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Modern portfolio theory
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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
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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
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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
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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
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Investors objective can be set of as:
Income
GrowthBoth
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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)
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Every investor should allocatetowards cash outfows in the formof:
administrative expenses
Salaries
Wages
Stationery
Incidental expenses
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5 to 10 % of investment needs to bekept in :
Cash
Bank deposits
Money market instruments
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The proportion in equity anddebentures would depend upon thespecific objective of invetment
Income
Growth
Mixture of both
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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
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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.
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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
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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
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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
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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.
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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
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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
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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
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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 .
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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
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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
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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
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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
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Standard deviation
Expected returnEfficient frontier
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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.
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Limitations of markowitz
It related each security to everyother security demanding the
sophistication and volume of workbeyond the capacity of all
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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
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The optimal portfolio of sharpe iscalled the single index model
The optimum portfolio is directly
related to the beta
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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
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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
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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
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Coefficient of correlation =Cov XY
-----------
x y= -32-----------
4 x 8
= -32/32 = -1
Correlation coefficient is negative and theyare perfectly negatively correlated
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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
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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
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CO VARIANCE
CV=1/2(7-9)(13-9)+1/2(11-9)(5-9)
= -8
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Coefficient of correlation =Cov XY
-----------
x y= -8-----------
2 x 4
= -8/8 = -1
Correlation coefficient is negative and theyare perfectly negatively correlated
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Portfolio management process
Planning
Investor conditions
Market conditions
Investment /speculative policies
Statement of investment policy
Strategic asset allocation
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Investor conditions
Financial situation marketable nonmarketable
Knowledge
Risk tolerance
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Market conditions
Long term expectations
Short term expectations
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Investors policy
1. Strategic asset allocation- current& passive rebalancing
2. Speculative strategy tacticalasset allocation
3. Internal and external management
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Statement of investment policy
1. Objectives
2. Strategies
3. constraints
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Implementation
Rebalance strategic asset allocation
Tactical asset allocation
Security selection
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Monitoring
Evaluate statement of investmentpolicy
Evaluate investment performance
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Statement of investment policy1.Compliance2. Periodic revision
Portfolio performance:Aggregate portfolioAsset classes and managersSpeculative strategy returns
Actions required control:Statement of investment policyManager selection
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INVESTMENT PROCESS
Investment policy
Security analysis
Valuation of securities
Portfolio construction
Portfolio evaluation
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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
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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
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advantages
Higher returns
Wide area of opportunities andinvestment avenues
different business conditions andtrends