Portfolio Construction 170

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PORTFOLIO CONSTRUCTION USING TEN

SECURITIES

DATE OF SUBMISSION: 16 MARCH, 2011



ToDr. Mahmood Osman ImamProfessorDepartment of FinanceUniversity of Dhaka

Subject: Submission of report on “optimum portfolio construction”

Dear Sir,

Here is a report on “Submission of report on “efficient portfolio construction. In this report i

have included the various tools and techniques to find out efficient portfolio and optimum

weiht allocated to each securit! to find out efficient portfolio.

I ac"nowlede the contributions to our course teacher for the uidance he rendered. I havetried to use m! academic "nowlede on real life.

I am pleased to be ranted this vital opportunit! and rateful for !our versatile assistance. Ihope that m! wor" will please !ou .I shall be available in the presentation for further

e#planations.

Sincerel!,

$aslima %"tar

&inance '(th batch

Department of finance

)niversit! of Dha"a

*nclosure:

$he +eport

3



*#ecutive Summar!:

e were assined to ma"e a report on portfolio construction. &or this purpose we

collected data from DS*. e "now, portfolio is the combination of securities of an

individual. the oals of investment var! with man to man, institutions to institutions based on their financial conditions, economic stabilit!, and ris" tolerance, need of

income stream, ae, and job status. +eardless of the ultimate oal, all face the same

set of challenes that e#tend be!ond just the choice of what asset classes to invest in.

Here our main objective is to find out optimum portfolio converence with individual

and institutions investment polic! objectives. -! portfolio approach I mean evaluatin

individual securities in relation to their contribution to the investment characteristics

of the whole portfolio.

Here we have ta"en ' companies that are listed in Dha"a stoc" e#chane from

different industries. e want to ma#imi/e the theta and want to minimi/e ris". e use

solver function throuh e#cel wor"sheet to find out portfolio weiht to be complied

with iven si# situation. $hese are,

'. 0a#imi/in $heta allowin short sell

1. 0a#imi/in $heta b! not allowin short sell

(. 0inimi/in +is" 2Standard Deviation3 b! allowin short sell

4. 0inimi/in +is" 2Standard Deviation3 b! not allowin short sell

5. 0inimi/in +is" 2Standard Deviation3 b! allowin short sell for a iven return

6. 0inimi/in +is" 2Standard Deviation3 b! not allowin short sell for a iven

return

%fter doin different mathematical and statistical tools and techniques finall! I et

that portfolio weiht for each situation. Here I have seen that if short sellin is allowed

individual can et hihest theta with minimum ris" than that of an! other

combinations

4



point of tan#ency is kno$n as optim!m or efficient portfolio.

There are many factors that $ork ehind the determination of portfolio.

(!ch as economic condition inside information the investors o5ective

and constraints risk tolerance etc. 6ere $e have tried to create a portfolio

on the asis of the Market Price Data and the Dividend ad5!stments. %e

have collected last 0 years data from D(,.

1. Planning process: Here I am iven different objectives to find out the optimal portfolio

construction.

2. A""#$ %&&'(%$)'*: 6ere I oserve the risk and ret!rn characteristics of

the availale investments. 6ere I analy7e f!ndamental and technicalanalysis to find o!t the est performin# ind!stry and from those I have

8



chosen the individ!al companies. 6ere I try to follo$ one famo!s ma9im

that don:t p!t yo!r all e##s in one asket.

S#&#($)'* '+ %""#$:

To diversify the risk it is etter to invest in different types of asset. That is$hy I have selected companies in different ind!stries or asset class. (!ch

as;

)ank

+ement

+hemical

on ankin# financial instit!tions )FI/

,n#ineerin#

Pharmace!ticals

Te9tile.

I have selected the companies $hich are<

listed in D(,

listed on or efore = >an!ary 2??8

@": +ate#ory sec!rities.

S#&#($# ('%*)#":

=. ") )ank2. Uttara )ank3. "ramit +ement4. I+)

0. Midas finance8. Aohinoor chemicalB. &on#p!r Fo!ndaryC. (!are pharma

E. (!are te9tile

=?. )e9imco te9tile

B



6ere I have chosen B ind!stries to #et the enefit of diversification and

optimi7e the ret!rn. 7ow I would li"e to describe what companies I have selected from

each industr!.

B%*/:

The total stock e9chan#e pe ratio is =B.=E $here the ank ind!stry:s pe

m!ltiple is only ==.8C $hich is the lo$est amon# all ind!stries. That

means i can cover or #et my principle investment $ithin ==.8C years if I

invest in ankin# ind!stry and $hich is l!crative also. Moreover there is

hi#h #ro$th potential for the ankin# ind!stry and here there is no threat

of entry as #overnment imposes restriction !pon ne$ entry.

N'* B%*/ +)*%*()%& )*"$)$$)'*":

onank financial instit!tions are most promisin# sector of )an#ladesh.

"s )an#ladesh is a developin# co!ntry there are potential chances for

#ro$th of these instit!tions. Increasin# importance of merchant ankin#

#oin# p!lic and risin# of p!lic conscio!sness leads to hi#h #ro$th of

this sector.

T#$)&#" )*"$3:

"s the te9tile ind!stry is the key of o!r economy the attraction of

investors are increasin# day y day to$ards the ind!stry. %e invest here

in the lon# r!n $e can e9pect a handsome ret!rn from it.

P%%(#$)(%&" I*"$3:

Pharmace!ticals companies are prod!cin# inelastic #oods $hich are also

the important contri!tor to o!r economy as $e e9port dr!#s thro!#ho!tthe $orld. Moreover the rep!tations and profitaility and class of

e9chan#e are 'ood compare to other ind!stries.

C##*$ I*"$)#"

In the recent trend of &eal ,state (ector )oom and the Infrastr!ct!ral

improvement in )an#ladesh the +ement Ind!stry is doin# $ell in their

!siness. "mon# the profit makers "&"MIT is one of the common names.

The face val!e is Tk. =?? $hich is c!rrently ein# traded at Tk. 1,591.00.

C



P'$+'&)' ('*"$($)'*

First of all I have collected past 0 years price data and dividend data of

the selected companies. "fter p!ttin# those data on e9cel sheet #athered

monthly closin# price of each companies from the year 2??8<2?=? and

ad5!sted those price $ith the dividend paid d!rin# the month.

") )"A

N+-(P&+

cashdivG

+ash

Div"mo!nt

+ash

Div"d5!sted Price )&

no. ofshares

S$'(/D)5

A"$#P)(#

1 370.25 ? 3B?.20 = 3B?.20

2 326.25 ? 328.20 = 328.20

3 324.25 ? 324.20 = 324.20

4 273.25 ? 2B3.20=?G =.=

3??.0B0

5 351.50 ? 30=.0? = 30=.0

6 364.25 ? 384.20 = 384.20

Then $e calc!lated ret!rn of each companies from fer!ary 2??8 to

decemer 2?=?. %e !sed the form!la to calc!late the monthly ret!rn +

8 972t;t<'3

$hen I calculated meanreturn b! addin return of

5= months and dividin b!

5=. I calculated mean return

for each compan!. $hus I

ot ' mean returns.

R)"/ +## %$#:

EF)# 1: #$* (%&(&%$)'*



F)# 2: )"/ +## #$* (%&(&%$)'*

To #et risk free rate I take )an#ladesh ank Treas!ry ill rate for five

years and then $e ad5!st the price y m!ltiplyin# each rate y t$elve anddivide the res!lt y t$elve and for the year 2??8 I divide the $hole y ==

eca!se for the first year I #ot == moths )an#ladesh ank treas!ry rate.

Then y avera#in# I finally #et the avera#e risk free rate if return. that is .46>5.

E(#"" R#$*:

$hen I calculated *#cess return b! subtractin ris" free return from 0ean return. $he

equation is, *#cess +eturn 8 +m <+f ʹ

=?



F)# !: #(#"" #$* (%&(&%$)'

V%)%*(# C'5%)%*(# M%$):$hen I calculated ?ariance and covariance of each compan! usin ?%+ and @A?%+

function.

F)# 4: ('5%)%*(# #$#)*%$)'*

Here I put equal weiht on each securit!, which is 'B. $hat means I invest 'B of m! asset

on ever! securities irrespectivel!.

==



E(#"" P'$+'&)' R#$*:

$hen @alculated *#cess portfolio returns b! multipl!in each e#cess return with respective

weiht and addin all.

F)# 8: '$+'&)' #$* (%&(&%$)'*

P'$+'&)' V%)%*(#:

$hen I calculated the portfolio variance Hp usin the theor! of matri# .e "now in

variance we need to multipl! individual variance covariance with weiht square. So,

m! multiplication was li"e followin<

Hp 8 C',1,(,4,..,'E

F F

=2

H=H=2H=3

JJJJJJH==?

H=2H2 H23

JJJJJJJH2=? H=3

H23 H3

JJJJJJH3=?

.

.

.

.

.

..

.

.

.

.

.

H==? H2=? H3=?

%=

%2

%3

%4

%0

%8

%B

%C

%E

%=?



P'$+'&)' S$%*% D#5)%$)'*:

e "now portfolio standard deviation Hp is the square root of standard deviation.

$hatGs wh! we calculated the square root of the portfolio standard deviation.

F)# 6: "$%*% #5)%$)'* (%&(&%$)'*

T#$% C%&(&%$)'*:

7e#t I calculated the theta. e "now<

8 2+m +f3;Ɵ ʹ Hp

*#cess +eturn 8 +m +f ʹ

So, 8 *#cess +eturn ;Ɵ Hp

F)# 7: THETA CALCULATION

U"# '+ "'&5# +*($)'*:

Finally I !sed the solver f!nction to find the optim!m $ei#ht for

follo$in# si9 sit!ations. The sit!ations are<

=3



B. Ma9imi7in# Theta allo$in# short sell

C. Ma9imi7in# Theta y not allo$in# short sell

E. Minimi7in# &isk (tandard Deviation/ y allo$in# short sell

=?. Minimi7in# &isk (tandard Deviation/ y not allo$in#

short sell

==. Minimi7in# &isk (tandard Deviation/ y allo$in# short

sell for a #iven ret!rn

=2. Minimi7in# &isk (tandard Deviation/ y not allo$in#

short sell for a #iven ret!rn

These sit!ations are descried elo$<

M%))9)* T#$% 3 *'$ %&&';)* "'$ "#&&:

In this sit!ation I ma9imi7ed theta y not allo$in# short sell. In this

sit!ations the constrains are<

=. K%i L =

2. %i L ?

=4



F)# <: MA=IMI>ING THETA BY NOT ALLO?ING SHORT SELL

6ere my findin#s are<

(o I don:t need to invest in ") )ank UTT"&" )ank

),1T,1 "D (!are pharma. 6ere my theta $ill e 3CG.

M%))9)* T#$% %&&';)* "'$ "#&&:"llo$in# short sell means the investor can sell certain sec!rity of

others in an e9pectation that the price $ill #o do$n in near f!t!re

then the investor $ill !y ack the sec!rity and ret!rn to the real

o$ner. In first sit!ation I allo$ed short sale. The only constraint $as<

=.K%i L =

=0



F)# @: %))9)* $#$% 3 %&&';)* "'$ "#&&

My findin#s is I have to short sell<

In Uttara ank =2G ),1T,1 y =CG (!are Pharma y 20G.

I sho!ld invest all of my investment in other sec!rities. "t this option

I $ill #et ma9im!m theta of 42G.

M)*))9)* R)"/ S$%*% D#5)%$)'* 3 *'$ %&&';)* "'$"#&&:

Then I tried to find the $ei#hts in $hich risk $ill e minim!m. I have not

allo$ed short sell. +onstraints are<

=. K%i L =

2. %i L ?

=8



F)# 10: )*))9)* "$%*% #5)%$)'* 3 *'$ %&&';)* "'$"#&&

6ere my findin#s are<

I don:t need to invest in Uttara )ank "&"MIT +ement ),1T,1

I+).

Th!s my standard deviation $ill e minim!m.

M)*))9)* R)"/ S$%*% D#5)%$)'* 3 %&&';)* "'$ "#&&: Then I allo$ed short sell to #et the $ei#ht at minim!m risk. The only

constraint is

=. K%i L =

=B



"ll my investment sho!ld e in other companies.

M)*))9)* R)"/ S$%*% D#5)%$)'* 3 %&&';)* "'$ "#&&

+' % )5#* #$*:

Then I considered a sit!ation in $hich I can earn a monthly ret!rn of 3.0G

and my risk $ill e minim!m. I have also allo$ed short sell. My only

constraint is<

=. K%i L =

F)# 12: )*))9)* )"/ 3 %&&';)* "'$ "#&&

From the !pper tale $e #et information that to #ain a CG ret!rn I

can short sell decision for Uttara ank "&"MIT ),1T,1 and I+) atminim!m risk level of 8.40G.

=E



@onclusion:

&rom above calculation I have shown that b! allocatin different weihts to

different securities the investor can ma#imi/e his return. He can also "eep his

ris" at desire level as well as he can achieve e#pected return. Here I have show

that if short sellin is possible the theta and return can be ma#imi/ed than if

short sellin is not allowed. -ut there is also disadvantae of short sellin that

is when mar"et falls , short sellin mechanism creates pressure to price fall

which is not e#pected for share mar"et. $hatGs wh! in -anladesh short sell is

not allowed.

2?



"ppendi9

2=

Portfolio Construction 170

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