international

Published on June 2016 | Categories: Documents | Downloads: 24 | Comments: 0 | Views: 225
of 21
Download PDF   Embed   Report

Comments

Content

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



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

Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close