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ONONONONPortfolio-Markowitz ModelPortfolio-Markowitz ModelPortfolio-Markowitz ModelPortfolio-Markowitz Model

PRESENTED BY:- SATYABRATA PRESENTED BY:- SATYABRATA PRESENTED BY:- SATYABRATA PRESENTED BY:- SATYABRATA PRADHANPRADHANPRADHANPRADHANKRUPAJAL BUSINESS SCHOOLKRUPAJAL BUSINESS SCHOOLKRUPAJAL BUSINESS SCHOOLKRUPAJAL BUSINESS SCHOOL

RRRREGD.NO.-11KB009EGD.NO.-11KB009EGD.NO.-11KB009EGD.NO.-11KB009BATCH.NO:-2011-2013BATCH.NO:-2011-2013BATCH.NO:-2011-2013BATCH.NO:-2011-2013

Markowitz Model

�Markowitz (1952) provides the tools for identifying portfolio which give the highest return for a particular level of risk.

�According to Markowitz, if an investor holds a portfolio of two assets he or she can reduce portfolio risk below the average risk attached to the individual assets.

�Markowitz Risk DiversificationMarkowitz Risk DiversificationMarkowitz Risk DiversificationMarkowitz Risk Diversification�This can be achieved by investing in assets that

have low positive correlation, or better still, a negative correlation.

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Security Market Line (SML))))

M

Rf

Expected Return SML

β

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Multi –Asset Portfolio B A

Return %

Risk (std. dev.)

The Efficient Frontier

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Risk

Risk� Possibility that actual future returns will be different

from expected return. � Risk implies that there is a chance for some

unfavourable event to occur.

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Measurement of Risk

� Risk is the possibility that actual outcome will deviates from expected outcome.

� Risk is measured by standard deviation

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Type of riskSystematic risk:

� Refers to that portion of risk of individual security ’ s returns caused by factors affecting the market as a whole such as interest rate changes, and inflation

Unsystematic risk � Risk unique to the firm. This caused by such factors such

as:� Strikes

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Systematic and Unsystematic Risk

30

Systematic ormarket risk

Total risk

Unsystematic risk

Riskstd. dev.

20 No of securities in a portfolio

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ExampleExampleExampleExample

Suppose the shares of two companies, C & D, have the following probability distributions: EconomyEconomyEconomyEconomy Probability Probability Probability Probability Return CReturn CReturn CReturn C Return DReturn DReturn DReturn D Boom 0.2 24% 5% Growth 0.6 12% 30% Slump 0.2 0% -5% RequiredRequiredRequiredRequired a) Calculate the expected return and the exp ected risk for each security separately and b) Calculate the expected return and expected risk for a portfolio comprising 75 per cent C and 25 percent D.

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Solution

a) Economy Prob. Return ri x pi ri ri – ri (ri – ri)2pi C Boom 0.2 +24 4.8 12 12 28.8 Growth 0.6 +12 7.2 12 0 0 Recession 0.2 0 0 12 -12 28.0 Expected Return 12 12 12 12 Variance 57.6 Standard Deviation 7.597.597.597.59%%%%

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Cont…

D Boom 0.2 5 1 18 -13 33.8 Growth 0.6 30 18 18 12 86.4 Recession 0.2 -5 -1 18 +23 105.8 Expected Return 18181818 Variance 226 Standard Deviation 15.03%15.03%15.03%15.03%

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Cont…

b)Expected return of the portfolio comprising C and D

Security Expected Return C 12x 0.75= 9 D 18x0.25= 4.5 13.5%13.5%13.5%13.5%

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Thank you…..