Portfolio Diversification

1. Module 4 : Investment Avenues
Mutual funds, Investor life cycle, Personal investment, Personal
Finance, Portfolio Management of funds in banks, insurance
companies, pension funds, International investing, international
funds management, emerging opportunities.
Module 1: Introduction to portfolio Management
Meaning of portfolio management, portfolio analysis, why
portfolios, Portfolio objectives, portfolio management process,
selection of securities.

2. Module II
Mohammed Umair: Dept of Commerce- Kristu Jayanti College

3. Company Name High Low Previous (LTP)
Hero Motocorp 2600 2400 2500
HDFC Bank 520 499 500
State Bank of India 2100 2029 2000
TCS 1020 998 1000
Tech Mahindra 108 105 100
Budget: Rs. 5000

4. Company Name High Low Previous (LTP)
Hero Motocorp 2600 2400 2600
HDFC Bank 520 499 550
State Bank of India 2100 2029 2000
TCS 1020 998 1050
Tech Mahindra 108 105 150
Situation A: Bullish Market

5. Company Name High Low Previous (LTP)
Hero Motocorp 2600 2400 2200
HDFC Bank 520 499 300
State Bank of India 2100 2029 1750
TCS 1020 998 850
Tech Mahindra 108 105 050
Situation B: Bearish Market

6. Portfolio Management
Security Portfolio Portfolio Portfolio Portfolio
Analysis Analysis Selection Revision Evaluation
1. Fundamental Diversification 1. Markowitz 1. Formula 1. Sharpe’s
Analysis
Model Plans index
2. Technical
Analysis 2. Sharpe’s 2. Rupee 2. Treynor’s
3. Efficient Single cost measure
Market index Averaging 3. Jenson’s
Hypothesis model measure
3. CAPM
4. APT

7. • Harry Max Markowitz (born August 24, 1927) is an
American economist.
• He is best known for his pioneering work in Modern
Portfolio Theory.
• Harry Markowitz put forward this model in 1952.
• Studied the effects of asset risk, return, correlation
and diversification on probable investment portfolio Harry Max Markowitz
returns.
Essence of Markowitz Model
“Do not put all your eggs in one basket”
1. An investor has a certain amount of capital he wants to invest over a single time horizon.
2. He can choose between different investment instruments, like stocks, bonds, options,
currency, or portfolio. The investment decision depends on the future risk and return.
3. The decision also depends on if he or she wants to either maximize the yield or minimize
the risk

8. Essence of Markowitz Model
1. Markowitz model assists in the selection of the most efficient by analysing various
possible portfolios of the given securities.
2. By choosing securities that do not 'move' exactly together, the HM model shows
investors how to reduce their risk.
3. The HM model is also called Mean-Variance Model due to the fact that it is based on
expected returns (mean) and the standard deviation (variance) of the various
portfolios.
Diversification and Portfolio Risk
p p the standard deviation
SR: Systematic Risk
USR: Unsystematic Risk
Portfolio Risk
SR
USR Total Risk
5 10 15 20
Number of Shares

9. • An investor has a certain amount of capital he wants to invest
over a single time horizon.
• He can choose between different investment instruments, like
stocks, bonds, options, currency, or portfolio.
• The investment decision depends on the future risk and return.
• The decision also depends on if he or she wants to either
maximize the yield or minimize the risk.
• The investor is only willing to accept a higher risk if he or she
gets a higher expected return.

10. Tools for selection of portfolio- Markowitz Model
1. Expected return (Mean)
Mean and average to refer to the sum of all values divided by
the total number of values.
The mean is the usual average, so:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
n 1. Expected return (Mean)
W
2. Standard deviation (variance)
Expected Return (ER)  i
 E ( Ri ) 3. Co-efficient of Correlation
Where: i 1
ER = the expected return on Portfolio
E(Ri) = the estimated return in scenario i
Wi= weight of security i occurring in the port folio
Rp=R1W1+R2W2………..n
Where: Rp = the expected return on Portfolio
R1 = the estimated return in Security 1
R2 = the estimated return in Security 1
W1= Proportion of security 1 occurring in the port folio
W2= Proportion of security 1 occurring in the port folio

11. Tools for selection of portfolio- Markowitz Model
2. Variance & Co-variance
n _ _
V ariance   Prob i ( R A  R A )  (R
2 2
B
- RB )
i 1
The variance is a measure of how far a set of numbers is spread out.
It is one of several descriptors of a probability distribution,
describing how far the numbers lie from the mean (expected value).
Co-variance
1. Covariance reflects the degree to which the returns of the two securities vary or change
together.
2. A positive covariance means that the returns of the two securities move in the same
direction.
3. A negative covariance implies that the returns of the two securities move in opposite
direction.
n _ _ _
1
COV AB

N
 Prob i
( R A  R A )(R B
- RB ) R A =Expected Return on security A
i 1 _
R B =Expected Return on security B
CovAB=Covariance between security A and B
RA=Return on security A
RB=Return on Security B

12. Tools for selection of portfolio- Markowitz Model
3. Co-efficient of Correlation
Covariance & Correlation are conceptually analogous in the sense
that of them reflect the degree of Variation between two variables.
1. The Correlation coefficient is simply covariance divided the product of standard
deviations.
2. The correlation coefficient can vary between -1.0 and +1.0
-1.0 0 1.0
Perfectly negative No Perfectly Positive
Opposite direction Correlation Opposite direction
Cov
r AB  AB
 Standard deviation of A and B
  A B
security
CovAB=Covariance between security A and B
rAB=Co-efficient correlation between security A and B

13. Returns
If returns of A and B are
%
20% perfectly negatively correlated,
a two-asset portfolio made up
of equal parts of Stock A and B
would be riskless. There would
15% be no variability
of the portfolios returns over
time.
10%
Returns on Stock A
Returns on Stock B
5%
Returns on Portfolio
Time 0 1 2
CHAPTER 8 – Risk, Return and Portfolio Theory

14. Returns
If returns of A and B are
%
20% perfectly positively correlated,
a two-asset portfolio made up
of equal parts of Stock A and B
would be risky. There would be
15% no diversification (reduction of
portfolio risk).
10%
Returns on Stock A
Returns on Stock B
5%
Returns on Portfolio
Time 0 1 2
CHAPTER 8 – Risk, Return and Portfolio Theory

15. • The riskiness of a portfolio that is made of different risky assets is a
function of three different factors:
• the riskiness of the individual assets that make up the portfolio
• the relative weights of the assets in the portfolio
• the degree of variation of returns of the assets making up the portfolio
• The standard deviation of a two-asset portfolio may be measured using
the Markowitz model:
   w   w  2 w A w B rAB  A B
2 2 2 2
p A A B B
A
The data requirements for a three-asset portfolio grows dramatically if we are using
Markowitz Portfolio selection formulae.
ρa,b ρa,c
B C
ρb,c
We need 3 (three) correlation coefficients between A and B; A and C; and B and C.
   A w A   B w B   C w C  2 w A w B rA , B  A B  2 w B w C rB , C  B  C  2 w A w C rA , C  A C
2 2 2 2 2 2
p

16. • Assets differ in terms of expected rates of return,
standard deviations, and correlations with one another
• While portfolios give average returns, they give lower risk
• Diversification works!
• Even for assets that are positively correlated, the
portfolio standard deviation tends to fall as assets are
added to the portfolio

17. • Combining assets together with low correlations reduces
portfolio risk more
• The lower the correlation, the lower the portfolio standard deviation
• Negative correlation reduces portfolio risk greatly
• Combining two assets with perfect negative correlation reduces the
portfolio standard deviation to nearly zero

18. n
Expected Return (ER)  W i
 E ( Ri )
i 1
Portfolio Rp IN % Return on Portfolio Risk  p Any portfolio which gives more
A 17 13 return for the same level of risk.
B 15 08
Or
C 10 03
D 7 02 Same return with Lower risk.
E 7 04
Is more preferable then any
F 10 12 other portfolio.
G 10 12
H 09 08
J 06 7.5
Amongst all the portfolios which offers the highest
return at a particular level of risk are called
efficient portfolios.

19. ABCD line is the efficient frontier along which
attainable and efficient portfolios are available.
18
Which portfolio investor should choose?
16
14
13
12
12 12
Risk and Return
10
Return
8 Risk
8 8
7.5
6
4
4
3
2
2
0
A B C D E F G H I
Portfolios

20. Utility of Investor
Risk Lover Risk Neutral Risk Averse
Description Property
Risk Seeker Accepts a fair Gamble
Risk Neutral Indifferent to a fair gamble
Risk Averse Rejects a fair gamble
A
B
Marginal utility of different Utility
class of investors. C
Return

21. Rp Rp
Indifference curves of the risk Indifference curves of the risk
Loving I4 Fearing I
I3 4
I3
I2 I2
I1 I1
Risk Risk
Rp
Indifference curves of the less Rp
risk Fearing Indifference curves & Efficient
I4 frontier. I4
I3 I3
I2 I2
I1 I1
R
Risk Risk
2 4 6 8 10 12 14 14 18

22. • The optimal portfolio concept falls under the modern portfolio
theory. The theory assumes that investors fanatically try to
minimize risk while striving for the highest return possible.

23. • WHAT IS A RISK FREE ASSET?
• DEFINITION: an asset whose terminal value is certain
• variance of returns = 0,
• covariance with other assets = 0
If i  0
then  ij   ij  i j
 0

24. • DOES A RISK FREE ASSET EXIST?
• CONDITIONS FOR EXISTENCE:
• Fixed-income security
• No possibility of default
• No interest-rate risk
• no reinvestment risk
24

25. • DOES A RISK FREE ASSET EXIST?
• Given the conditions, what qualifies?
• a U.S. Treasury security with a maturity matching the investor’s horizon
• DOES A RISK FREE ASSET EXIST?
• Given the conditions, what qualifies?
• a U.S. Treasury security with a maturity matching the investor’s horizon

26. • ALLOWING FOR RISK FREE LENDING
• investor now able to invest in either or both,
• a risk free and a risky asset

27. • ALLOWING FOR RISK FREE LENDING
• the addition expands the feasible set
• changes the location of the efficient frontier
• assume 5 hypothetical portfolios
27

28. • INVESTING IN BOTH: RISKFREE AND RISKY ASSET
PORTFOLIOS X1 X2 ri di
A .00 1.0 4 0
B .25 .75 7.05 3.02
C .50 .50 10.10 6.04
D .75 .25 13.15 9.06
E 1.00 .00 16.20 12.08
28

29. • RISKY AND RISK FREE PORTFOLIOS
rP E
D
C
B
A
rRF = 4% P
0
29

30. • IN RISKY AND RISK FREE PORTFOLIOS
• All portfolios lie on a straight line
• Any combination of the two assets lies on a straight line connecting the risk
free asset and the efficient set of the risky assets
rP
• The Connection to the Risky Portfolio
0
P

31. • The Connection to the Risky Portfolio
rP
S
R
P
P
0
31