1. A
REPORT
ON
Portfolio-Markowitz Model
PRESENTED BY:- SATYABRATA PRADHAN
KRUPAJAL BUSINESS SCHOOL
REGD.NO.-11KB009
BATCH.NO:-2011-2013
2. 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 Diversification
� This can be achieved by investing in assets that
have low positive correlation, or better still, a
negative correlation.
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4. Multi –Asset Portfolio
The Efficient Frontier
Return %
B
A
Risk (std. dev.)
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5. 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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6. 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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7. Type of risk
Systematic 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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8. Systematic and Unsystematic Risk
Risk
std. dev.
Unsystematic risk
Total risk
Systematic or
market risk
20 30 No of securities in a portfolio
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9. Example
Suppose the shares of two companies, C & D, have the following probability
distributions:
Economy Probability Return C Return D
Boom 0.2 24% 5%
Growth 0.6 12% 30%
Slump 0.2 0% -5%
Required
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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10. Solution
a)
Economy Prob. Return ri x pi ri r i – 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 Variance 57.6
Standard Deviation 7.59%
7.59%
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