank LimitedMCB

Pakistan State OilPSO

Sitara ChemicalsSITC

Pakistan Oilfields LimitedPOL

4.1. Levered Portfolio Calculations 4.1.1. Realized Percentage Return Realized RL = {(W9 W0)-Interest } / W0 - Loan AmountRealized RL = {(PKR 136,090,770 PKR 150,000,000) - PKR 1,035,000}/ (PKR 150,000,000-PKR 50,000,000RL = -14.94%4.1.2. Risk Calculation (Variance)Total Risk of Stock i = (VARi) = ( Rit Average Ri)2/ n

Levered Portfolio


18.229.7695.2

22.914.4519.8

3-3.80-2.265.1

4-2.19-0.650.4

5-0.590.950.9

6-2.96-1.422.0

7-3.76-2.224.9

8-1.300.240.1

9-10.36-8.8277.8



(VARi) = 206.31/9 = 22.92% 4.1.3. Standard Deviation SD L= VAR MarketSD L= 22.92= 4.78%

4.1.4. Standard Deviation for 9 weeksSD for 9 week = SD L X 9 = 14.36%

4.1.5. Beta Calculation (Using Calculator)L = 2.785. Passive Portfolio This portfolio was a silent portfolio. No active was done in this portfolio apart from the initial buying of the stocks in Week 0. The companies in which investments were done are listed below;Company NameSymbol

Kohinor TextileKTML

Arif Habib LimitedAHL

Nishat Mills LimitedNML

Shell PakistanSHEL

5.1. Passive Portfolio Calculations 5.1.1. Realized Percentage Return Realized Rp = (W9 W0) / W0Realized Rp = (PKR 94,339,306.60 PKR 100,000,000.00) / PKR 100,000,000.00Rp = -5.66%5.1.2. Risk Calculation (Variance)Total Risk of Stock i = (VARi) = ( Rit Average Ri)2/ n

Passive Portfolio


13.684.2718.21

26.346.9348.06

30.200.790.62

4-4.05-3.4611.98

5-2.38-1.793.19

6-3.04-2.455.99

7-0.68-0.090.01

8-2.90-2.315.35

9-2.50-1.913.64



(VARi) = 97.06/9 = 10.78% 5.1.3. Standard Deviation SD p= VAR MarketSD p= 10.78= 3.28%

5.1.4. Standard Deviation for 9 weeksSD for 9 week = SD p x 9 = 9.85%

5.1.5. Beta Calculation (Using Calculator)P = 1.61

6. Sharpes IndexSharpes Excess Return to Volatility RatioRp Rf / SDp where Rf is 1.38% for 9 weeks6.1. Market Portfolio (KSE-100 Index)Market Portfolio

RmRfSDp

-7.951.384.42

= (-7.95-1.38)/4.42 = -2.116.2. Active PortfolioActive Portfolio

RaRfSDp

7.931.3813.45

= (7.93-1.38)/13.45 = 0.48696.3. Passive PortfolioPassive Portfolio

RpRfSDp

-5.661.389.85

= (-5.66-1.38)/9.85 = -0.7146.4. Levered PortfolioLevered Portfolio

RLRfSDp

-14.941.3814.36

= (-14.94-1.38)/14.36 = -1.136

Ranking According to Sharpes Ratio

RankPortfolio

1Active

2Passive

3Levered

4Market

7. Tryenors Index Tryenors Excess Return to Relevant Risk RatioRp Rf / Where Rf is 1.38% for 9 weeks7.1. Market Portfolio (KSE-100 Index)Market Portfolio

RmRf

-7.951.381

= (-7.95-1.38)/1 = -9.337.2. Active PortfolioActive Portfolio

RaRf

7.931.381.21

= (7.93-1.38)/1.21 = 5.41

7.3. Passive PortfolioPassive Portfolio

RpRf

-5.661.381.61

= (--5.66-1.38)/1.61 = -4.377.4. Levered PortfolioLevered Portfolio

RLRf

-14.941.382.78

= (-14.94-1.38)/2.78 = -5.87

Ranking According to Tryenors Ratio

RankPortfolio

1Active

2Passive

3Levered

4Market

8. Differential CML

Differential CML = Rf +

Data For CML Calculation

Rf1.38

Rm-7.95

Ra7.93

Rp-5.66

RL-14.94

SDm4.42

SDa13.45

SDp9.85

SDL14.36

8.1. Market Portfolio= = -7.95Differential Return: -7.95 + 7.95 = 0%8.2. Active Portfolio= = -27.01Differential Return: 7.93- 27.01 = -19.08%

8.3. Passive Portfolio= = -19.41Differential Return: -5.6 + 19.41 = 13.81%8.4. Levered Portfolio= = -28.93%Differential Return: -14.94+28.93= 13.99%

9. Differential SML

= Rf + (Rm Rf) x p

Data For SML Calculation

Rf1.38

Rm-7.95

Ra7.93

Rp-5.66

RL-14.94

m1

A1.21

p1.61

L2.78

9.1. Market Portfolio

= 1.38 + (-7.95 1.38) x 1

= -7.95

Differential Return: -7.95 + 7.95= 0%9.2. Active Portfolio

= 1.38 + (-7.95 1.38) x 1.21

= -9.90

Differential Return: 7.93 - 9.90 = -1.97%

9.3. Passive Portfolio

= 1.38 + (-7.95 1.38) x 1.61

= -13.64

Differential Return: -5.66 + 13.64 = 7.98%

9.4. Levered Portfolio

= 1.38 + (-7.95 1.38) x 2.78

= -24.55

Differential Return: -14.94+ 24.55 = 9.61%

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market portfolio

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