Dr.BRR

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 is by purchasing riskier investments.

IAPM

Dr. BRR

Dr.BRR

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

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Dr. BRR

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 superior gains consistently. Dr. BRR

Dr.BRR

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.

IAPM

Dr. BRR

Dr.BRR

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

R p = ∑ W i R i i=1

n E (R p) = ∑ W i E (R i)

n

i=1

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Dr. BRR

Dr.BRR

Diversification of Risk – Portfolio Approach

S.D.

of

Portfolio

Return

( %)

Number of securities in the portfolio

Non-Systematic Risk

Systematic Risk How to mitigate? Ans: Hedging Systematic Risk

How to mitigate? Ans: IAPM

IAPM

Dr. BRR

Dr.BRR

Capital Asset Pricing Model

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.

E (R i) = R f + βi [ E (R M) – R f ]

CAPM

William Sharpe (1964)

published the CAPM

Parallel work by

John Lintner (1965)

Jan Mossin (1966)

Extension of Markowitz

Portfolio theory by

Introducing systematic

& specific risk

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Dr. BRR

Dr.BRR

Portfolio Risk

Risk of a Two-Asset Portfolio

Var (R p) = WA2 Var (RA) + WB

2 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 an n-Asset Portfolio

σ 2p = ∑ ∑ W i W j r ij σ i σ j

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]

Risk in the context of Stocks

Risk = Systematic [market/non-diversifiable] Risk + Unsystematic Risk Let, j = security, R = return, M = Market or Index, β = Beta (a) Systematic Risk = [βj

2 ] x σ 2M = r2jM x σ 2j

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

IAPM

Dr. BRR Note: σ2 = ∑ Pi (Ki - K )2 = rAB = Cov AB / σ A σ B

∑ (Ki - K )2

n-1

2

2 2

Cov*

2Cov

y xy

x y xy

w

Minimum Risk or Min Variance Portfolio

Cov AB = rAB σ A σ B

=

σ2 A + σ2

B - 2σ A σ B ρ AB

σ2 B - σ A σ B ρ AB

WA

Dr.BRR

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.

IAPM

Dr. BRR

Dr.BRR

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

σ p

E (R p)

R f

S

A

C

B

D

E

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

CML

But, S can not remain so. There will be adjustment. Refer Next Slide

But, S can not remain so. There will be adjustment. Refer Next Slide

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Dr. BRR

Dr.BRR

Security Market Line [SML]

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)

SML Graph:

SML

Risk [Beta j ]

E (r m)

β = 1

R f

Re

turn

( %

)

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Dr. BRR

Dr.BRR

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

BETA

R m

R j

Alpha

Characteristic Line

NOTE:

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

IAPM

Dr. BRR

Dr.BRR

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

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Dr. BRR

Dr.BRR

Portfolio Management Framework

Portfolio Management Process:

Policy Statement

Formulation of Portfolio Strategy

Selection of Securities

Portfolio Execution

Portfolio Revision

Performance Evaluation

IAPM

Dr. BRR

Dr.BRR

Policy Statement – Step 1 Objectives

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

Risk Tolerance = Number from 0 to 100.

Utility = [R p – Risk Penalty] NOTE: Risk Penalty =

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]

Re

turn

Risk

PPF

Mid Caps

Blue-Chip Shares

M.Funds

Bonds

FDs

Penny Stocks

Small Caps

σ 2p

Risk Tolerance

Risk Tolerance

Pe

rce

nt

In

ve

ste

d

Equities

IAPM

Dr. BRR

Dr.BRR

Formulation of Portfolio Strategy – Step 2

Active

Market Timing Sector Rotation

Security Selection Specialized Philosophy

Passive Create

Well-diversified Portfolio &

Hold on to it

Selection of Securities – Step 3

EMH: Random-Walk Theory Technical Analysis Fundamental Analysis

Ma

rke

t E

ffic

ien

cy

Ze

ro

We

ak

S

em

i-S

tro

ng

S

tro

ng

Approach

More of Fundamental

Fundamental + EMH

EMH

Technical

IAPM

Dr. BRR

Dr.BRR

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

Note: By definition, Market Index = 0 [for Jensen Measure] Jensen Measure is also known as Jensen’s Alpha Fama Model =

R p – R f

β p

σ p Sharpe Measure =

R p – R f Jensen Measure =

Treynor Measure =

R p – [R f + β p (R M – R f)]

IAPM

Dr. BRR R p – [R f + σ p /σ M (R M – R f)]

Dr.BRR

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 %.

IAPM

Dr. BRR

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

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

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Dr. BRR

3. From the following find characteristic line and the systematic and unsystematic risk components of RNRL stock.

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Dr. BRR

Month Price of RNRL Nifty Values

1 81 4128

2 83 4169

3 87 4210

4 88 4272

5 92 4210

6 107 4315

7 110 4335

8 99 4324

9 95 4189

10 94 4231

11 92 4215

12 90 4200

Dr.BRR

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

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Dr. BRR

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 26.9 22.3 %

-0.12 JP Associates 17.5 51.0 %

IAPM

Dr. BRR

= σ2

A + σ2 B - 2σ A σ B ρ AB

σ2 B - σ A σ B ρ AB

WA

WB = 1 - WA

Var (R p) = WA2 Var (RA) + WB

2 Var (RB) + 2 WAWB CovAB

Note: CovAB = rAB σ A σ B

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