Efficient Market Hypothesis & Random Walk Theory

The EMH evolved in the 1960s from the Ph.D.

dissertation of Eugene Fama. Fama persuasively made

the argument that the securities will be appropriately

priced and reflect all available information. If a market

is efficient, no information or analysis can be expected

to result in out performance of an appropriate

benchmark. An investment theory that states that it is

impossible to "beat the market" because stock market

efficiency causes existing share prices to always

incorporate and reflect all relevant information.

According to the EMH, this means that stocks always

trade at their fair value on stock exchanges, and thus it

is impossible for investors to either purchase

undervalued stocks or sell stocks for inflated prices.

Thus, the crux of the EMH is that it should be

impossible to outperform the overall market through

expert stock selection or market timing, and that the

only way an investor can possibly obtain higher returns

Dr.BRR

is by

purchasing riskier investments.

Dr. BRR

IAPM

IAPM

Degrees of efficiency [Forms of EMH]

Weak efficiency [Weak Form]:

It claims: the current prices of stocks already fully reflect all the

information that is contained in the historical sequence of prices.

This means:

(1) No relationship between the past & future price movements.

(2) No investment pattern can be discerned/detected as prices take

Random Walk

Hence:

Technical analysis can’t be used to predict and beat the market &

simply follow buy and hold policy

Semi-strong efficiency [Semi-strong Form]:

This form of EMH implies / asserts that the current prices of stocks

not only reflect all informational content of historical prices but also

reflect all public information [earnings, dividends, splits, mergers etc]

about the corporations being studied. The stock prices adjust rapidly

to all publicly available information.

Hence:

Neither Fundamental nor Technical Analysis can be used to achieve

Dr.BRR

superior

gains consistently.

Dr. BRR

IAPM

Strong efficiency [Strong Form]:

This is the strongest version, which states that all information in a

market, whether public or private, is accounted for in a stock price.

Not even insider information could give an investor an advantage.

It has two forms: (1) Near strong [conclusions & opinions of

Analysts & Fund managers based on publicly available Information is

also reflected in the prices]

(2) Super strong [stock prices also reflect private

information held & known by Insiders] form.

Conclusion: All forms of efficiency can not be accepted all time and

everywhere. Weak form is acceptable. Semi-strong is also o.k. but

the question remains whether all public information is reflected

quickly & accurately. Strong form [that to super strong] may not be

found in India.

Dr.BRR

Dr. BRR

IAPM

Portfolio

Theory

Modern portfolio theory (MPT)—or portfolio theory—was introduced by Harry

Markowitz with his paper "Portfolio Selection," which appeared in the 1952

Journal of Finance. Thirty-eight years later [1990], he shared a Nobel Prize

with Merton Miller and William Sharpe for what has become a broad theory

for portfolio selection. Markowitz’s approach is defining risk & return for the

entire portfolio.

Portfolio Return

Let, p is portfolio of assets i (i =1,2,3,…n), W i = weight of assets i ,

n = assets from 1 to n, R= Actual or Realised Rate of Return,

E (R) = Expected Rate of Return

Actual Portfolio Return

Expected Portfolio Return

n

Rp=∑WiRi

i=1

n

E (R p) = ∑ W i E (R i)

i=1

Dr.BRR

Dr. BRR

IAPM

S.D.

of

Portfolio

Return

( %)

Diversification of Risk – Portfolio Approach

Non-Systematic Risk

How to mitigate? Ans: IAPM

Systematic Risk

How to mitigate? Ans: Hedging

Number of securities in the portfolio

Dr.BRR

Dr. BRR

IAPM

Capital Asset

Extension of Markowitz

Portfolio theory by

Introducing systematic

& specific risk

Pricing Model

CAPM

William Sharpe (1964)

published the CAPM

Parallel work by

John Lintner (1965)

Jan Mossin (1966)

E (R i) = R f + βi [ E (R M) – R f ]

For his work on CAPM, Sharpe shared the 1990 Nobel Prize in

Economics with Harry Markowitz and Merton Miller.

CAPM essentially answers questions like:

CML: What is the relationship between risk and return of an efficient

portfolio? [Macro context]

SML: What is the relationship between risk and return of an individual

security? [Micro context]

CAPM produces bench mark for evaluation of investments

It helps to make an informed guess about the expected return from a

security which is yet to hit/debut the market [IPO]. It serves as a

model for the pricing of risky securities. CAPM says that the expected

return of a security or a portfolio equals the rate on a risk-free

security plus a risk premium.

Dr.BRR

Dr. BRR

Portfolio Risk

IAPM

Risk of a Two-Asset Portfolio

Var (R p) = WA2 Var (RA) + WB2 Var (RB) + 2 WAWB Cov (RA , RB)

Note: Cov (RA , RB) = ∑ pi [RAi - E(RA)] [RBi - E(RB)]

Var (RA) = ∑ pi [RAi - E(RA)]2

Risk of Three-Asset Portfolio:

σ 2ABC= σ 2AW 2 A + σ 2 BW

2

B

+ σ 2 CW

2

C

+ 2 [CovABWAWB+CovBCWBWC+CovCAWCWA]

Risk of Four-Asset Portfolio:

σ 2ABCD= σ 2AW 2 A + σ 2 BW 2 B + σ 2 CW 2 C + σ 2 DW 2 D +

2 [CovABWAWB+CovBCWBWC+CovCAWCWA+CovADWAWD+CovBDWBWD+CovCDWCWA]

Minimum Risk or Min Variance Portfolio

Risk of an n-Asset Portfolio

2

y Cov xy

σ 2p = ∑ ∑ W i W j r ij σ i σ j w*

2

2

2Cov xy

x

y

Risk in the context of Stocks

WA =

σ2 B - σ A σ B ρ AB

σ2 A + σ2 B - 2σ A σ B ρ AB

Risk = Systematic [market/non-diversifiable] Risk + Unsystematic Risk

Let, j = security, R = return, M = Market or Index, β = Beta

(a)

(b)

Systematic Risk = [βj2 ] x σ 2M = r2jM x σ 2j

Unsyst. Risk = [σ 2j – Systematic Risk] = σ 2j [1 – r2jM]

Dr.BRR

2

Note: σ2 = ∑ Pi (Ki - K )2 = ∑ (Ki - K )

n-1

rAB = Cov

Cov

AB

/σ

A

σ

B

AB

= rAB σ

A

σ

B

Dr. BRR

IAPM

Assumptions of CAPM

1. Perfect Market-There are no taxes or transaction costs, securities

are divisible and market is competitive.

2. Individuals have identical investment / time horizons.

3. Homogeneous expectations- Individuals have identical opinions

about expected returns [Means], volatilities [Variance] and

correlations

[Co-variances among variables] of available investments. OR All

investors have the same information and interpret it in the same

manner.

4. Individuals are risk averse.

5. Individuals can borrow and lend freely at risk less rate of interest.

6. The quantity of risky securities in the market is given.

7. The market portfolio exists, measurable & is on the MVE frontier.

[The portfolios that have the highest return for a given level of risk are

called the mean-variance efficient frontier (MVE)].

→ Assumptions make CAPM unrealistic but empirical studies suggest that

conclusions of CAPM are reasonably valid.

Dr.BRR

Dr. BRR

IAPM

Capital market line [CML]

The CML is derived by drawing a tangent line from the intercept point [i.e.,

the R f]. through the market portfolio S. The CML is considered to be superior

to the efficient frontier since it takes in to account the inclusion of a risk free

asset in the portfolio. It is linear relationship between E (R p) and σ p.

CML EQUATION: E (R p) = R f + λ σ p

Where, λ = Slope of CML = Price of risk = [E(R M) – R f ] / σ M

E

E (R p)

D

C

S

B

Rf

CML

A

F

G

S is Super Efficient Portfolio

Due to leverage/De-leverage,

D & B are better than G & F

Respectively. Again thanks

to R f , A is better than F

But, S can not remain so.

There will be adjustment. Refer Next Slide

σp

Dr.BRR

Dr. BRR

Security Market Line [SML]

IAPM

There is a linear relationship between individual securities’ expected return

and their covariance with the market portfolio. This relationship is called SML

[equation (1) or (2)]. CML is a special case of the SML [refer next slide].

E (R j ) = R f + {[E (R M) – R f] / σ2M} σ j M ………….(1)

Where, E (R j ) = expected return on security j, R f = risk free return,

R M = expected return on market Portfolio, σ2M = Variance of return

on market portfolio, σ j M= Covariance of return between security j

and market Portfolio, Note: {[E (R M) – R f] / σ2M} = Price per unit of risk

As, βj = σj M / σ2M SML: E (R j ) = R f + [E (R M) – R f] β j ………….(2)

Return ( %)

SML Graph:

Dr.BRR

E (r m)

SML

Rf

Risk [Beta j ]

Dr. BRR

IAPM

CHARACTERISTIC LINE [Hypothetical Regression Line]

A line that best fits the points representing the returns on the

Asset and the market is called characteristic line. The slope of the

line is the beta of the asset which measures the risk of a security

relative to the market.

(R j – R f) = α j + βj (R M – R f)

R j = a + βj R M

Rj

Characteristic Line

BETA

NOTE:

Alpha of Stock A = R A – E ( R A) as per CAPM

Alpha

Dr.BRR

Rm

Dr. BRR

IAPM

Arbitrage Pricing Theory

An alternative asset pricing model to the CAPM. Unlike the Capital

Asset Pricing Model, which specifies returns as a linear function of

only systematic risk, Arbitrage Pricing Theory specifies returns as

a linear function of more than a single factor. It was developed by

Stephen Ross. A few Assumptions are akin to CAPM but the different

ones are: It does not assume [unlike CAPM] single period time

horizon, absence of taxes, unrestricted lending and borrowing at Rf.

APT assumes that the return on any stock is linearly related to a set of

factors also referred to as systematic factors or risk factors as given

in the following equation.

R i = a i + b i 1 I 1 + b i 2 I 2 +………..+ b i j I j + e i

Where, R i = Return on stock i

a i = Expected return on stock i if all factors have a value zero

I j = Value of jth factor which influences the return on stock i ( j =

1,2,…)

b i j = Sensitivity of stock i’s return to the jth factor

e i = Random error term

Dr.BRR

Dr. BRR

IAPM

Portfolio Management Framework

Portfolio Management Process:

Policy Statement

Formulation of Portfolio Strategy

Selection of Securities

Portfolio Execution

Portfolio Revision

Performance Evaluation

Dr.BRR

Dr. BRR

Policy Statement – Step 1

IAPM

Return

Percent Invested

Objectives

Specify Investment Objectives: Returns-Income, Growth, Stability & Risk Tolerance & Utility

Risk Tolerance = Number from 0 to 100.

σ 2p

Utility = [R p – Risk Penalty]

NOTE: Risk Penalty =

Risk Tolerance

More the Utility, the better

Constraints

liquidity, Time horizon, laws/regulations, tax considerations etc

Policy

Asset Mix & allocation, diversification, Quality criteria [minimum rating for bonds]

Penny Stocks

Mid Caps

Equities

Small Caps

M.Funds

FDs

Blue-Chip Shares

Bonds

PPF

Dr.BRR

Risk Tolerance

Risk

Dr. BRR

IAPM

Formulation of Portfolio Strategy – Step 2

Passive

Active

Create

Well-diversified

Portfolio &

Hold on to it

Market Timing

Sector Rotation

Security Selection

Specialized Philosophy

Selection of Securities – Step 3

Market Efficiency

Zero Weak Semi-Strong Strong

Fundamental Analysis

Dr.BRR

Technical Analysis

EMH: Random-Walk Theory

EMH

Fundamental + EMH

More of Fundamental

Technical

Approach

Dr. BRR

IAPM

Portfolio Execution –– Step 4

Implement Steps 1-3

Portfolio Revision –– Step 5

Portfolio Rebalancing: Buy & Hold, Constant Mix, Portfolio Insurance

Portfolio Upgrading: Sell overpriced securities & Buy underpriced

Portfolio Evaluation –– Step 6

Compute: Risk and Return of portfolio

Performance measures: Treynor Measure, Sharpe Measure & Jensen Measure

Treynor Measure =

Sharpe Measure =

R p– R f

σp

R p– R f

Jensen Measure = R

βp

p–

[R f + β p (R M – R f)]

Note: By definition, Market Index = 0 [for Jensen Measure]

Jensen Measure is also known as Jensen’s Alpha

Fama Model = R

Dr.BRR

p–

[R f + σ p /σ M (R M – R f)]

Dr. BRR

IAPM

1. From the following find Under priced and

over priced securities given that return on Nifty is

28 % and return on T-bill is 8 %.

Securities

Beta

Actual returns %

ACC

1.2

30

RIL

1.3

59

Sterlite

1.3

61

TV 18

1.5

40

BHEL

0.9

26

Apollo Tyres

0.98

31

Praj Industries

1.6

37

RCOM

1.8

52

Dr.BRR

Dr. BRR

IAPM

2. The following information brings out the performance

of the three mutual funds for the latest concluded fiscal.

The 182 day Treasury bill fetches 7 percent return.

Rank the above funds according to Sharpe, Treynor and

Jensen’s alpha measures.

Fund houses

Mean Return

S.D.

Beta

SBI Fund

25.35

15.6

1.3

Templeton Fund

35.1

20

1.6

HDFC Fund

30

22.5

0.9

NIFTY

15

12.2

1

Dr.BRR

Dr. BRR

IAPM

3. From the following find characteristic line

and the systematic and unsystematic risk

components of RNRL stock.

Month

1

2

3

4

5

6

7

8

9

10

11

12

Price of RNRL Nifty Values

81

83

87

88

92

107

110

99

95

94

92

90

4128

4169

4210

4272

4210

4315

4335

4324

4189

4231

4215

4200

Dr. BRR

IAPM

4. Dr. Anil, the Chief Economist of Reliance Investment advisory

services has developed an economic forecast in terms of three economic

scenarios vis-à-vis probabilities. The company’s investment analyst, Mr.

Lloyd, based on Anil’s forecast, has projected the annual returns of

stocks of HUL, Dabur and ITC. The return on 182 day T-Bill is 8 %.

(a) Find the Expected return and Variance of returns for a portfolio

comprising 50% of HUL, 20% of Dabur and 30% of ITC.

(b) Find the Expected return and Variance of returns for a portfolio

comprising 50% of ITC, 30% of Dabur and 20% of HUL.

(c) Which of the above do you prefer? Why?

Scenarios

Probabilities

Conditional return (%)

HUL

Dabur

ITC

Recession

0.1

-3

-6

-10

Normal

0.6

30

36

35

Boom

0.3

40

42

45

Dr.BRR

Dr. BRR

IAPM

5. Given the following data for a two security portfolio, find the minimum

variance portfolio. Also calculate the return and risk of the portfolio.

Security

Return

Standard deviation

ρCD

Coal India

JP Associates

26.9

17.5

22.3 %

51.0 %

-0.12

WA =

σ2 B - σ A σ B ρ AB

σ2 A + σ2 B - 2σ A σ B ρ AB

WB = 1 - WA

R p = WA (RA) + WB (RB)

Var (R p) = WA2 Var (RA) + WB2 Var (RB) + 2 WAWB CovAB

Note: CovAB = rAB σ

A

σ

B

Dr. BRR

The EMH evolved in the 1960s from the Ph.D.

dissertation of Eugene Fama. Fama persuasively made

the argument that the securities will be appropriately

priced and reflect all available information. If a market

is efficient, no information or analysis can be expected

to result in out performance of an appropriate

benchmark. An investment theory that states that it is

impossible to "beat the market" because stock market

efficiency causes existing share prices to always

incorporate and reflect all relevant information.

According to the EMH, this means that stocks always

trade at their fair value on stock exchanges, and thus it

is impossible for investors to either purchase

undervalued stocks or sell stocks for inflated prices.

Thus, the crux of the EMH is that it should be

impossible to outperform the overall market through

expert stock selection or market timing, and that the

only way an investor can possibly obtain higher returns

Dr.BRR

is by

purchasing riskier investments.

Dr. BRR

IAPM

IAPM

Degrees of efficiency [Forms of EMH]

Weak efficiency [Weak Form]:

It claims: the current prices of stocks already fully reflect all the

information that is contained in the historical sequence of prices.

This means:

(1) No relationship between the past & future price movements.

(2) No investment pattern can be discerned/detected as prices take

Random Walk

Hence:

Technical analysis can’t be used to predict and beat the market &

simply follow buy and hold policy

Semi-strong efficiency [Semi-strong Form]:

This form of EMH implies / asserts that the current prices of stocks

not only reflect all informational content of historical prices but also

reflect all public information [earnings, dividends, splits, mergers etc]

about the corporations being studied. The stock prices adjust rapidly

to all publicly available information.

Hence:

Neither Fundamental nor Technical Analysis can be used to achieve

Dr.BRR

superior

gains consistently.

Dr. BRR

IAPM

Strong efficiency [Strong Form]:

This is the strongest version, which states that all information in a

market, whether public or private, is accounted for in a stock price.

Not even insider information could give an investor an advantage.

It has two forms: (1) Near strong [conclusions & opinions of

Analysts & Fund managers based on publicly available Information is

also reflected in the prices]

(2) Super strong [stock prices also reflect private

information held & known by Insiders] form.

Conclusion: All forms of efficiency can not be accepted all time and

everywhere. Weak form is acceptable. Semi-strong is also o.k. but

the question remains whether all public information is reflected

quickly & accurately. Strong form [that to super strong] may not be

found in India.

Dr.BRR

Dr. BRR

IAPM

Portfolio

Theory

Modern portfolio theory (MPT)—or portfolio theory—was introduced by Harry

Markowitz with his paper "Portfolio Selection," which appeared in the 1952

Journal of Finance. Thirty-eight years later [1990], he shared a Nobel Prize

with Merton Miller and William Sharpe for what has become a broad theory

for portfolio selection. Markowitz’s approach is defining risk & return for the

entire portfolio.

Portfolio Return

Let, p is portfolio of assets i (i =1,2,3,…n), W i = weight of assets i ,

n = assets from 1 to n, R= Actual or Realised Rate of Return,

E (R) = Expected Rate of Return

Actual Portfolio Return

Expected Portfolio Return

n

Rp=∑WiRi

i=1

n

E (R p) = ∑ W i E (R i)

i=1

Dr.BRR

Dr. BRR

IAPM

S.D.

of

Portfolio

Return

( %)

Diversification of Risk – Portfolio Approach

Non-Systematic Risk

How to mitigate? Ans: IAPM

Systematic Risk

How to mitigate? Ans: Hedging

Number of securities in the portfolio

Dr.BRR

Dr. BRR

IAPM

Capital Asset

Extension of Markowitz

Portfolio theory by

Introducing systematic

& specific risk

Pricing Model

CAPM

William Sharpe (1964)

published the CAPM

Parallel work by

John Lintner (1965)

Jan Mossin (1966)

E (R i) = R f + βi [ E (R M) – R f ]

For his work on CAPM, Sharpe shared the 1990 Nobel Prize in

Economics with Harry Markowitz and Merton Miller.

CAPM essentially answers questions like:

CML: What is the relationship between risk and return of an efficient

portfolio? [Macro context]

SML: What is the relationship between risk and return of an individual

security? [Micro context]

CAPM produces bench mark for evaluation of investments

It helps to make an informed guess about the expected return from a

security which is yet to hit/debut the market [IPO]. It serves as a

model for the pricing of risky securities. CAPM says that the expected

return of a security or a portfolio equals the rate on a risk-free

security plus a risk premium.

Dr.BRR

Dr. BRR

Portfolio Risk

IAPM

Risk of a Two-Asset Portfolio

Var (R p) = WA2 Var (RA) + WB2 Var (RB) + 2 WAWB Cov (RA , RB)

Note: Cov (RA , RB) = ∑ pi [RAi - E(RA)] [RBi - E(RB)]

Var (RA) = ∑ pi [RAi - E(RA)]2

Risk of Three-Asset Portfolio:

σ 2ABC= σ 2AW 2 A + σ 2 BW

2

B

+ σ 2 CW

2

C

+ 2 [CovABWAWB+CovBCWBWC+CovCAWCWA]

Risk of Four-Asset Portfolio:

σ 2ABCD= σ 2AW 2 A + σ 2 BW 2 B + σ 2 CW 2 C + σ 2 DW 2 D +

2 [CovABWAWB+CovBCWBWC+CovCAWCWA+CovADWAWD+CovBDWBWD+CovCDWCWA]

Minimum Risk or Min Variance Portfolio

Risk of an n-Asset Portfolio

2

y Cov xy

σ 2p = ∑ ∑ W i W j r ij σ i σ j w*

2

2

2Cov xy

x

y

Risk in the context of Stocks

WA =

σ2 B - σ A σ B ρ AB

σ2 A + σ2 B - 2σ A σ B ρ AB

Risk = Systematic [market/non-diversifiable] Risk + Unsystematic Risk

Let, j = security, R = return, M = Market or Index, β = Beta

(a)

(b)

Systematic Risk = [βj2 ] x σ 2M = r2jM x σ 2j

Unsyst. Risk = [σ 2j – Systematic Risk] = σ 2j [1 – r2jM]

Dr.BRR

2

Note: σ2 = ∑ Pi (Ki - K )2 = ∑ (Ki - K )

n-1

rAB = Cov

Cov

AB

/σ

A

σ

B

AB

= rAB σ

A

σ

B

Dr. BRR

IAPM

Assumptions of CAPM

1. Perfect Market-There are no taxes or transaction costs, securities

are divisible and market is competitive.

2. Individuals have identical investment / time horizons.

3. Homogeneous expectations- Individuals have identical opinions

about expected returns [Means], volatilities [Variance] and

correlations

[Co-variances among variables] of available investments. OR All

investors have the same information and interpret it in the same

manner.

4. Individuals are risk averse.

5. Individuals can borrow and lend freely at risk less rate of interest.

6. The quantity of risky securities in the market is given.

7. The market portfolio exists, measurable & is on the MVE frontier.

[The portfolios that have the highest return for a given level of risk are

called the mean-variance efficient frontier (MVE)].

→ Assumptions make CAPM unrealistic but empirical studies suggest that

conclusions of CAPM are reasonably valid.

Dr.BRR

Dr. BRR

IAPM

Capital market line [CML]

The CML is derived by drawing a tangent line from the intercept point [i.e.,

the R f]. through the market portfolio S. The CML is considered to be superior

to the efficient frontier since it takes in to account the inclusion of a risk free

asset in the portfolio. It is linear relationship between E (R p) and σ p.

CML EQUATION: E (R p) = R f + λ σ p

Where, λ = Slope of CML = Price of risk = [E(R M) – R f ] / σ M

E

E (R p)

D

C

S

B

Rf

CML

A

F

G

S is Super Efficient Portfolio

Due to leverage/De-leverage,

D & B are better than G & F

Respectively. Again thanks

to R f , A is better than F

But, S can not remain so.

There will be adjustment. Refer Next Slide

σp

Dr.BRR

Dr. BRR

Security Market Line [SML]

IAPM

There is a linear relationship between individual securities’ expected return

and their covariance with the market portfolio. This relationship is called SML

[equation (1) or (2)]. CML is a special case of the SML [refer next slide].

E (R j ) = R f + {[E (R M) – R f] / σ2M} σ j M ………….(1)

Where, E (R j ) = expected return on security j, R f = risk free return,

R M = expected return on market Portfolio, σ2M = Variance of return

on market portfolio, σ j M= Covariance of return between security j

and market Portfolio, Note: {[E (R M) – R f] / σ2M} = Price per unit of risk

As, βj = σj M / σ2M SML: E (R j ) = R f + [E (R M) – R f] β j ………….(2)

Return ( %)

SML Graph:

Dr.BRR

E (r m)

SML

Rf

Risk [Beta j ]

Dr. BRR

IAPM

CHARACTERISTIC LINE [Hypothetical Regression Line]

A line that best fits the points representing the returns on the

Asset and the market is called characteristic line. The slope of the

line is the beta of the asset which measures the risk of a security

relative to the market.

(R j – R f) = α j + βj (R M – R f)

R j = a + βj R M

Rj

Characteristic Line

BETA

NOTE:

Alpha of Stock A = R A – E ( R A) as per CAPM

Alpha

Dr.BRR

Rm

Dr. BRR

IAPM

Arbitrage Pricing Theory

An alternative asset pricing model to the CAPM. Unlike the Capital

Asset Pricing Model, which specifies returns as a linear function of

only systematic risk, Arbitrage Pricing Theory specifies returns as

a linear function of more than a single factor. It was developed by

Stephen Ross. A few Assumptions are akin to CAPM but the different

ones are: It does not assume [unlike CAPM] single period time

horizon, absence of taxes, unrestricted lending and borrowing at Rf.

APT assumes that the return on any stock is linearly related to a set of

factors also referred to as systematic factors or risk factors as given

in the following equation.

R i = a i + b i 1 I 1 + b i 2 I 2 +………..+ b i j I j + e i

Where, R i = Return on stock i

a i = Expected return on stock i if all factors have a value zero

I j = Value of jth factor which influences the return on stock i ( j =

1,2,…)

b i j = Sensitivity of stock i’s return to the jth factor

e i = Random error term

Dr.BRR

Dr. BRR

IAPM

Portfolio Management Framework

Portfolio Management Process:

Policy Statement

Formulation of Portfolio Strategy

Selection of Securities

Portfolio Execution

Portfolio Revision

Performance Evaluation

Dr.BRR

Dr. BRR

Policy Statement – Step 1

IAPM

Return

Percent Invested

Objectives

Specify Investment Objectives: Returns-Income, Growth, Stability & Risk Tolerance & Utility

Risk Tolerance = Number from 0 to 100.

σ 2p

Utility = [R p – Risk Penalty]

NOTE: Risk Penalty =

Risk Tolerance

More the Utility, the better

Constraints

liquidity, Time horizon, laws/regulations, tax considerations etc

Policy

Asset Mix & allocation, diversification, Quality criteria [minimum rating for bonds]

Penny Stocks

Mid Caps

Equities

Small Caps

M.Funds

FDs

Blue-Chip Shares

Bonds

PPF

Dr.BRR

Risk Tolerance

Risk

Dr. BRR

IAPM

Formulation of Portfolio Strategy – Step 2

Passive

Active

Create

Well-diversified

Portfolio &

Hold on to it

Market Timing

Sector Rotation

Security Selection

Specialized Philosophy

Selection of Securities – Step 3

Market Efficiency

Zero Weak Semi-Strong Strong

Fundamental Analysis

Dr.BRR

Technical Analysis

EMH: Random-Walk Theory

EMH

Fundamental + EMH

More of Fundamental

Technical

Approach

Dr. BRR

IAPM

Portfolio Execution –– Step 4

Implement Steps 1-3

Portfolio Revision –– Step 5

Portfolio Rebalancing: Buy & Hold, Constant Mix, Portfolio Insurance

Portfolio Upgrading: Sell overpriced securities & Buy underpriced

Portfolio Evaluation –– Step 6

Compute: Risk and Return of portfolio

Performance measures: Treynor Measure, Sharpe Measure & Jensen Measure

Treynor Measure =

Sharpe Measure =

R p– R f

σp

R p– R f

Jensen Measure = R

βp

p–

[R f + β p (R M – R f)]

Note: By definition, Market Index = 0 [for Jensen Measure]

Jensen Measure is also known as Jensen’s Alpha

Fama Model = R

Dr.BRR

p–

[R f + σ p /σ M (R M – R f)]

Dr. BRR

IAPM

1. From the following find Under priced and

over priced securities given that return on Nifty is

28 % and return on T-bill is 8 %.

Securities

Beta

Actual returns %

ACC

1.2

30

RIL

1.3

59

Sterlite

1.3

61

TV 18

1.5

40

BHEL

0.9

26

Apollo Tyres

0.98

31

Praj Industries

1.6

37

RCOM

1.8

52

Dr.BRR

Dr. BRR

IAPM

2. The following information brings out the performance

of the three mutual funds for the latest concluded fiscal.

The 182 day Treasury bill fetches 7 percent return.

Rank the above funds according to Sharpe, Treynor and

Jensen’s alpha measures.

Fund houses

Mean Return

S.D.

Beta

SBI Fund

25.35

15.6

1.3

Templeton Fund

35.1

20

1.6

HDFC Fund

30

22.5

0.9

NIFTY

15

12.2

1

Dr.BRR

Dr. BRR

IAPM

3. From the following find characteristic line

and the systematic and unsystematic risk

components of RNRL stock.

Month

1

2

3

4

5

6

7

8

9

10

11

12

Price of RNRL Nifty Values

81

83

87

88

92

107

110

99

95

94

92

90

4128

4169

4210

4272

4210

4315

4335

4324

4189

4231

4215

4200

Dr. BRR

IAPM

4. Dr. Anil, the Chief Economist of Reliance Investment advisory

services has developed an economic forecast in terms of three economic

scenarios vis-à-vis probabilities. The company’s investment analyst, Mr.

Lloyd, based on Anil’s forecast, has projected the annual returns of

stocks of HUL, Dabur and ITC. The return on 182 day T-Bill is 8 %.

(a) Find the Expected return and Variance of returns for a portfolio

comprising 50% of HUL, 20% of Dabur and 30% of ITC.

(b) Find the Expected return and Variance of returns for a portfolio

comprising 50% of ITC, 30% of Dabur and 20% of HUL.

(c) Which of the above do you prefer? Why?

Scenarios

Probabilities

Conditional return (%)

HUL

Dabur

ITC

Recession

0.1

-3

-6

-10

Normal

0.6

30

36

35

Boom

0.3

40

42

45

Dr.BRR

Dr. BRR

IAPM

5. Given the following data for a two security portfolio, find the minimum

variance portfolio. Also calculate the return and risk of the portfolio.

Security

Return

Standard deviation

ρCD

Coal India

JP Associates

26.9

17.5

22.3 %

51.0 %

-0.12

WA =

σ2 B - σ A σ B ρ AB

σ2 A + σ2 B - 2σ A σ B ρ AB

WB = 1 - WA

R p = WA (RA) + WB (RB)

Var (R p) = WA2 Var (RA) + WB2 Var (RB) + 2 WAWB CovAB

Note: CovAB = rAB σ

A

σ

B

Dr. BRR