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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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