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Copyright 2009 Pearson Addison-Wesley. All rights reserved.

Chapter 7

The Pricing

of RiskyFinancial

Assets

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Copyright 2009 Pearson Addison-Wesley. All rights reserved. 7-2

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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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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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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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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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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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

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