Modern Port Folio Theory

7/31/2019 Modern Port Folio Theory

1/49

Modern portfolio theory


2/49

MPT postulates that savers aregenerally risk averse and try toreduce risk by all possible methods

The markets are perfect and absorball information perfectly and returnsare the same whenever you enter

the marketThe principle of dominance is

applied to select a portfolio on the

frontier line


3/49

Basis of modern portfolio theory The tripod on which this theory depends

are:

A Diversification Investment in morethan one security ,asset ,industry etcwith a view to reduce risks

B CAPM theory and concept ofDominance

C Role of beta it is a measure ofsensitivity ofthe return of one asset to the market

return


4/49

Modern portfolio theory postulates thefollowing axioms

1. Diversification reduces the total risk butapplicable only to co specific unsystematic risk

2. CAPM states that where shares are correctlypriced every security is expected to earnreturns commensurate with the risk it carries

3. The riskiness of a security is to be seen inthe context of portfolio or market related risk,but not in isolation

4. The importance of Beta is for managing nondiversifiable part of the risk


5/49

Asset allocation decision

Investors data base is the starting pointfor designing an investment strategy

Factors for investment strategy:

Need for regular income

Regularity - monthly or yearlyNeed for cash inflow to meet the

liabilities

Asset liability mix or inflow outflow

patternNeed for capital appreciation or a

mixture of both income and capitalappreciation


6/49

Investors objective can be set of as:

Income

GrowthBoth


7/49

The following major asset classesare used for in the portfolios

A) Equities (variable incomeinstruments)

B) Debenturess,Bonds (Fixedincome instruments)

C)Cash and money marketinstruments (Short durationinstruments)


8/49

Every investor should allocatetowards cash outfows in the formof:

administrative expenses

Salaries

Wages

Stationery

Incidental expenses


9/49

5 to 10 % of investment needs to bekept in :

Cash

Bank deposits

Money market instruments


10/49

The proportion in equity anddebentures would depend upon thespecific objective of invetment

Income

Growth

Mixture of both


11/49

DIVERSIFICATION

The traditional theory lays down thatdiversification as a technique ofselection of securities in a portfolio

This is called random diversifiaction orsimple diversification

It is based on a simple rule of two isbetter than one

Simple diversification was found to bemore remunerative


12/49

Nave diversification or superfluousdiversification may result from random andindiscriminate selection of securities ,whichdoes not lead to any reduction of risk

Thus an investor may have 10 scrips insteel,mini steel and ferrous metals,which willonly increase risk

But an investor having 10 scrips spread incycles,electronics,sugar,steel,auto etc,will have

less risk as these industries are not co relatedand their risks are independent of each other oreven negatively related.


13/49

Why diversification

It is never prudent to put all oneseggs in one basket,as it may lead tototal ruin if the basket itself is

broken or lostThe human behaviour is normally

risk averse


14/49

Diversification is a technique ofreducing the risk involved in investmentand portfolio management

It is a process of conscious selection ofassets ,instruments and scrips of cosand govt securities ,in a manner thattotal risks are brought down

This process helps in the reduction ofrisk ,under category of what is known asunsystematic risk and promotesoptimisation of returns


15/49

Forms of diversification:

Types of asets:gold,real estate,govtsecurities ,corporate securities

Instrumentsor security typebonds,debentures stocks

Industry lines:plastics ,chemicals

,engineeringCompanies:new cos,growing

cos,new product cos


16/49

Principles of diversification:

A single co/industry is more risky thantwo cos/industries

Two cos in say,steel industry are morerisky than one co in tyre and tubes andone co in steel

Two cos or two industries which aresimilar in nature of demand or marketare more risky than the two in dissimilarindustry.


17/49

Methods of diversification

Randomness of selection of cos andindustries: the probability of reducingrisk is more with a random selection asthe statistical error of choosing wrong

cos will come down due to randomnessof selection which is a statisticaltechnique

Optimisation of selection process

Adequate diversification: this involvesas many industries and cos as possibleto get the best results


18/49

Markowitz diversification

He postulated that diversificationshould not only aim at reducingrisk of a security by reducing its

variability and standarddeviation,but by reducing the covariance or interactive risk of twoor more securities

The theory attaches importance tostandard deviation ,to reduce it tozero and co variance


19/49

Assumptions of markowitz theory: Investors are rational and behave in a manner

as to maximise their utility with a given level ogincome or money

Investors have free access to fair and correctinformation

The markets are efficient and absorbinformation quickly

Investors are risk averse and try to maximiserisk and return

Investors prefer higher returns to lower return

for a given level of risk


20/49

Guidelines for diversification diversification involve s a proper no of

securities ,not too few or many which have noco relation

To build up a efficient port folio the followingparameters are to be seen

1. expected return 2.variability of returns as measured by standard

deviation from the mean

3.co variance or variance of one asset return toanother asset returns. The higher the expected return ,lower the

standard deviation ,lower the correlation ,thebetter will be the security for investment .


21/49

Whatever is the risk of theindividual securities in isolation,the total risk of portfolio of

securities may be lower,if thecovariance of their returns isnegative or negligible


22/49

Dominant and efficient portfolio

Dominance refers to the superiorityof one portfolio over the other

A set can dominate over the other,if

with the same return ,the risk islower or with the same risk,thereturn is higher

Dominance principle involves thetrade off between risk and return


23/49

The concept of dominance tells thatno investor should invest in one coalone and if there are two or more

cos with the same risk ,then he hasto choose the one with higherreturns and if both have the sane

return he has to choose the onewith lower risk


24/49

A portfolio is efficient when it is expected toyield the highest return for the level of riskaccepted or,alternatively ,the smallest possiblerisk for a specified level of expected return

To build an efficient portfolio an expected

return level is chosen ,and assets aresubstituted until the portfolio combination withthe small variance at the return level is found

As this process is repeated for other expectedreturns,a setof efficient portfolios is

generated. A single asset or portfolio is efficient if no other

asset or portfolio offers higher expected returnwith the same or lower risk or lower risk withthe same expected return


25/49

Standard deviation

Expected returnEfficient frontier


26/49

Corner portfolios

The number of portfolios on theefficiency frontier are called cornerportfolios

A corner portfolio is defined as onein which either

The new security is added to apreviously efficient portfolio

A security is dropped from apreviousy efficient portfolio.


27/49

Limitations of markowitz

It related each security to everyother security demanding the

sophistication and volume of workbeyond the capacity of all


28/49

Sharpe model

Sharpe model relates their return ina security to a single market index

This will reflect all well traded

securities in the market

It will reduce and simplify the workinvolved in compiling elaborate

matrices of variances as betweenindividual securities


29/49

The optimal portfolio of sharpe iscalled the single index model

The optimum portfolio is directly

related to the beta


30/49

Calculate the co variance andcoefficient of variance from thefollowing data stocks are X and Y

and their returns are given belowreturn expected return

X 14 18

Y 26 18X 22 18

Y 10 18


31/49

X Y dx dy d^2x d^2y

14 26 -4 8 16 64

22 10 4 -8 16 64

----- ---- ---- ----

36 36 32 128

SD X= 32/2=4

SD Y = 128/2=8


32/49

CO VARIANCE

CV=1/2(14-18)(26-18)+1/2(22-18)(10-1

=1/2(-4 x +8)+1/2(4 x -8)

=1/2(-32)+1/2(-32)

=-16 -16 =-32


33/49

Coefficient of correlation =Cov XY

-----------

x y= -32-----------

4 x 8

= -32/32 = -1

Correlation coefficient is negative and theyare perfectly negatively correlated


34/49

Calculate the co variance andcoefficient of variance from thefollowing data stocks are X and Y

and their returns are given belowreturn expected return

X 7 9

Y 13 9X 11 9

Y 5 9


35/49

X Y dx dy d^2x d^2y

7 13 -2 4 4 16

11 5 2 -4 4 16

----- ---- ---- ----

18 18 16 32

SD X= 16/2=2

SD Y = 32/2=4


36/49

CO VARIANCE

CV=1/2(7-9)(13-9)+1/2(11-9)(5-9)

= -8


37/49

Coefficient of correlation =Cov XY

-----------

x y= -8-----------

2 x 4

= -8/8 = -1

Correlation coefficient is negative and theyare perfectly negatively correlated


38/49

Portfolio management process

Planning

Investor conditions

Market conditions

Investment /speculative policies

Statement of investment policy

Strategic asset allocation


39/49

Investor conditions

Financial situation marketable nonmarketable

Knowledge

Risk tolerance


40/49

Market conditions

Long term expectations

Short term expectations


41/49

Investors policy

1. Strategic asset allocation- current& passive rebalancing

2. Speculative strategy tacticalasset allocation

3. Internal and external management


42/49

Statement of investment policy

1. Objectives

2. Strategies

3. constraints


43/49

Implementation

Rebalance strategic asset allocation

Tactical asset allocation

Security selection


44/49

Monitoring

Evaluate statement of investmentpolicy

Evaluate investment performance


45/49

Statement of investment policy1.Compliance2. Periodic revision

Portfolio performance:Aggregate portfolioAsset classes and managersSpeculative strategy returns

Actions required control:Statement of investment policyManager selection


46/49

INVESTMENT PROCESS

Investment policy

Security analysis

Valuation of securities

Portfolio construction

Portfolio evaluation


47/49

Phases of portfolio management1. Specification of investment

objectives and constraints

2. Choice of asset mix3. Formulations of investment

strategy

4. Portfolio execution5. Portfolio revision

6. Portfolio evaluation


48/49

International diversification

Many in developed countriesstarted investing in foreign bonds ,stocks and other instruments

Diversification was extended toforeign assets to improve returnsfor a given risk by adopting proper

techniques of diversifiocation


49/49

advantages

Higher returns

Wide area of opportunities andinvestment avenues

different business conditions andtrends

Modern Port Folio Theory

Documents

Transcript of Modern Port Folio Theory