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Chapter 7
The Pricing
of RiskyFinancial
Assets
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Learning Objectives
Understand what risk aversion means and theresulting necessity of compensating risk averseinvestors with higher expected returns to holdrisky assets
Calculate the basic measures of risk
See how diversification can reduce or eliminate
all nonsystematic risk in a portfolio ofinvestments
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Introduction
Risk is a double-edged swordIt complicates decisionmaking but makes things interesting
Understand how investors are compensated for holding
risky securities and how portfolio decisions impact theoutcome
A financial asset is a contractual agreement that entitlesthe investor to a series of future cash payments from the
issuer
Value of a security is dependent on nature of the futurecash payments and credibility of the issuer in makingthose payments
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Introduction (Cont.)
Every risky security must compensate investor for
Delayed payment of cash flow
Uncertainty over those future cash flows
The expected return to the investor takes both issues into
account
Ultimate objective is to determine the equilibrium
expected return on a risky security
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A World of Certainty
Individuals are predictable and live up to contractualagreements on financial securities
In this case, the same interest rate is applicable to each
and every loan Charge morepeople would not borrow
Charge lesslenders would be deluged with requests forfunds
All securities are prefect substitutes for each othersellat the same price and yield the same return
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A World of Certainty (Cont.)
In this world, the key decisions influenced by theriskless rate of interest are consumption versus saving
The individual investor would forgo consumption for a
minimum riskless rate of return Depends on the individuals preference between current and
future consumption
Is the rate high enough to persuade individual to forgoconsumption in favor of saving
The higher the rate, the more people will elect to save forfuture consumption
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Consequences of Uncertainty and
Risk Aversion
In contrast to a perfect world, investors faceuncertainty
Outcome may be better or worse than expected
Risk aversion
Investors must be compensated for risk
Will hold risky securities if higher expected returns willoffset the undesirable uncertainty
Trade-off of higher return versus risk is subjective anddifferent for every individual
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Consequences of Uncertainty and
Risk Aversion (Cont.)
Portfolio diversification
A strategy employed by investors to reduce risk
Holding many different securities rather than justone with the highest possible return
In real life, most people are risk averters
since they hold diversified portfolios
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Consequences of Uncertainty and
Risk Aversion (Cont.)
An Aside on Measuring Risk
Probability DistributionA listing of the various outcomes
and the probability of each outcome occurring
Expected returnA weighted average of the different
outcomes multiplied by their respective probability
Standard deviation
The square root of the sum of the squared deviations between the
actual outcomes and the expected outcome
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Consequences of Uncertainty and
Risk Aversion (Cont.)
An Aside on Measuring Risk (Cont.)
Standard deviation (Cont.)
Standard deviation is a good representation of riskevidence to
suggest that outcomes are symmetric and have a normal distribution When comparing securities, the one with the largest standard
deviation is the riskier
If returns and standard deviations between two securities are different,
the investor must make a decision between the tradeoff of the
expected return and the standard deviation of each
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Principles of Diversification
Modern Portfolio TheoryAsset may seem very risky in
isolation, but when combined with other assets, risk of portfolio
may be substantially lesseven zero
When combining different securities, it is important tounderstand how outcomes are related to each other
ProcyclicalReturns of two or more securities are positively
correlated indicating they move in same direction
CountercyclicalReturns of two or more securities are negativelycorrelated-move in opposite directions
Combining a procyclical and countercyclical securities would greatly
reduce the risk of the portfolio
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Principles of Diversification (Cont.)
Therefore, the important consideration of adding
another security is the assets contribution to the
total portfolios risk CovarianceA measure of how asset returns
are interrelated with each other
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Principles of Diversification (Cont.)
As long as assets do not have preciselythe same
patternof returns, then holding a group of assets
can reduce risk If the returns of each security are totally
independent of each other, combining a large
number of securities tends to produce theaverage return of the portfolio
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The Risk Premium on Risky
Securities
The standard deviation of returns is a good measure of
risk for analyzing a security
However, it is a relatively poor measure of the risk
contribution of a single security to an entire portfolio
This depends on the covariance of returns with other
securities
Non-systematic Riskof a portfolio is diversified awayas the number of securities held increases
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The Risk Premium on Risky
Securities (Cont.)
Market portfolioA widely diversified portfolio that
contains virtually every security in the marketplace
Investor earns a return above the risk-free rate that
compensates for the co-movement of returns among all
securities, rather than the risks inherent in every security
The risk of the market portfolio is less than the sum of each
securitys risk because some of the individual variability
tends to cancel out
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The Risk Premium on Risky
Securities (Cont.)
Systematic Riskrelates to the risk of an individualsecurity in relation to the movement of the entire
portfolio
The risk premium that investors demand will be inproportion to the systematic risk of the security
Riskier security must offer investors higher expected returns
Extra expected return on a risky security above the risk-free
rate will be proportional to the risk contribution of a securityto a well-diversified portfolio