The Pricing of Risky The Pricing of Risky Financial AssetsFinancial Assets

Risk and ReturnRisk and Return

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IntroductionIntroduction

Risk is a double-edged sword—It complicates Risk is a double-edged sword—It complicates decision making but makes things interestingdecision making but makes things interesting

Understand how investors are compensated for Understand how investors are compensated for holding holding risky securitiesrisky securities and how portfolio and how portfolio decisions impact the outcomedecisions impact the outcome

A financial asset is a contractual agreement A financial asset is a contractual agreement that entitles the investor to a series of future that entitles the investor to a series of future cash payments from the issuercash payments from the issuer

Value of a security is dependent on nature of Value of a security is dependent on nature of the future cash payments and credibility of the the future cash payments and credibility of the issuer in making those paymentsissuer in making those payments

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A World of CertaintyA World of Certainty

Individuals are predictable and live up to Individuals are predictable and live up to contractual agreements on financial securitiescontractual agreements on financial securities

In this case, the same interest rate is In this case, the same interest rate is applicable to each and every loanapplicable to each and every loan Charge more—people would not borrowCharge more—people would not borrow Charge less—lenders would be deluged with Charge less—lenders would be deluged with

requests for fundsrequests for funds All securities are prefect substitutes for each All securities are prefect substitutes for each

other—sell at the same price and yield the other—sell at the same price and yield the same returnsame return

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A World of Certainty A World of Certainty

Consumption versus savingConsumption versus saving The individual investor would forgo The individual investor would forgo

consumption for a minimum riskless rate of consumption for a minimum riskless rate of returnreturn

Depends on the individual’s preference Depends on the individual’s preference between between current and futurecurrent and future consumption consumption

Is the rate high enough to persuade Is the rate high enough to persuade individual to forgo consumption in favor of individual to forgo consumption in favor of savingsaving

The higher the rate, the more people will The higher the rate, the more people will elect to save for future consumptionelect to save for future consumption

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Consequences of Consequences of UncertaintyUncertainty

In contrast to a “perfect world,” In contrast to a “perfect world,” investors face uncertaintyinvestors face uncertainty

Outcome may be better or worse Outcome may be better or worse than expectedthan expected

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Risk AversionRisk Aversion

Investors must be compensated for Investors must be compensated for riskrisk

Will hold risky securities if higher Will hold risky securities if higher expected returns will offset the expected returns will offset the undesirable uncertaintyundesirable uncertainty

Trade-off of higher return versus risk Trade-off of higher return versus risk is subjective and different for every is subjective and different for every individualindividual

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Portfolio DiversificationPortfolio Diversification

A strategy employed by investors to A strategy employed by investors to reduce riskreduce risk

Holding many different securities Holding many different securities rather than just one rather than just one

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Risk and ReturnRisk and Return

Probability DistributionProbability Distribution A listing of the various outcomes and the A listing of the various outcomes and the

probability of each outcome occurringprobability of each outcome occurring Expected returnExpected return

A weighted average of the different outcomes A weighted average of the different outcomes multiplied by their respective probabilitymultiplied by their respective probability

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Example: Expected ReturnsExample: Expected Returns

Suppose you have predicted the following returns Suppose you have predicted the following returns for stocks C and T in three possible states of for stocks C and T in three possible states of nature. What are the expected returns?nature. What are the expected returns? StateState ProbabilityProbability CC TT BoomBoom 0.30.3 0.150.15 0.250.25 NormalNormal 0.50.5 0.100.10

0.200.20 RecessionRecession 0.20.2 0.020.02 0.010.01

RRCC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.99% = .3(.15) + .5(.10) + .2(.02) = .099 = 9.99% RRTT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7% = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

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Variance and Standard Variance and Standard DeviationDeviation

Variance and standard deviation Variance and standard deviation measure the volatility of returnsmeasure the volatility of returns

Weighted average of squared Weighted average of squared deviationsdeviations

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Example: Variance and Example: Variance and Standard DeviationStandard Deviation

Consider the previous example. What are the Consider the previous example. What are the variance and standard deviation for each stock?variance and standard deviation for each stock?

Stock CStock C 22 = .3(.15-.099) = .3(.15-.099)22 + .5(.1-.099) + .5(.1-.099)22

+ .2(.02-.099)+ .2(.02-.099)22 = .002029 = .002029 = .045= .045

Stock TStock T 22 = .3(.25-.177) = .3(.25-.177)22 + .5(.2-.177) + .5(.2-.177)22

+ .2(.01-.177)+ .2(.01-.177)22 = .007441 = .007441 = .0863= .0863

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Standard DeviationStandard Deviation

When comparing securities, the one When comparing securities, the one with the largest standard deviation is with the largest standard deviation is the riskier the riskier

If returns and standard deviations If returns and standard deviations between two securities are different, the between two securities are different, the investor must make a decision between investor must make a decision between the tradeoff of the expected return and the tradeoff of the expected return and the standard deviation of eachthe standard deviation of each

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Modern Portfolio TheoryModern Portfolio Theory AssetAsset may seem very risky in isolation, but may seem very risky in isolation, but

when combined with other assets, risk of when combined with other assets, risk of portfolio may be substantially less—even zeroportfolio may be substantially less—even zero

When combining different securities, it is When combining different securities, it is important to understand how outcomes are important to understand how outcomes are related to each otherrelated to each other ProcyclicalProcyclical—Returns of two or more securities are —Returns of two or more securities are

positively correlatedpositively correlated indicating they move in indicating they move in same directionsame direction

CountercyclicalCountercyclical—Returns of two or more securities —Returns of two or more securities are are negatively correlatednegatively correlated-move in opposite -move in opposite directionsdirections

Combining a procyclical and countercyclical Combining a procyclical and countercyclical securities would greatly reduce the risk of the securities would greatly reduce the risk of the portfolioportfolio

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Principles of DiversificationPrinciples of Diversification

As long as assets do not have As long as assets do not have preciselyprecisely the same the same patternpattern of of returns, then holding a group of returns, then holding a group of assets can reduce riskassets can reduce risk

If the returns of each security are If the returns of each security are totally totally independentindependent of each other, of each other, combining a large number of combining a large number of securities tends to produce the securities tends to produce the average return of the portfolioaverage return of the portfolio

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The Risk Premium on Risky The Risk Premium on Risky SecuritiesSecurities

The standard deviation of returns is a good The standard deviation of returns is a good measure of risk for analyzing a securitymeasure of risk for analyzing a security

However, it is a relatively poor measure of However, it is a relatively poor measure of the risk contribution of a single security to the risk contribution of a single security to an entire portfolioan entire portfolio

This depends on the covariance of returns This depends on the covariance of returns with other securitieswith other securities

Nonsystematic RiskNonsystematic Risk of a portfolio is of a portfolio is diversified away as the number of diversified away as the number of securities held increasessecurities held increases

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Market PortfolioMarket Portfolio

AA widely diversified portfolio that contains widely diversified portfolio that contains virtually every security in the marketplacevirtually every security in the marketplace Investor earns a return above the Investor earns a return above the risk-free risk-free

raterate that compensates for the co-movement of that compensates for the co-movement of returns among all securities, rather than the returns among all securities, rather than the risks inherent in every securityrisks inherent in every security

The risk of the market portfolio is less than the The risk of the market portfolio is less than the sum of each security’s risk because some of sum of each security’s risk because some of the individual variability tends to cancel outthe individual variability tends to cancel out

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Systematic RiskSystematic Risk

Relates to the risk of an individual security Relates to the risk of an individual security in relation to the movement of the entire in relation to the movement of the entire portfolioportfolio The The risk premiumrisk premium that investors demand will be that investors demand will be

in proportion to the systematic risk of the in proportion to the systematic risk of the security security

Riskier securities must offer investors higher Riskier securities must offer investors higher expected returnsexpected returns

Extra expected return on a risky security above Extra expected return on a risky security above the the risk-freerisk-free rate will be proportional to the risk rate will be proportional to the risk contribution of a security to a well-diversified contribution of a security to a well-diversified portfolioportfolio

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PortfoliosPortfolios

A portfolio is a collection of assetsA portfolio is a collection of assets An asset’s risk and return is important An asset’s risk and return is important

in how it affects the risk and return of in how it affects the risk and return of the portfoliothe portfolio

The risk-return trade-off for a portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected is measured by the portfolio expected return and standard deviation, just as return and standard deviation, just as with individual assetswith individual assets

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Portfolio Expected ReturnsPortfolio Expected Returns

The expected return of a portfolio is the The expected return of a portfolio is the weighted average of the expected returns for weighted average of the expected returns for each asset in the portfolioeach asset in the portfolio

You can also find the expected return by finding You can also find the expected return by finding the portfolio return in each possible state and the portfolio return in each possible state and computing the expected value as we did with computing the expected value as we did with individual securitiesindividual securities

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Portfolio VariancePortfolio Variance

Compute the portfolio return for each Compute the portfolio return for each state:state:RRPP = w = w11RR11 + w + w22RR22 + … + w + … + wmmRRmm

Compute the expected portfolio return Compute the expected portfolio return using the same formula as for an using the same formula as for an individual assetindividual asset

Compute the portfolio variance and Compute the portfolio variance and standard deviation using the same standard deviation using the same formulas as for an individual assetformulas as for an individual asset

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ExampleExample

Consider the following informationConsider the following information StateState ProbabilityProbability XX ZZ BoomBoom .25.25 15%15% 10%10% NormalNormal .60.60 10%10% 9%9% RecessionRecession .15.15 5%5% 10%10%

What is the expected return and standard What is the expected return and standard deviation for a portfolio with an deviation for a portfolio with an investment of $6000 in asset X and investment of $6000 in asset X and $4000 in asset Y?$4000 in asset Y?

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Expected versus Expected versus Unexpected ReturnsUnexpected Returns

Realized returns are generally not Realized returns are generally not equal to expected returnsequal to expected returns

There is the expected component There is the expected component and the unexpected componentand the unexpected component At any point in time, the unexpected At any point in time, the unexpected

return can be either positive or negativereturn can be either positive or negative Over time, the average of the Over time, the average of the

unexpected component is zerounexpected component is zero

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Announcements and NewsAnnouncements and News

Announcements and news contain both an Announcements and news contain both an expected component and a surprise expected component and a surprise componentcomponent

It is the surprise component that affects a It is the surprise component that affects a stock’s price and therefore its returnstock’s price and therefore its return

This is very obvious when we watch how This is very obvious when we watch how stock prices move when an unexpected stock prices move when an unexpected announcement is made or earnings are announcement is made or earnings are different than anticipateddifferent than anticipated

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Efficient MarketsEfficient Markets

Efficient markets are a result of Efficient markets are a result of investors trading on the unexpected investors trading on the unexpected portion of announcementsportion of announcements

The easier it is to trade on surprises, The easier it is to trade on surprises, the more efficient markets should bethe more efficient markets should be

Efficient markets involve random Efficient markets involve random price changes because we cannot price changes because we cannot predict surprisespredict surprises

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Systematic RiskSystematic Risk

Risk factors that affect a large Risk factors that affect a large number of assetsnumber of assets

Also known as non-diversifiable risk Also known as non-diversifiable risk or market riskor market risk

Includes such things as changes in Includes such things as changes in GDP, inflation, interest rates, etc.GDP, inflation, interest rates, etc.

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Unsystematic RiskUnsystematic Risk

Risk factors that affect a limited Risk factors that affect a limited number of assetsnumber of assets

Also known as unique risk and asset-Also known as unique risk and asset-specific riskspecific risk

Includes such things as labor strikes, Includes such things as labor strikes, part shortages, etc.part shortages, etc.

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ReturnsReturns

Total Return = expected return + Total Return = expected return + unexpected returnunexpected return

Unexpected return = systematic portion Unexpected return = systematic portion + unsystematic portion+ unsystematic portion

Therefore, total return can be expressed Therefore, total return can be expressed as follows:as follows:

Total Return = expected return + Total Return = expected return + systematic portion + unsystematic systematic portion + unsystematic portionportion

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DiversificationDiversification

Portfolio diversification is the investment in Portfolio diversification is the investment in several different asset classes or sectorsseveral different asset classes or sectors

Diversification is not just holding a lot of Diversification is not just holding a lot of assetsassets

For example, if you own 50 internet stocks, For example, if you own 50 internet stocks, you are not diversifiedyou are not diversified

However, if you own 50 stocks that span 20 However, if you own 50 stocks that span 20 different industries, then you are diversifieddifferent industries, then you are diversified

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The Principle of The Principle of DiversificationDiversification

Diversification can substantially reduce Diversification can substantially reduce the variability of returns without an the variability of returns without an equivalent reduction in expected returnsequivalent reduction in expected returns

This reduction in risk arises because This reduction in risk arises because worse than expected returns from one worse than expected returns from one asset are offset by better than expected asset are offset by better than expected returns from anotherreturns from another

However, there is a minimum level of risk However, there is a minimum level of risk that cannot be diversified away and that that cannot be diversified away and that is the systematic portionis the systematic portion

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Diversifiable RiskDiversifiable Risk

The risk that can be eliminated by The risk that can be eliminated by combining assets into a portfoliocombining assets into a portfolio

Often considered the same as Often considered the same as unsystematic, unique or asset-specific unsystematic, unique or asset-specific riskrisk

If we hold only one asset, or assets in the If we hold only one asset, or assets in the same industry, then we are exposing same industry, then we are exposing ourselves to risk that we could diversify ourselves to risk that we could diversify awayaway

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Total RiskTotal Risk Total risk = systematic risk + Total risk = systematic risk +

unsystematic riskunsystematic risk The standard deviation of returns is a The standard deviation of returns is a

measure of total riskmeasure of total risk For well diversified portfolios, For well diversified portfolios,

unsystematic risk is very smallunsystematic risk is very small Consequently, the total risk for a Consequently, the total risk for a

diversified portfolio is essentially diversified portfolio is essentially equivalent to the systematic riskequivalent to the systematic risk

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Systematic Risk PrincipleSystematic Risk Principle

There is a reward for bearing riskThere is a reward for bearing risk There is not a reward for bearing risk There is not a reward for bearing risk

unnecessarilyunnecessarily The expected return on a risky asset The expected return on a risky asset

depends only on that asset’s depends only on that asset’s systematic risk since unsystematic systematic risk since unsystematic risk can be diversified awayrisk can be diversified away