Portfolio Management

1. ReturnReturnReturnReturn Portfolio ManagementPortfolio Management
RiskRiskRiskRisk

2. Raju Indukoori
What is a portfolio?
 It is a combination of investments in
different asset classes with financial and
real in nature for a period of time.
 It is a combination of n number of assets
 It is done by investors or any one else on
behalf of the investor.
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3. Raju Indukoori
Types of Portfolios
 Investment Portfolio
Includes all financial and non financial
investments
 Security Portfolio
Consists of equity, bonds, derivatives,
money market instruments
 Equity portfolio
Combination of equity shares of different
companies from different sectors
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4. Raju Indukoori
Why Portfolio?
 More diversification less is the risk
 Risk is composition of systematic and
unsystematic risk
 Unsystematic risk can be nullified with a
portfolio
 Systematic risk still remains in the
portfolio
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5. Raju Indukoori
Objectives of Portfolio Management
Diversify the portfolio to
 To minimize the risk for a given expected
return
 To maximize the return for a given level
risk
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6. Raju Indukoori
Portfolio Management Process
1. Portfolio Planning : As per objectives
2. Portfolio Strategy: To time the market and risk
protection with derivatives
3. Portfolio Analysis: Securities analysis and
valuation
4. Portfolio Selection / Construction
5. Portfolio Evaluation
6. Portfolio Revision
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7. Raju Indukoori
Who does professional Portfolio Management ?
 AMCs
 Hedge funds
 Life Insurance companies
 Wealth management Companies
 Portfolio Management Companies
 Pension fund managers
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8. Raju Indukoori
Portfolio Analysis & Selection ProblemPortfolio Analysis & Selection Problem
 Portfolio Returns
 Weighted Average Return
 Expected Return
 Annualized Return
 Portfolio Risk
 Covariance & Correlation
 Variance & Standard Deviation
 Beta
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9. Raju Indukoori
Portfolio Analysis & Selection ProblemPortfolio Analysis & Selection Problem
1. Modern Portfolio Theory
2. Single Index Model
3. Multiple Index Model
4. Capital Asset Pricing Model (CAPM)
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10. Raju Indukoori
1. Modern Portfolio Theory1. Modern Portfolio Theory
Harry Markowitz,Harry Markowitz,
Personal Profile:
 Professor in Finance, Rady School of Management, University
of California, San Deigo (UCSD).
 Recipient of ‘John von Neumann Thoery Prize and Nobel
Memorial Prize in Economic Sciences.
 Introduced MPT in 1952 in an article “Portfolio Selection” in
Journal of Finance (March 1952) Pages 77-91
 Book:Portfolio Selection: Efficient Diversification of Investments,
John Wiley in 1959 ISBN 978030001372 and Black well in 1991
ISBN 9781557861085.
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11. Raju Indukoori
Assumptions
 Asset returns are normally distributed
 Correlation between assets are fixed and constant forever
 All investors aim to maximize economic utility
 All investors are rational and risk averse
 All investors have the same information at the same time
 Investors have an accurate conception of probable returns
 No taxes or transaction costs
 All investors are price takers
 Any investor can borrow lend and borrow an unlimited amount
at risk free rate
 All securities can be divided into parcels of any size
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12. Raju Indukoori
The theory
 Assets in a portfolio should not be selected
individually rather selection should be based on the
relationship between each asset in the portfolio which
should not be positive.
 Higher the risk higher the returns
 Investing is trade-off between risk and return.
 Investors would prefer lower risk portfolio but the
investors looking for higher returns should be
prepared to take higher risk.
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13. Raju Indukoori
The theory
 Base of selection: low risk high return
 Return: Expected return with PD
 Risk: Standard deviation
 Portfolio Return: Weighted Average
 Portfolio Risk: Weighted SD with Correlationnnp RWRWRWRWR .............332211 +++=
212112
2
2
2
2
2
1
2
1 2 σσσσσ wwrwwp ++=
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14. Raju Indukoori
Portfolio Returns
- Weighted Average Return
Mr Ashok invested Rs 10,00,000 in real estate by buying a
plot of government approved layout, Rs 3,00,000 in shares and
Rs 7,00,000 in bank term deposits for which he got 25%, 70%
and 8% returns respectively after one year. Calculate WAR
nn RWRWRWRWWAR .............332211 +++=
Investment Investment Value in Rs Return in
%
Weightage
Bonds 10,00,000 25% 0.50
Shares 3,00,000 70% 0.15
Bank Term Deposit 7,00,000 8% 0.35
Total 20,00,000 1.00
)35.0)(8()15.0)(70()50.0)(25( ++=WAR 8.25.105.12 ++= %8.25=
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15. Raju Indukoori
Portfolio Returns
- Weighted Average Return
Example - Following are the details of an investor who
invested Rs 2,00,000 in a portfolio of stocks and sold later.
Calculate individual investment weight, profit, rate of return and
portfolio return
# Company Name
Gross Buy Price
on 21-01-10
Qty
Net Selling Price
0n 21-11-11
1 GMR Infra 223.06 100 68.30
2 Deccan Aviation /Kingfisher 256.18 100 54.00
3 Reliance Communication 581.64 60 173.45
4 DLF 894.15 50 373.00
5 Shanthi Gears 72.47 1,000 41.75
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16. Raju Indukoori
Portfolio Returns
- Weighted Average Return
# Company Name
Gross
Buy Price
Qty Total Weight
Net
Selling
Price
Net Sale
Value
Absolute
Profit per
share
Absolute Total
Profit / Loss
Rate of
Return
1 GMR Infra 223.06 100 22,306 0.11 68.30 6,830 -154.76 -15,476.00 -69.38
2
Deccan Aviation /
King Fisher
256.18 100 25,618 0.13 54.00 5,400 -202.18 -20,218.00 -78.92
3
Reliance
Communication
581.64 60 34,898 0.17 173.45 10,407 -408.19 -24,491.40 -70.18
4 DLF 894.15 50 44,708 0.22 373.00 18,650 -521.15 -26,057.50 -58.28
5 Shanthi Gears 72.47 1000 72,470 0.36 41.75 41,750 -30.72 -30,720.00 -42.39
)39.42)(36.0()28.58)(22.0()18.70)(17.0()92.78)(13.0()38.69)(11.0( −+−+−+−+−=WAR
90.31Re
%90.57
−=
−=
turnAnnulized 16

17. Raju Indukoori
Portfolio Risk
It is the volatility in returns of all
securities in the portfolio for a given
Weight of each security in a portfolio for
a give period of time.
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18. Raju Indukoori
Portfolio Risk Measurement
- Covariance & Correlation
211212 σσγ=Cov
21
12
)(nCorrelatio
σσ
γ
Cov
=
∑=
−−
=
n
i
ii
n
YYXX
ianceCo
1
))((
var
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19. Raju Indukoori
Correlation
 Perfectly positively correlated returns
 Perfectly negatively correlated returns
 Uncorrelated returns
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20. Raju Indukoori
Portfolio Risk Measurement
- Variance & Standard Deviation
Example
Calculate standard deviation of an equally weighed portfolio of 2
securities with 15 percent and 24 percent returns and a standard
deviation of 35 percent and 52 percent respectively with a correlation of
-0.9
212112
2
2
2
2
2
1
2
1
2
2 σσγσσσ wwwwp ++= 2
pp σσ =
)52)(35)(5.0)(5.0)(9.0(2)52()5.0()35()5.0( 22222
−++=pσ
81925.270425.1225
2
−+=pσ
50.3110
2
=pσ
50.3110=pσ
57.55=pσ
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21. Raju Indukoori
Choice of combination
 Risky assets with correlation
 Positive
 Negative
 Risky assets with no correlation
 Only SD to be considered
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22. Raju Indukoori
Portfolio Choice
 Wealth Curves – Marginal Utility
 Indifference Curves
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23. Raju Indukoori
Portfolio Choice
Wealth Curves
 Concave
 Straight
 Convex
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24. Raju Indukoori
Portfolio Choice
Indifference Curves
 Two curves
 Median curve
 Extended Curves
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25. Raju Indukoori
Portfolio Choice
Indifference Curves
 High Risk Averse Investor
 Moderately Risk Averse Investor
 Slightly Risk Averse Investor
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26. Raju Indukoori
Efficient Set of Portfolio
Portfoli
o No
Expected
Return in %
Risk measure
in terms of S D
1 5.6 4.5
2 7.8 5.8
3 9.2 7.6
4 10.5 8.1
5 11.7 8.1
6 12.4 9.3
7 13.5 9.5
8 13.5 11.3
9 15.7 12.7
10 16.8 12.9
Risk Return Trade Off
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
SD
Return
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27. Raju Indukoori
Efficient frontier & Optimum Portfolio
 All possible combinations of risky assets can be
plotted in risk and expected return space.
 Efficient frontier: Upper edge of the space
 Markowitz bullet : Hyperbola
 Efficient portfolio is the north west frontier which
adjoins optimum set of portfolios
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28. Raju Indukoori
Risk Return Trade Off
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
0.00 5.00 10.00 15.00 20.00 25.00
SD
Return
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29. Raju Indukoori 29

30. Raju Indukoori
Critics of MPT
 Asset returns are normally distributed random variables
 In reality they are not normally distributed
 Correlation between assets are fixed and constant forever
 Systematic relationship changes in some circumstances like market
crash due to war situation where all the stocks are positively
correlated.
 Efficient market hypothesis
 All investors aim to maximize economic utility
 All investors are rational and risk averse
 All investors have the same information at the same time
 Investors have an accurate conception of probable returns
 Investors expectations could be biased making market prices
informationally inefficient
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31. Raju Indukoori
Critics of MPT
 No taxes or transaction costs
 In reality it is not possible
 All investors are price takers
 Large sale of individual assets would shift the prices
 Any investor can borrow lend and borrow an unlimited amount
at risk free rate
 Investors have credit limit
 All securities can be divided into parcels of any size
 Divisibilty of unit of an individual stock is not practical with all
shares
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32. Raju Indukoori
Other Critics
 Measures are based on expected returns
 Tedious calculations
 High cost due to diversification
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33. Raju Indukoori
2. Single Index / Market Model
William Sharpe
m
P
σ
σ
=)(ßBeta 2
)(ßBeta
m
PmCov
σ
=
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34. Raju Indukoori
Single Index / Market Model
- William Sharpe
 Equity Return
 Equity Risk
returnresiduale
markettotindependenreturnsurity
Where
eRR
i
imiii
=
=∞
++∞=
'sec
β
2222
eimii σσβσ +=
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35. Raju Indukoori
Single Index / Market Model
- William Sharpe
 Portfolio Return
 Portfolio Risk
nnp
nnp
mppp
wwww
wwww
where
RR
βββββ
β
.............
.............
332211
332211
+++=
∞+∞+∞+∞=∞
+∞=
22
1
222
eii
n
i
mpp w σσβσ
=
∑+=
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36. Raju Indukoori
3. Multiple Index Model3. Multiple Index Model
• Equity Return
• Equity Risk
immii eRRRRR +++++∞= 332211 ββββ
22
3
2
3
2
2
2
2
2
1
2
1
222
eimmi σσβσβσβσβσ ++++=
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37. Raju Indukoori
Multiple Index ModelMultiple Index Model
• Portfolio Return
• Portfolio Risk
nnp
nnp
mppp
wwww
wwww
where
RR
βββββ
β
.............
.............
332211
332211
+++=
∞+∞+∞+∞=∞
+∞=
22
1
222
eii
n
i
mpp w σσβσ
=
∑+=
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38. Raju Indukoori
4. Capital Asset Pricing Model (CAPM)
– Sharpe, Mossin, Lintner
Assumptions
 Investors make their investment decisions on the basis of risk-return assessments
measured in terms of expected returns and standard deviation of returns
 The purchase or sale of a security can be undertaken in infinitely divisible units
 Purchases and sales by a single investor cannot affect prices.
 No transactions cost.
 No personal income taxes
 Lend and borrow at risk less security interest rate
 Investor can short
 Homogeneity of expectations
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39. Raju Indukoori
Capital Asset Pricing Model (CAPM)
– Sharpe, Mossin, Lintner
Implications
 Risk is the variance of expected portfolio return
 Risk is decomposed into systematic and unsystematic
 Diversification can reduce unsystematic risk
 Beta is the relevant measure of risk for investors with diversified portfolios
 Risk and return are linearly related to beta, Risk and return are in equilibrium
 Return is the total return
 Investor holds portion of two portfolios risk free and market portfolio
 Two return sources
• Risk proportional market return
• Non systematic random return
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40. Raju Indukoori
Choice of combination
 Risky and Risk free investment
 Risky assets with Beta
• High Beta
• Low Beta
• One Beta
• Negative Beta
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41. Raju Indukoori
Capital Asset Pricing Model (CAPM)
– Sharpe, Mossin, Lintner
Q What is the return of an equated risky and risk free returns are
15% and 7% respectively with a standard deviation of 8%
%117)5.01()15(5.0 =−+=pR
%355.250.3710)125.1()30(25.1 =−=−−=LR
%40)5.01()8(5.0 =−+=pσ
%5.12)10(25.1 ==Lσ
Q What is the return of a leveraged portfolio of 25% risk free borrowing rate and risky return are
10% and 30% respectively with a standard deviation of 10%
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42. Raju Indukoori
Capital Asset Pricing Model (CAPM)
– Sharpe, Mossin, Lintner
Capital Market Line
Where
 Rf is risk free
 Rm is market return
 is security risk
 is market risk
σ
i
m
fm
fi
RR
RR σ
σ





 −
+=
mσ
iσ
iσ
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43. Raju Indukoori
Capital Asset Pricing Model (CAPM)
– Sharpe, Mossin, Lintner
Security Market Line
Expected return on a security = Risk free return – Beta times market risk
premium
Where
 Rf is risk free
 Rm is market return
 B is the impact of Rm on Ri
 Rm-Ri is the risk Premium
)( fmifi RRRR −+= β
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44. Raju Indukoori
Capital Asset Pricing Model (CAPM)
– Sharpe, Mossin, Lintner
)( fmi RR −β
)( fmi RR −β
Security Market Line (SML)
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45. Questions