Do a Series of Investments Outweigh Lump Sum Investments in KSE

8/9/2019 Do a Series of Investments Outweigh Lump Sum Investments in KSE

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This report is submitted in partialfulfillment of the requirements for

the degreeof

B.S. Actuarial Science and Risk

Management

Department of Statistics

University Of Karachi

DO

SERIES

OF

INVESTMENTS

OUTWEIGH

LUMP

SUM

INVESTMENTIN KARACHI STOCKEXCHANGE?

Submitted

Farheen Aqeeq Wasti


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ABSTRACT

This report is intended to introduce the concept and significance of

Investment through variable annuities in Karachi Stock Exchange. The

hypothesis following this study is, whether investment through

annuities offer improved returns than lump sum investment -- or not. It

is a widely experienced piece of evidence that investments returns in

equity markets customarily outperform risk-free investments by more

than 100% year by year. However, Underperformance of a single year

could change the directions of decade long investments into negative

zone. In order to minimize losses or to receive an early indication, an

algorithm has been designed in this report using index and volumes of

both,-- KSE All share index and KSE 100 indexas per requirement.

Data as, is the most pivotal ingredient of any research, KSE index data

has been used which is limited from year 1992 to 2008 and volumes

from December 2005 to June 2009,whereas data for all other indices is

from 1995 to 2008.


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Contents

Abstract

Table of Contents

1. Introduction 1

2. Models3

2.1 Methodology: Model 3

2.2 Strategy: Model 4

2.3 Product: Model 4

3. Analysis & Results 6

3.1 Analysis: Momentum 6

3.2 Analysis: Projections 6

3.3. Results 7

3.3.1 Comparison of Indices 7

3.3.2. Strategy 8

3.3.3 Product 8

3.4. Regulations 8

3.5 Conclusion 9


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Appendix : Tables and Charts 11

References and important websites 22

Endnotes 24


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1Introducti

on

Does a series of investments outweigh a lumpsum investment in Pakistan equity market:

Karachi Stock Exchange?

1.1 Introduction

The political driven financial drive-down that began in 2007 and

accelerated greatly in 2008, has posed a unique challenge for the

regulators of financial intermediaries. The rate of knots and severity of

the events that transpired have been quite a shock to the financial and

political system in Pakistan, and subsequently, to its markets. As

December 2008 closing level of KSE 100 describes steep loses from

index level 14077 of December 2007 to index leveled at 5865 of

December 2008 a decline of 58%. Much can be figured out from history

as right from its establishment, Pakistan inhabits a turmoil situation, a

few good years here and a few left some where are the ones on itsresume.

Stock exchange existed even before partition of sub-continent,

yet history and statistics demonstrate us that a very undersized group

of people including market makers, corporate sector and individuals

knows about it, so whether there is a gain or loss it is associated with

this small group. Financial disasters in stock exchanges arent the

newbie here but perceptibly their upshot on a country as whole is

negligible. Last three major calamities occurred in 1998, 2005 and

2008. Comparing these with USA and similar number of market

turnaround would be found, if not more, in the last decade but their

impact was substantial and hazardous. Therefore certainly, no market

is immune to crisis whether developed markets like in US or

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1Introducti

on

underdeveloped markets like in Pakistan, ( Our markets are driven by

political stability and there markets, actually driven by capital

stability).

Another crisis due, as soon we are out of current one. My

motivation behind this report is whenever next crisis happened, some

products, regulations, strategies should be in place which could

minimize individual loses.

As economic data suggests the need of derivatives, most of us

know how to trade derivatives but a very small group has information

about why we need derivatives. Even in that particular group not all

has information about several kinds of derivatives like Put and Call

options because our exchanges not started trading in them yet. One

important thing I like to mention, there are approximately 700

companies registered with Karachi Stock Exchange and probably 70

outperform market. So if an investor looks for places where he can put

his investment it has few choices to pick, than if investor wants tosafeguard his investment no options available other than future market

above all short selling is not an option. So, where to invest, in equity

directly or in mutual funds, both ways we dont have much space.

Smart investments not only certain where to invest but they also took

care how to invest to maximize profit or minimize loss. I intend to limit

this report on a subject how to invest further emphasize whether series

of investments provide better returns than lump sum investment. To

support my hypothesis I will use data of 4 indices DOW 30, S&P 500,

Nikkei 225 and FTSE 100 and later will compare them with KSE 100.

More precisely this report is about KSE so other indices are used for

data analysis only or anyway demonstrate any mutual or contrary

trends with Pakistan economy, KSE and its indices.

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3Analysis &Results

Annuities and Lump sum Investments

2.1 Methodology: Model

Series of payments could be termed as annuity, there are two

type of annuities fixed annuities and variable annuities. In fixed

annuities investors are protected and get fixed amount of returns no

matter how actual investment behaves. In variable annuities returns

are varied to profit gain on investment, here we are working on

variable monthly annuities having 2 time periods which are 5 years

and 10 years and their payouts are lump sum amount including returns

and principal at the end of each annuity.

Indices are benchmarks, which are Nikkei 225, S&P 500, DOW

30, FTSE 100 and KSE 100. Using monthly closings of above mentioned

indices calculated for period between years 1999 to 2008 for 5 years

annuity and time between years 1995 to 2008 for 10 years. In case of

KSE 100 index only, following time interval is used 1992 to 2008 for

both terms 5 and 10 years. Returns are calculated in between any two

time period which should be any two consecutive months through

simple difference formula, instead of log difference for no specific

reason.

Positive or negative returns are then added in current annuity

value, month by month basis. Annual returns are calculated using

Rateiii function: Rate function returns the interest rate per period of an

annuity. In summary (see table 1C and 1D) rate function being

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3Analysis &Results

changed to calculate annual returns, as it is known rate function

calculates period returns and in this case retuning a monthly value.

RATE(nper,pmt,pv,fv,type)

Lump sum investment could be termed as investment being

made at the beginning of any term and no further investment done

after that. For Lump sum investment, year end closings are used to

calculate annual returns over the same terms 5 and 10 years as used

in calculating annuities returns. Yearly returns are calculated through

simple difference equation. Returns then added to investment value

over year to year basis. Time interval as mentioned above in annuities

returns remains the same for all indices. Returns after expiring the

terms will be lump sum also.

2.2 Strategy: Model

It has been assumed that abnormal variation in volumes of KSE

All share index and KSE 100 index can be an indication that market

conditions will be more volatile in near future and consequently, will

generate steep losses. Availability of data restricts to calculate the

difference of volumes of KSE all share index over KSE 100 index from

November 2005 to latest. Besides, calculated standard deviation of

KSE 100 index where differences are over certain limits, difference

greater than 25% and difference greater than 35%, for minimum at

least 5 consecutive values. Different limits are used due to a trend

seen in KSE, high volumes till 2006 than gradually decreasing volume

with increasing index. Compare them with monthly and yearly

standard deviation of available data. Due to unavailability and

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3Analysis &Results

Analysis & Results Summary

3.1 Analysis: Momentum

Positive trend can be spotted out while analyzing data of KSE

100 index. Closing index of December 2008 was 5865 points, 58%

down from last year closing. Now stand at 7400s level up 26%. Major

rating agencies including Moodys and Fitch holds the current

investment rating for Pakistan which is only a step higher than

becoming a bankrupt not a preferable situation for foreign investors

looking for investment in current global financial crisis. Political

government is more stable than 6 months before. Budget deficits and

BOP could be made through IMF and other made arrangements. About

6 month before to insure 5 years short term loans to Pakistan it cost

34% while now down to 22% but well above 2.5% level of January2007. Since 1997 the time span in negative trend in KSE remains for 1

year only, happened in 1998, 2001 and 2008. Energy crisis could be

resolved or contained in the end of 2009. Volumes in KSE are back in

normal condition but in low side, average trading in 1st 6 months of

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3Analysis &Results

2009 in KSE was 163 million, while last 6 months and 1st 6 month of

year 2008 record 38 million and 220 million shares respectively.

Global recession will further ease commodities prices especially wheat

and oil, which will lower inflation. Most important P.E ratio is 6-8 times

of companies trading in KSE 100 which is down from 10-14 level back

in 2007-2008.

3.2 Analysis: Projections

Using forecast function KSE projected to gain 28% from last year

closing. Current gain also demonstrate same positive trend but much

better. There is a trend forming since 1994 after every six years KSE

returns positive or negative single digit growth first happened in 1994

than in 2000 than in 2006 and next term is due in 2012 which is also a

election campaign year. Rest of the years remain in double digit

territory with most gain in 2002 of 112% and losses of 2008 returns

negative 58% remain on top on other side. Average return from 1992is 17%, for last 10 years its 30% and for last 5 years its 16%.

3.3 Results

3.3.1Comparison of indices

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3Analysis &Results

Based on our findings, both 10 years and 5 years results exhibit

KSE 100 annuity returns are better than lump sum investment;

average gain of annuity to annuity over lump sum investment in 5 and

10 years are 220% and 56% respectively. 5-year values upholds much

deviation from mean therefore, if one value from each of the extremes

is skipped over, then average annuity gain over lump sum investment

will trim down to 14.5%. It is also noted that FTSE 100 follows S&P 500

and DOW 30, premium over risk free rate of equity investment is

adequate, DOW 30 results better returns than both of other

exchanges, Nikkei 225 still is in restructuring phase after the financial

melt down of 80s and that is the reason it doesnt follow the North

American exchanges as FTSE does. In case of FTSE 100, S&P 500 and

DOW 30 lump sum investment returns are better than annuity returns.

While Nikkei 225 and KSE 100 produces a trend where annuity returns

are superior to lump sum investment, initiating from 1995 Nikkei 225

dropped down almost 55% of its value yearly return of (5.5) %, S&P

500 reaped 96% with a yearly return of 4.9%; DOW 30 achieved 130%with a return of 6% yearly; FTSE 100 gained 43% of its value with

yearly returns of 2.6%.As for KSE 100 index, it raised up to 250% of its

value and yielding returns of 7.6% annually over a time horizon of 17

years-- from 1992 to 2008. In 2008 Nikkei 225, S&P 500, DOW 30, FTSE

100 and KSE 100 lost (42%), (38%), (34%), (32) and (58%) of there

value respectively from year 2007.

KSE 100 performed exceptionally better in case of returns as it is

shown (See table 1C and table 1D) for 10 years annuity in contrast to

lump sum investment not any single term in either format of any

equity market indices including DOW 30, Nikkei 225, S&P 500 and FTSE

100 performed better than KSE 100. In case of 5 years annuities the

last term from years 2004-2008 annuity returns of KSE 100 remain the

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3Analysis &Results

lowest among all indices but lump sum investment still remains on top.

We also know that one factor producing high returns as our risk free

rate is much higher than other markets. If we add Inflation variable or

associate index value with US dollars than market returns may decline

further.

3.3.2Strategy

In strategy model, the differences in volumes of KSE all share

index and KSE 100 may amplify the volatility. Finding of analysis

cannot be deduced as data integrity is a subject to qualm as it is

insufficient. More specific results could be concluded in future if lack of

data problem gets resolved. Though volatility did increase several

times after a period of increased differences in volumes but volatility

remains low while we are in the period. Steep decline in December

2008 also couldnt help our results because decline was imminent due

to lower cap in index. Even before it started political uncertainty,

security situation and global financial crisis should drag down theindex.

3.3.3Product

Limited availability of data starting from year 1992, being a

major reason, product analysis on returns can be executed on 5 years

annuities only. Analysis shows losses could be minimized while

applying given approach, as losses distributed to other annuities and

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3Analysis &Results

investor may outgain losses by other annuities as it is happened in 7

out of 9 observations in table 2A.

3.4 Regulations

The regulatory authority over Karachi Stock Exchange

(Guarantee Ltd.) is SECP. Foreign investment in KSE approximately

worth 500 million US Dollari in 2008 with market capital over 50 billion

US Dollars, which now stand at 27 billion US Dollar. None of any single

foreign investment company relies heavily on KSE on its portfolio

returns. Loses or gain in KSE doesnt greatly effect their earnings. So

whenever rating agencies downgrade Pakistan rating not necessarily

due to financial crisis mostly because of instability in government to

run the system. These foreign investment companies quickly unload

their portfolios having KSE securities because they dont want to risk

their own rating downgrades from these agencies for having low level

securities. So in my proposal SECP should regulate these foreign

investments by not allowing bias investment directly related with

rating agencies. If its a financial sector to blame for rating downgrade,

if equity not performing well they can offload their portfolios but due to

rating downgrade from international rating agencies which may not

effect equities in KSE All Share they should hold their investments a

quarter or two. There should be a cool down period for all investment

funds, financial investment firms both local and international.

3.5 Conclusion

Revealed in table 1A-- 7 out of 8 terms of 10 years disclose

improved returns than those of lump sum investment. On run of the

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3Analysis &Results

mill, returns from annuity investments are 56% elevated than lump

sum investment over the years 1992 to 2008. Highest returns on

annuity and lump sum investment in years 1998-2007 are 34% and

23% respectively, is displayed whilst, investment losses with its

maximum amount in years 1992-2001 which are (2%) for annuities and

(3%) for lump sum investment is shown. Short term investment may

present higher returns in lump sum investment as it is determined by

several observations in 5-year investment plan, due to a incessant

positive growth years from 2002 to 2007, however, we also

experienced huge fall off in short term investments divergent to long

term investments as extreme losses show decline in portfolio (20%)

and (15%) in years 1994-1998 for annuities and lump sum investments

respectively. In case of equity investment, pension & retirement funds,

private investors and all other kinds of long term investments should

be invested in annuities to achieve higher returns.

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Reference

Appendix: Tables and ChartsTable 1A: 10 years annuities & lump sum investment

returns

Term 92-01 KSE MonthlyAnnuity 1200000 1064835 -0.02389585

KSE Yearly 1200000 906355 -0.027674426

Term 93-02 KSE MonthlyAnnuity 1200000 2197671 0.116386859

KSE Yearly 1200000 2606469 0.080655161

Term 94-03 KSE Monthly

Annuity 1200000 3384473 0.196820081KSE Yearly 1200000 2479332 0.07526459


KSE Yearly 1200000 3641620 0.117406872


KSE Yearly 1200000 7656722 0.203611042




KSE Yearly 1200000 9631884 0.231552697


KSE Yearly 1200000 7445740 0.200252618

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Reference

Table 1B: 5 years annuities & lump sum investmentreturns


KSE Yearly 600000 476982 -0.04485315


KSE Yearly 600000 846091 0.071157086Term 94-98 KSE MonthlyAnnuity 600000 358099 -0.200110945

KSE Yearly 600000 262049 -0.152682353


KSE Yearly 600000 412543 -0.072180289


KSE Yearly 600000 603937 0.001308902


KSE Yearly 600000 570056 -0.01018677


KSE Yearly 600000 924180 0.090237367


KSE Yearly 600000 2838390 0.364533378

Term 2000-04 KSE MonthlyAnnuity 600000 1813196 0.459614124KSE Yearly 600000 2648174 0.345733468


KSE Yearly 600000 3803398 0.446785357

Term 2002-06

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Reference

KSE MonthlyAnnuity 600000 1550357 0.390804086

KSE Yearly 600000 4732141 0.511406499



Term 2004-08 KSE MonthlyAnnuity 600000 414260 -0.144113812KSE Yearly 600000 786967 0.055749913

Table 1C: 10 years annuities & lump sum investmentreturns

Term 92-01

KSE MonthlyAnnuity 1200000 1064835

-0.0238958

5

KSE Yearly 1200000 906355

-0.0276744

26

Term 93-02 KSE MonthlyAnnuity 1200000 2197671

0.116386859

KSE Yearly 1200000 26064690.0806551

61


0.196820081

KSE Yearly 1200000 24793320.0752645

9

Term 95-04

IndexTotal Investment(Rs.)

End Term Total Amnt(Rs.)

TotalReturn %

NIKKEI MonthlyAnnuity 1200000 1001498

-0.0363198

52

NIKKEI Yearly 1200000 699006

-0.0526074

49

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Reference

S&P MonthlyAnnuity 1200000 1565919

0.051978746

S&P Yearly 1200000 31665550.1018959

3

DOW MonthlyAnnuity 1200000 1641248

0.061008411

DOW Yearly 1200000 33745760.1089291

42

FTSE MonthlyAnnuity 1200000 1242522

0.00689143

FTSE Yearly 1200000 18845730.0461721

92


0.250453302

KSE Yearly 1200000 36416200.1174068

72

Term 96-05

IndexTotal Investment

(Rs.)End Term Total Amnt

(Rs.)Total

Return %


0.037303096


-0.0207400

8

S&P MonthlyAnnuity 1200000 1454605 0.037726752

S&P Yearly 1200000 24320100.0731944

33


0.038537171

DOW Yearly 1200000 25133270.0767299

04


0.027194842

FTSE Yearly 1200000 1827598 0.0429655


0.315179622

KSE Yearly 1200000 76567220.2036110

42

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Reference

Table 1C: 10 years annuities & lump sum investment

returns

Term 97-06



(Rs.)Total

Return %NIKKEI MonthlyAnnuity 1200000 1581284

0.05385846


-0.0116171

22


0.047061827

S&P Yearly 1200000 22976480.0671125

44


0.052008016

DOW Yearly 1200000 23193470.0681160

68


0.038572345

FTSE Yearly 1200000 18184290.0424410

63


0.304983685

KSE Yearly 1200000 89919620.2231150

83

Term 98-07



(Rs.)Total

Return %

NIKKEI Monthly

Annuity 1200000 1413348

0.0321369

21

NIKKEI Yearly 1200000 12038360.0003192

08


0.042736798

S&P Yearly 1200000 18157220.0422857

76

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Reference


0.052424152

DOW Yearly 1200000 20128070.0530817

56


0.039529168

FTSE Yearly 1200000 15134410.0234777

95


0.347272285

KSE Yearly 1200000 96318840.2315526

97

Term 99-08



(Rs.)Total

Return %


-0.0737575

1


-0.0436413

99


-0.0573815

15

S&P Yearly 1200000 881771

-0.0303445

19


-0.0353547

98

DOW Yearly 1200000 1147061

-0.0045016

91


-0.0369812

75

FTSE Yearly 1200000 896069

-0.0287835

7

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Reference


0.150090056

KSE Yearly 1200000 74457400.2002526

18

Table 1D: 5 years annuities & lump sum investmentreturns

Term 92-96


-

0.058148608

KSE Yearly 600000 476982

-0.0448531

5


0.030611724

KSE Yearly 600000 846091 0.0711570

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Reference

86

Term 94-98


-0.2001109

45

KSE Yearly 600000 262049

-0.1526823

53


0.009114457

KSE Yearly 600000 412543

-0.0721802

89


0.038741411

KSE Yearly 600000 603937 0.001308902

Term 97-01


-0.0177711

58

KSE Yearly 600000 570056

-0.0101867

7


0.280903216

KSE Yearly 600000 924180

0.0902373

67Term 99-03


End Term TotalAmount (Rs.)

TotalReturn %


-0.0504895

69


-0.0506070

99

S&P Monthly

Annuity 600000 582308

-0.0117634

25

S&P Yearly 600000 542739

-0.0198603

55


0.02622457

DOW Yearly 600000 6831560.0262985

78

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Reference


-0.0572973

48

FTSE Yearly 600000 456624

-

0.053149317


0.428626075

KSE Yearly 600000 28383900.3645333

78


Term 00-04


End Term Total Amnt(Rs.)

TotalReturn %


0.004581052


-0.0950916

8


0.033284982

S&P Yearly 600000 494913

-0.0377774

68


0.038076778

DOW Yearly 600000 562732

-0.0127433

4


-0.0045184

58


-0.0702688

63


0.459614124

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Reference

KSE Yearly 600000 26481740.3457334

68

Term 01-05


(Rs.)End Term TotalAmount (Rs.)

TotalReturn %


0.161256239

NIKKEI Yearly 600000 7012240.0316707

18


0.056450242

S&P Yearly 600000 567284

-0.0111512

77


0.037056556

DOW Yearly 600000 596079

-0.0013104

3


0.071899579


-0.0202040

81


0.550993421

KSE Yearly 600000 3803398 0.446785357

Term 02-06



TotalReturn %


0.169688443

NIKKEI Yearly 600000 9803530.1031796

61


0.101313737

S&P Yearly 600000 741220

0.0431798

17DOW MonthlyAnnuity 600000 751392

0.089295277

DOW Yearly 600000 7461790.0445719

38


0.110608943

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Reference

FTSE Yearly 600000 7177130.0364775

8



0.390804086

KSE Yearly 600000 47321410.5114064

99

Term 03-07



TotalReturn %


0.083624784

NIKKEI Yearly 600000 10706050.1227824

18


0.085740464

S&P Yearly 600000 10013590.1078672

16


0.087994667

DOW Yearly 600000 9541170.0972108

07


0.101716646

FTSE Yearly 600000 9862290.1044989

41


0.339332194

KSE Yearly 600000 31266240.3911849

84

Term 04-08



(Rs.)Total

Return %


-0.1596255

84


-0.0366249

74

S&P MonthlyAnnuity

600000 430813 -0.1290014

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Reference

49

S&P Yearly 600000 487400

-0.0407167

64


-0.0970561

7

DOW Yearly 600000 503718

-0.0343777

95


-0.0794052

02


-0.0037913

06


-0.1441138

12

KSE Yearly 600000 7869670.0557499

13

Table 2A: 9 years annuities plan consisting of 5 years annuities

1992-2000

1995-2003

1998-2006

112000

12000 1

12000

12000 1

12000

12000

224000

36000 2

24000

36000 2

24000

36000

3

360

00

7200

0 3

360

00

7200

0 3

360

00

7200

0

448000

120000 4

48000

120000 4

48000

120000

560000

180000

-0.058

15 5600

001800

000.009

11 560000

180000

0.28090

448000

228000

0.03061 4

48000

228000

0.03874 4

48000

228000

0.42863

3 36000

264000

-0.200

3 36000

264000

-0.017

3 36000

264000

0.45961

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Reference

11 77

224000

288000

0.00911 2

24000

288000

0.28090 2

24000

288000

0.55099

112000

300000

0.03874 1

12000

300000

0.42863 1

12000

300000

0.39080

1993-2001

-0.035

961996-2004

0.14792

1999-2007

0.42219

112000

12000 1

12000

12000 1

12000

12000

224000

36000 2

24000

36000 2

24000

36000

336000

72000 3

36000

72000 3

36000

72000

448000

120000 4

48000

120000 4

48000

120000

560000

180000

0.03061 5

60000

180000

0.03874 5

60000

180000

0.42863

448000

228000

-0.200

11 4480

002280

00

-0.017

77 448000

228000

0.45961

336000

264000

0.00911 3

36000

264000

0.28090 3

36000

264000

0.55099

224000

288000

0.03874 2

24000

288000

0.42863 2

24000

288000

0.39080

112000

300000

-0.017

77 1120

003000

000.459

61 112000

300000

0.33933

1994-2002

-0.027

881997-2005

0.23802

2000-2008

0.43387

112000

12000 1

12000

12000 1

12000

12000

224000

36000 2

24000

36000 2

24000

36000

336000

72000 3

36000

72000 3

36000

72000

448000

120000 4

48000

120000 4

48000

120000

560000

180000

-0.200

11 5600

001800

00

-0.017

77 560000

180000

0.45961

4

480

00

2280

00

0.009

11 4

480

00

2280

00

0.280

90 4

480

00

2280

00

0.550

99

336000

264000

0.03874 3

36000

264000

0.42863 3

36000

264000

0.39080

224000

288000

-0.017

77 2240

002880

000.459

61 224000

288000

0.33933

112000

300000

0.28090 1

12000

300000

0.55099 1

12000

300000

-0.144

110.022 0.340 0.319

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Reference

18 47 33

Table 2B: 19 years annuities plan consisting of 10years annuities

1992-2000

1992 1 12000 12000

1993 2 24000 36000

1994 3 36000 72000

1995 4 48000

12000

0

1996 5 6000018000

0

1997 6 7200025200

0

1998 7 8400033600

0

1999 8 9600043200

0

2000 910800

054000

0

2001 1012000

066000

0-

0.0239

2002 910800

076800

00.1163

87

2003 8 9600086400

00.1968

2

2004 7 8400094800

00.2504

53

2005 6 7200010200

000.3151

8

2006 5 6000010800

000.3049

84

2007 4 4800011280

000.3472

72

2008 3 3600011640

000.1500

9

2009 2 2400011880

00

2010 1 1200012000

00Avera

ge

Note:Incomplete data, period returns could be calculated if data was available prior to 1990 or will

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Reference

be calculated after

2010 retrns.

Chart 1A Abbreviations

KSE Karachi stock exchangeKSE All share Index comprise of all companies listed in KSE

KSE 100 Index comprise of top 100 companies listed in KSE sorted by market

capitalKSE 30 Index comprise of top 30 companies listed in KSE sorted by their floating

share capital

SECP Security exchange commission of PakistanSBP State bank of Pakistan

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Reference

References

Annual Report 2007-2008 (Volume I & II) SBP

The State of Pakistans Economy Quarterly Reports(2007, 2008 & 2009) SBP

Handbook of Statistics on Pakistan Economy 2005 SBP

Financial Markets Review SBP

Financial Stability Review 2007-2008 SBP

International Energy Outlook 2009 Energy Information Administration (EIA)

Prospects for the Global Economy www.worldbank.org/globaloutlook

The Theory of Interest 2nd Edition by Stephen G Kellison

The Handbook of Fixed Income Securities 7th Edition by Frank Fabozzi

Fixed Income Securities 2nd Edition by Bruce Tuckman

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Reference

References and websites

KSE www.kse.com.pk

SBP www.sbp.org.pk

SECP www.secp.gov.pk

Ministry of Finance www.finance.gov.pk

Business Recorder www.brecorder.com

Yahoo Finance finance.yahoo.com

Variable Annuities www.sec.gov/investor/pubs/varannty.htm

Bloomberg News www.bloomberg.com

Forbes www.forbes.com

Resource www.wikipedia.org

Investors guide www.investopedia.com

New York Stock Exchange www.nyse.com

NASDAQ Stock Market www.nasdaq.com

Tokyo Stock Exchange www.tse.or.jp/english/

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Reference

FTSE The Index Company www.ftse.com

CIA- The World Fact book www.cia.gov/library/publications/the-world-factbook/

World Economic Data www.imf.org/external/data.htm

Energy Information www.eia.doe.gov

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Endnotes

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i SBP economic report, CIA-The world fact book and other economic reportsii The theory of interest chapter 3 Basic annuities 2nd edition by Stephen G Kellisoniii For rate and forecast functions see Microsoft Office Excel help

Documents

Do a Series of Investments Outweigh Lump Sum Investments in KSE