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Chapter 3

Market Risk andReturns

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Market risk (Beta)Risk that arises due to fluctuations in security

prices/stock prices

Return

Income of investment

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Efficient FinancialMarkets

Market efficiency

Market uses all information publicallyavailable

Economy

Financial markets

Specific company

Price movements follow a random walk

Past prices of stock cannot predict the futureprices of stock

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Efficient market hypothesis

- Large number of investors- Wanted to earn profit

- Receive and analyze all publically available

information

Stages of EMH Weak-form market efficiency

Historical information

Semi strong-form market efficiency

Not based on Publicly available information

Strong-form market efficiency

Publicly available and private information(insiders)

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Arbitrage efficiency

-Two securities of same type, Buying the

cheaperone and selling the expensive one.

- Demand and supply determine prices until

equilibrium point

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Security A B

Number of bonds 8 10

Purchase costeach

(Rs.)

1000 800

Each year return(Rs.)

100 100

Bond tenure(years)

2 2

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Security Portfolios

Expected return for a portfolio is a weightedaverage of expected returns for securities in theportfolio

Where m is number of securities, rj is return on

securityj and Aj is proportion of total funds

invested in securityj (probability)

Portfolio riskis the total risk involved in a portfolioof securities.

- Depends on riskiness of securities as well as theirrelation

(little relationship between securities).-

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=

=m

j

jjp Arr1

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Covariance

Measures how closely returns move together

jk= rjkj k

rjk is the expected correlation between security j and kj is the standard deviation of security j

kis the standard deviation of security j

Range of correlation

-1 to +1

Covariance of returns/ portfolio risk

It is the standard deviation of probability distribution of

possible returns.

m mr= Pj Pkjk

j=1 k=1

Double summation sign means that we will sum all thevariances and

co variances in the matrix of all possible pair wise securities 7

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Harry Markowitz formula for portfolio risk

p= (P1)^2(1)^2+(P2)^2(2)^2 * 2(P1)(1)(P2)(2)(r)

Two-Security Efficient Set

Opportunity set for investment in two securityportfolios

Risk-return relation

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Portfolio Portfolio Return(%) Portfolio Risk(%)

1 12 11

2 13.2 10.26

3 14.4 11.02

4 15.6 13.01

5 16.8 15.79

6 18 19

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Opportunity set of two securities withdifferent portfolios

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Multiple Security PortfolioAnalysis and Selection

Efficient set Combination of securities Highest expected return for a given

standard deviation

Efficient set theorem states that an investor will

choose aportfolio from the set of portfolios that:

1.Offer maximum expected return for varyinglevels of

risk,2.Offer minimum risk for varying levels ofexpected return.

Utility functions and investorchoice 11

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ap a sse r c ngModel

CAPM is an equilibrium model of the trade-off

betweenexpected portfolio return and unavoidable risk

(market risk).

William F sharpe and John Lintner

CAPM Assumptions

Capital markets are highly efficient

Investors are well informed

Zero transaction costsNegligible restrictions on investment

No taxes

No investor can affect market price

Common holding period is 1 year 13

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The Characteristics Line It is used to measure market risk

Beta= Cov (Ra,Rp)

Var. Rp

Higher the risk higher the return 14

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Alpha

< 0: rational investor will avoid investing instock and will invest in risk free security or willprefer portfolio investing.

= 0 The investment has earned a return

adequate for the risk taken

> 0the investment has a return in excess of thereward for the assumed risk and characteristicline will move upward.

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CAPM formula

Rt=Rf+(Rm-Rf)B Risk-free rate (Rf)

Return for the market return (Rm)

Beta (market risk)

BetaA measure of volatility or risk

Beta = 1 (security price will move with themarket)

Beta> 1 (security price will be more volatile thanmarket)

Beta< 1 (security price will be less volatile thanmarket)

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The Security Market Line

Its depicts the market equilibrium relationship

between expected rate of return and

systematic risk (beta)

No reward for unsystematic risk

Important to differentiate systematic risk from

total risk

Total risk= systematic risk + un-systematic 17

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SML

RmEq. risk premium

Rf

RtRisk free return

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Equity risk premium

The excess return that an individual stock or theoverall stock

market provides over a risk-free rate.

ERP= Rm-Rf

ERP is greater when interest rate (k) is lower

ERP is lesser when interest rate (k) is higher

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CAPM affect on valuation of

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CAPM affect on valuation offirm

P= Dt/(1+k)^t

P is market price per share

Dt is expected dividend at time tK is investors required rate of return=Rt

Greater Rt/K lower will be the stock price

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