Description
estimate risk and return from the past data. It explains risk and return of a portfolio. It covers Markowitz theory of portfolio and problems with markowitz model. How this problems is overcome by CAPM (Capital asset pricing model) model.
EQUITY INVESTMENTS AND
PORTFOLIO THEORY
EQUITY INVESTMENT
BONDS VS. EQUITY
Bonds
? Defined lifetime
? Maturity date
? Normally pays a known interest
rate
? Return is defined as YTM.
? Risk is defined in terms of
sensitivity.
? Less risky than equity
? No voting right
? Negotiable
Equity
? Shared ownership, assets and
profits
? Variable dividend
? Normally, voting rights
? Infinite life.
? Return is measured directly in
terms of dividend plus capital
gains.
? Risk is defined as variation in
terms of standard deviation.
? Negotiable
RETURN ON EQIITY INVESTMENT
?Return on an equity share consists of
?dividend income; and
?capital gain/loss
RETURN
1
1
÷
÷
÷
=
t
t t
t
P
P P
R
assuming that the compounding is discrete
assuming that the compounding is continuous
) ln( ) ln(
1 ÷
÷ =
t t t
P P R
(one may include any other cash flow that may arise during the
period.)
RETURN ON INFOSYS TECH.
? Price on 19 May 2009 Rs 1558.95
? Price on 19 May 2010 Rs 2642.60
? Dividend per Share
?October 15, 2009 Rs. 10.00
?Return 70.15%
RETURNS AND TAX
? Returns are affected by tax.
? In India dividend is not taxed in the hand of
an Investors,( but companies pay dividend distribution tax @ 15 %)
? On short term (less than 12 months) capital
gain 10% tax is payable. (without STT tax according to income-tax
slab)
? No tax is payable on long-term capital gain.
(without STT tax 20%)
EXPECTED RETURN
Current Price Future Price Prob. Return
130 8% 30%
120 30% 20%
110 25% 10%
100 100 15% 0%
90 12% -10%
80 8% -20%
70 2% -30%
Expected Return 7.50%
HOW DO WE FORM EXPECTATIONS
REGARDING THE FUTURE
? One possible way- on the basis of the past
behaviour of the variable.
RISK
? Risk is often defined as the variability of
expected returns
? We use statistical measures like standard
deviation, variance and coefficient of
variation to measure risk.
EXPECTED RETURN AND RISK
Current Price Future Price Prob. Return
130 8% 30%
120 30% 20%
110 25% 10%
100 100 15% 0%
90 12% -10%
80 8% -20%
70 2% -30%
Expected Return 7.50%
Standard Deviation 14.92%
HOW TO ESTIMATE RISK AND RETURN FROM
THE PAST DATA?
? The mean of the return can be taken as a
proxy for the Expected Return.
? The standard deviation (or variance) of
the past data can be taken as a proxy of
the risk.
M
o
n
t
h
l
y
R
e
t
u
r
n
s
HUL
Tata Steel
HUL TS
Average 1.14 3.51
SD 8.78 16.43
EQUITY VS BOND : RISK AND
RETURN
BSE SENSEX
180 days Govt Bill
Risk Free Securities
Government Securities
Corporate Bonds
Preference Shares
Equity of Large Companies
Equities of Small Companies
Risk
R
e
t
u
r
n
RISK RETURN AND TIME HORIZON
Distribution of Daily Returns on NSE Nifty
Mean =0.06% (15.66%)
SD =1.85% (461.58%)
CV =2947%
Distribution of Monthly (20 days) Returns on NSE
Mean =1.15% (14.31%)
SD =9.04% (112.94%)
CV =789%
Mean =12.68% (12.68%)
SD =32.02% (32.02%)
CV =253%
Distribution of Annual (250 days) Returns on NSE Nifty
Distribution of 2500 days Returns on NSE Nifty
Mean =94.17% (9.42%)
SD =45.49% (4.55%)
CV =48.31%
Distribution of 4000 days Returns on NSE Nifty
Mean =199.65% (12.48%)
SD =51.67% (3.32%)
CV =25.88%
RISK AND RETURN OF A
PORTFOLIO
WHAT IS PORTFOLIO
? When we invest our money in more than one
asset it is called a ‘portfolio’
EXPECTED RETURN OF A PORTFOLIO
? The expected return of a portfolio is equal to
the weighted average of the return on
individual assets constituting it.
n n p
R w R w R w R ...... ..........
2 2 1 1
+ + =
RISK IN A PORTFOLIO
? The standard deviation of a portfolio is not
equal to the weighted average of the
standard deviation of the individual security
returns. It will be less than the weighted
average unless the returns are perfectly
correlated.
? We get the benefit of diversification in the
form of reduced risk.
MARKOWITZ THEORY OF
PORTFOLIO: MEAN VARIANCE
ANALYSIS
? Although it was known earlier
that diversification reduces the
risk, but how does it work it
was not known.
? Harry Markowitz (1952) was
first to demonstrate statistically
how diversification works.
? He was given Nobel Memorial
Prize in Economic Science in
1990.
Harry Markowitz
CONCEPTS REVISITED
) )( (
1
,
y y x x
n
Cov
y x
÷ ÷ =
¿
Covariance
Correlation
y x
y x
y x
Cov
r
o o
,
,
=
CONCEPTS REVISITED
xy
y x y x
Cov . 2
2
2 2
+ + =
+
o o o
PORTFOLIO RISK: CASE OF TWO
SECURITIES
2 , 1 1 1 2 1
2
2
2
2
2
1
2
1
2 , 1
2
2 r w w w w o o o o o + + =
or
2 , 1 2 1
2
2
2
2
2
1
2
1
2 , 1
2
cov 2 w w w w + + = o o o
FOR YOUR DISCUSSION
? What will happen if:
r = 1
r = 0
r = -1
HOW DO THE RETURN AND THE
RISK CHANGES WITH CHANGE IN
WEIGHTS
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
7.50 8.50 9.50 10.50 11.50
Stdev
R
e
t
Minimum Variance Portfolio
Non-Efficient Portfolios
Efficient Portfolio Frontier
MINIMUM VARIANCE PORTFOLIO
2 , 1 2 1
2
2
2
2
2
1
2
1
2 , 1
2
cov 2 w w w w + + = o o o
2 , 1 1 1
2
2
2
1
2
1
2
1
2 , 1
2
cov ) 1 ( 2 ) 1 ( w w w w ÷ + ÷ + = o o o
Portfolio Variance is
OR
Differentiate w.r.t. w1 and obtain minima
2 , 1
2
2
2
1
2 , 1
2
2
1
cov 2
cov
÷ +
÷
=
o o
o
w
MIN-VARIANCE OPPORTUNITY SET
WITH DIFFERENT CORRELATION
BETWEEN TWO SECURITIES
r=1
13%
% 8
12% 20%
r = +0.3
?
p
E(r
p
)
r =-1
r =-1
CASE OF MULTIPLE SECURITIES
¿¿
= =
=
n
j
n
i
j i j i p
Cov w w
1 1
,
2
o
CASE OF MULTIPLE SECURITIES
Sec 1 Sec 2 Sec 3 Sec n
Sec 1 …… ….
Sec 2 ……….
Sec 3 ……..
.
. ………
Sec n ………..
2
1
2
1
o w
2 , 1 2 1
o w w
3 , 1 3 1
o w w
n n
w w
, 1 1
o
2 , 1 2 1
o w w
2
2
2
2
o w
3 , 2 3 2
o w w
n n
w w
, 2 2
o
3 , 1 3 1
o w w
3 , 2 3 2
o w w
2
3
2
3
o w
n n
w w
, 3 3
o
n n
w w
, 1 1
o
n n
w w
, 2 2
o
n n
w w
, 3 3
o
2 2
n n
w o
Variance Terms
Co-Variance Terms
n
s d
Diversifiable or Unsystematic Risk
Non-diversifiable
or Systematic Risk
Company
Industry
National Economy
International Economy
INTUITIVE EXPLANATION OF
DIVERSIFICATION
? Risk in a single company
?International Economy Risk + National Economy
Risk + Industry Specific Risk + Company’s
Unique Risk
INTUITIVE EXPLANATION OF
DIVERSIFICATION
? Risk in a single industry
?International Economy Risk + National Economy
Risk + Industry’s unique Risk
?Risk unique to individual company diversified
away
INTUITIVE EXPLANATION OF
DIVERSIFICATION
? Risk in different industries within a national
economy
?International Economy Risk + National Economy
Risk
?Risk unique to individual company and unique to
specific industry diversified away
OPPORTUNITY SET AND EFFICIENT
FRONTIER FOR MULTIPLE SECURITIES
EQUILIBRIUM OF INDIVIDUAL
INVESTOR
A
B
R
i
s
k
Return
PROBLEM WITH MARKOWITZ MODEL
? As the number of securities increase
Markowitz Model becomes unmanageable.
We need to compute all the variances and
Covariance for all the possible pairs of the
securities
CAPITAL ASSET PRICING
MODEL (CAPM)
DEVELOPMENT OF CAPM
• CAPM was developed by William
Sharpe, building on Portfolio
Theory of Markowitz and Two
Fund Separation Theory of Tobin
• Sharpe was awarded Noble Prize
in Economic Science for his work
in 1990
William Sharpe
TWO FUNDS SEPARATION AND
CAPITAL MARKET LINE
Market
Portfolio
Rf
Rm
A
B
?m
James Tobin
EQUATION OF CAPITAL MARKET LINE
(CML)
( )
f m
m
p
f p
R R R R ÷ + =
o
o
Return on Portfolio=
Risk free Return
+Relative risk of Portfolio * Market Risk Premium
Rf
Optimization with Borrowing Restrictions
RL
Different Lending and Borrowing Rates
RB
y = 1.570x + 0.778
R² = 0.634
E
x
c
e
s
s
R
e
t
u
r
n
o
n
T
a
t
a
S
t
e
e
l
Excess Return on Market
Characteristic Line
Equation of Charecteristic Line
t m i
R R c | o + + =
Beta
Alfa
BETA
? What is Beta:
?Beta of a security (or portfolio) is the
sensitivity of the expected return on that
security in response to a change in
expected return on market portfolio.
m
M i
i
R R Cov
2
,
) (
o
| =
WHAT IS THE IMPORTANCE OF BETA
? Beta is the measurement of the
systematic risk.
? When an investor invests in a well
diversified market portfolio he can
diversify away all the unsystematic risk
and only systematic risk is the relevant
measure of the risk for him.
E
x
c
e
s
s
R
e
t
u
r
n
Beta
Security Market Line
HUL
SML
Infosys
Wipro
SBI
Tata
Steel
SAIL
EQUATION OF SECURITY MARKET
LINE
( ) ( )
f m j f j
R R R R ÷ = ÷ |
) (
f m j f j
R R R R ÷ + = |
or
doc_179524587.pptx
estimate risk and return from the past data. It explains risk and return of a portfolio. It covers Markowitz theory of portfolio and problems with markowitz model. How this problems is overcome by CAPM (Capital asset pricing model) model.
EQUITY INVESTMENTS AND
PORTFOLIO THEORY
EQUITY INVESTMENT
BONDS VS. EQUITY
Bonds
? Defined lifetime
? Maturity date
? Normally pays a known interest
rate
? Return is defined as YTM.
? Risk is defined in terms of
sensitivity.
? Less risky than equity
? No voting right
? Negotiable
Equity
? Shared ownership, assets and
profits
? Variable dividend
? Normally, voting rights
? Infinite life.
? Return is measured directly in
terms of dividend plus capital
gains.
? Risk is defined as variation in
terms of standard deviation.
? Negotiable
RETURN ON EQIITY INVESTMENT
?Return on an equity share consists of
?dividend income; and
?capital gain/loss
RETURN
1
1
÷
÷
÷
=
t
t t
t
P
P P
R
assuming that the compounding is discrete
assuming that the compounding is continuous
) ln( ) ln(
1 ÷
÷ =
t t t
P P R
(one may include any other cash flow that may arise during the
period.)
RETURN ON INFOSYS TECH.
? Price on 19 May 2009 Rs 1558.95
? Price on 19 May 2010 Rs 2642.60
? Dividend per Share
?October 15, 2009 Rs. 10.00
?Return 70.15%
RETURNS AND TAX
? Returns are affected by tax.
? In India dividend is not taxed in the hand of
an Investors,( but companies pay dividend distribution tax @ 15 %)
? On short term (less than 12 months) capital
gain 10% tax is payable. (without STT tax according to income-tax
slab)
? No tax is payable on long-term capital gain.
(without STT tax 20%)
EXPECTED RETURN
Current Price Future Price Prob. Return
130 8% 30%
120 30% 20%
110 25% 10%
100 100 15% 0%
90 12% -10%
80 8% -20%
70 2% -30%
Expected Return 7.50%
HOW DO WE FORM EXPECTATIONS
REGARDING THE FUTURE
? One possible way- on the basis of the past
behaviour of the variable.
RISK
? Risk is often defined as the variability of
expected returns
? We use statistical measures like standard
deviation, variance and coefficient of
variation to measure risk.
EXPECTED RETURN AND RISK
Current Price Future Price Prob. Return
130 8% 30%
120 30% 20%
110 25% 10%
100 100 15% 0%
90 12% -10%
80 8% -20%
70 2% -30%
Expected Return 7.50%
Standard Deviation 14.92%
HOW TO ESTIMATE RISK AND RETURN FROM
THE PAST DATA?
? The mean of the return can be taken as a
proxy for the Expected Return.
? The standard deviation (or variance) of
the past data can be taken as a proxy of
the risk.
M
o
n
t
h
l
y
R
e
t
u
r
n
s
HUL
Tata Steel
HUL TS
Average 1.14 3.51
SD 8.78 16.43
EQUITY VS BOND : RISK AND
RETURN
BSE SENSEX
180 days Govt Bill
Risk Free Securities
Government Securities
Corporate Bonds
Preference Shares
Equity of Large Companies
Equities of Small Companies
Risk
R
e
t
u
r
n
RISK RETURN AND TIME HORIZON
Distribution of Daily Returns on NSE Nifty
Mean =0.06% (15.66%)
SD =1.85% (461.58%)
CV =2947%
Distribution of Monthly (20 days) Returns on NSE
Mean =1.15% (14.31%)
SD =9.04% (112.94%)
CV =789%
Mean =12.68% (12.68%)
SD =32.02% (32.02%)
CV =253%
Distribution of Annual (250 days) Returns on NSE Nifty
Distribution of 2500 days Returns on NSE Nifty
Mean =94.17% (9.42%)
SD =45.49% (4.55%)
CV =48.31%
Distribution of 4000 days Returns on NSE Nifty
Mean =199.65% (12.48%)
SD =51.67% (3.32%)
CV =25.88%
RISK AND RETURN OF A
PORTFOLIO
WHAT IS PORTFOLIO
? When we invest our money in more than one
asset it is called a ‘portfolio’
EXPECTED RETURN OF A PORTFOLIO
? The expected return of a portfolio is equal to
the weighted average of the return on
individual assets constituting it.
n n p
R w R w R w R ...... ..........
2 2 1 1
+ + =
RISK IN A PORTFOLIO
? The standard deviation of a portfolio is not
equal to the weighted average of the
standard deviation of the individual security
returns. It will be less than the weighted
average unless the returns are perfectly
correlated.
? We get the benefit of diversification in the
form of reduced risk.
MARKOWITZ THEORY OF
PORTFOLIO: MEAN VARIANCE
ANALYSIS
? Although it was known earlier
that diversification reduces the
risk, but how does it work it
was not known.
? Harry Markowitz (1952) was
first to demonstrate statistically
how diversification works.
? He was given Nobel Memorial
Prize in Economic Science in
1990.
Harry Markowitz
CONCEPTS REVISITED
) )( (
1
,
y y x x
n
Cov
y x
÷ ÷ =
¿
Covariance
Correlation
y x
y x
y x
Cov
r
o o
,
,
=
CONCEPTS REVISITED
xy
y x y x
Cov . 2
2
2 2
+ + =
+
o o o
PORTFOLIO RISK: CASE OF TWO
SECURITIES
2 , 1 1 1 2 1
2
2
2
2
2
1
2
1
2 , 1
2
2 r w w w w o o o o o + + =
or
2 , 1 2 1
2
2
2
2
2
1
2
1
2 , 1
2
cov 2 w w w w + + = o o o
FOR YOUR DISCUSSION
? What will happen if:
r = 1
r = 0
r = -1
HOW DO THE RETURN AND THE
RISK CHANGES WITH CHANGE IN
WEIGHTS
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
7.50 8.50 9.50 10.50 11.50
Stdev
R
e
t
Minimum Variance Portfolio
Non-Efficient Portfolios
Efficient Portfolio Frontier
MINIMUM VARIANCE PORTFOLIO
2 , 1 2 1
2
2
2
2
2
1
2
1
2 , 1
2
cov 2 w w w w + + = o o o
2 , 1 1 1
2
2
2
1
2
1
2
1
2 , 1
2
cov ) 1 ( 2 ) 1 ( w w w w ÷ + ÷ + = o o o
Portfolio Variance is
OR
Differentiate w.r.t. w1 and obtain minima
2 , 1
2
2
2
1
2 , 1
2
2
1
cov 2
cov
÷ +
÷
=
o o
o
w
MIN-VARIANCE OPPORTUNITY SET
WITH DIFFERENT CORRELATION
BETWEEN TWO SECURITIES
r=1
13%
% 8
12% 20%
r = +0.3
?
p
E(r
p
)
r =-1
r =-1
CASE OF MULTIPLE SECURITIES
¿¿
= =
=
n
j
n
i
j i j i p
Cov w w
1 1
,
2
o
CASE OF MULTIPLE SECURITIES
Sec 1 Sec 2 Sec 3 Sec n
Sec 1 …… ….
Sec 2 ……….
Sec 3 ……..
.
. ………
Sec n ………..
2
1
2
1
o w
2 , 1 2 1
o w w
3 , 1 3 1
o w w
n n
w w
, 1 1
o
2 , 1 2 1
o w w
2
2
2
2
o w
3 , 2 3 2
o w w
n n
w w
, 2 2
o
3 , 1 3 1
o w w
3 , 2 3 2
o w w
2
3
2
3
o w
n n
w w
, 3 3
o
n n
w w
, 1 1
o
n n
w w
, 2 2
o
n n
w w
, 3 3
o
2 2
n n
w o
Variance Terms
Co-Variance Terms
n
s d
Diversifiable or Unsystematic Risk
Non-diversifiable
or Systematic Risk
Company
Industry
National Economy
International Economy
INTUITIVE EXPLANATION OF
DIVERSIFICATION
? Risk in a single company
?International Economy Risk + National Economy
Risk + Industry Specific Risk + Company’s
Unique Risk
INTUITIVE EXPLANATION OF
DIVERSIFICATION
? Risk in a single industry
?International Economy Risk + National Economy
Risk + Industry’s unique Risk
?Risk unique to individual company diversified
away
INTUITIVE EXPLANATION OF
DIVERSIFICATION
? Risk in different industries within a national
economy
?International Economy Risk + National Economy
Risk
?Risk unique to individual company and unique to
specific industry diversified away
OPPORTUNITY SET AND EFFICIENT
FRONTIER FOR MULTIPLE SECURITIES
EQUILIBRIUM OF INDIVIDUAL
INVESTOR
A
B
R
i
s
k
Return
PROBLEM WITH MARKOWITZ MODEL
? As the number of securities increase
Markowitz Model becomes unmanageable.
We need to compute all the variances and
Covariance for all the possible pairs of the
securities
CAPITAL ASSET PRICING
MODEL (CAPM)
DEVELOPMENT OF CAPM
• CAPM was developed by William
Sharpe, building on Portfolio
Theory of Markowitz and Two
Fund Separation Theory of Tobin
• Sharpe was awarded Noble Prize
in Economic Science for his work
in 1990
William Sharpe
TWO FUNDS SEPARATION AND
CAPITAL MARKET LINE
Market
Portfolio
Rf
Rm
A
B
?m
James Tobin
EQUATION OF CAPITAL MARKET LINE
(CML)
( )
f m
m
p
f p
R R R R ÷ + =
o
o
Return on Portfolio=
Risk free Return
+Relative risk of Portfolio * Market Risk Premium
Rf
Optimization with Borrowing Restrictions
RL
Different Lending and Borrowing Rates
RB
y = 1.570x + 0.778
R² = 0.634
E
x
c
e
s
s
R
e
t
u
r
n
o
n
T
a
t
a
S
t
e
e
l
Excess Return on Market
Characteristic Line
Equation of Charecteristic Line
t m i
R R c | o + + =
Beta
Alfa
BETA
? What is Beta:
?Beta of a security (or portfolio) is the
sensitivity of the expected return on that
security in response to a change in
expected return on market portfolio.
m
M i
i
R R Cov
2
,
) (
o
| =
WHAT IS THE IMPORTANCE OF BETA
? Beta is the measurement of the
systematic risk.
? When an investor invests in a well
diversified market portfolio he can
diversify away all the unsystematic risk
and only systematic risk is the relevant
measure of the risk for him.
E
x
c
e
s
s
R
e
t
u
r
n
Beta
Security Market Line
HUL
SML
Infosys
Wipro
SBI
Tata
Steel
SAIL
EQUATION OF SECURITY MARKET
LINE
( ) ( )
f m j f j
R R R R ÷ = ÷ |
) (
f m j f j
R R R R ÷ + = |
or
doc_179524587.pptx