Chapter 08 Risk & Return

8/8/2019 Chapter 08 Risk & Return

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Slides developed by:

Pamela L. Hall, Western Washington University

Risk and Return

Chapter 8


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Why Study Risk and Return?

Returns to equity investments (stock) havehistorically been much higher than the return todebt investments Equity returns averaged more than 10% while debt

returns average between 3% and 4% Inflation also averaged about 3% during the same time

period

Returns on equity investments are much more

volatile than the returns on debt instruments inthe short-run


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Why Study Risk and Return?

Since equity earns a much higher return but withhigher risk, it would be nice if we could investand earn a high return but reduce the riskassociated with such investments Investing in portfolios of securities can help manage

risk A portfolio is a collection of financial assets by investors

We wish to capture the high average returns ofequity investing while limiting the associated riskas much as possible


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The General RelationshipBetween Risk and Return Risk in finance is defined as the probability of

losing some or all of the money invested in adeal Generally investments that offer higher returns

involve higher risks

Suppose you could invest in a stock that wouldeither return you 15% or a loss of everything (-100%) Also, suppose the chance of losing everything is 1%

and the chance of earning 15% is 99% The risk associated with this investment is the 1%

chance of losing everything


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The General RelationshipBetween Risk and Return Investors more or less expect to receive a

positive return but they realize that there is riskassociated with these investments and thechance that they can lose their money

Stocks offering a higher likely return also havehigher probabilities of total loss

It is difficult to determine how much risk is

associated with a given level of return Need to define risk in a measurable way

The definition has to include all the probabilities of loss

Have to relate that measurement to return


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Portfolio TheoryModernThinking about Risk and Return

Portfolio theory defines investment risk ina measurable way and relates it to theexpected level of return from an

investment Has had major impact on practical

investing activities


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The Return on an Investment

The rate of return allows an investment's returnto be compared with other investments

One-Year Investments The return on a debt investment is

K = interest paid loan amount

A return is what the investor receives divided by what isinvested

The return on a stock investment is K = D

1+ (P

1 P

0) P

0


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Returns, Expected andRequired

The expected return on a stock is thereturn investors feel is most likely to occurbased on currently available information Anticipated return based on the dividends

expected as well as the future expected price No rational person makes any investment

without some expectation of return


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Returns, Expected andRequired

The required return on a stock is the minimumrate at which investors will purchase or hold astock based on their perceptions of its risk

People will only invest in an asset if they believe theexpected return is at least equal to the required return

Different people have different levels of both expected andrequired return

Significant investment in a stock occurs only if the expected

return exceeds the required return for a substantial number ofinvestors


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RiskA Preliminary Definition

A preliminary definition of investment risk is theprobability that return will be less than expected This definition includes both positive and negative returns that

are lower than expected

Feelings About Risk Most people have negative feelings about bearing risk

Risk averse investors prefer lower risk when expected returnsare equal

Most people see a trade-off between risk and return However risk isn't to be avoided, but higher risk investments

must offer a higher expect return to encourage investment


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Portfolio Theory

Review of the Concept of a RandomVariable In statistics a random variable is the outcome

of a chance process and has a probabilitydistribution

Discrete variables can take only specificvariables

Continuous variables can take any valuewithin a specified range


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Review of the Concept of aRandom Variable

The Mean or Expected Value The most likely outcome for the random

variable

For symmetrical probability distributionsthe mean is the center of the distribution

Statistically it is the weighted average ofall possible outcomes

( )n

i ii=1

X = XP X


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Portfolio Theory

Variance and Standard Deviation Variability relates to how far a typical observation of

the variable is likely to deviate from the mean

There's is a great deal of difference in variability around themean for different distributions

Telephone poles don't vary much in height from pole to poleactual pole heights are closely clustered around the mean

Office buildings do vary a great deal in terms of heightwidelydispersed around the mean

The standard deviation gives an indication of how far fromthe mean a typical observation is likely to fall


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Portfolio Theory

Variance and Standard Deviation Variance Formula

( ) ( )

n 22

x i ii=1Var X X X P X

= =

( ) ( )n 2

X x i ii=1

SD X X P X = =

Variance is the average squared deviation fromthe mean

Standard deviation formula


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Portfolio TheoryExample

1.0000

0.06254

0.25003

0.37502

0.25001

0.06250

P(X)X

The mean of thisdistribution is 2, since it isa symmetrical distribution.

Examp

le

Q:If you toss a coin four times what is the chance ofreceiving heads (x)?


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1.00SD X =1.00Var X =

0.250.0625424

0.250.2500113

0.000.3750002

0.250.25001-110.250.06254-20

(Xi )2 x P(Xi)P(Xi)(Xi )

2(Xi )Xi X

Since the varianceis 1.0, thestandard deviation

is also 1.0.Example

A: The Variance and Standard Deviation of thedistribution is:


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Review of the Concept of aRandom Variable The Coefficient of Variation

A relative measure of variationthe ratio of thestandard deviation of a distribution to its mean

CV = Standard Deviation Mean

For example, if the CV = 0.5, then the typical variation is50% the size of the mean, or

Continuous Random Variable Can take on any numerical value within some range

We talk about the probability of an actual outcomebeing within a range of values rather than being anexact amount


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The Return on a Stock Investmentas a Random Variable

In financial theory, the return on a stock investment isconsidered a random variable Return is influenced by the future price of the stock and the

expected dividends There is an element of uncertainty in both of these variables

Return is a continuous random variable with a low valueof -100% but no limit to the high value

The mean of the distribution of returns is the stock'sexpected return

The variance and standard deviation show how likely it isthat an actual return will be some distance from theexpected value Actual return in a distribution with a large variance is likely to be

different from the mean


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Figure 8.4: Probability DistributionsWith Large and Small Variances


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Risk Redefined as Variability

In financial theory risk is defined as variability inreturn

A risky stock has a high probability of earning a

return that significantly differs from the mean ofthe distribution While a low-risk stock is more like to earn a return

similar to the expected return

In practical terms risk is the probability thatreturn will be less than expected


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Figure 8.5: Investment Risk Viewedas Variability of Return Over Time

While both stocks have thesame expected return, the

high risk stock has agreater variability in

returns.


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Risk Aversion

Risk aversion means investors preferlower risk when expected returns areequal

When expected returns are not equal thechoice of investment depends on theinvestor's tolerance for risk


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Figure 8.6: Risk Aversion


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Q: Harold MacGregor is considering buying stocks for the first timeand is looking for a single company in which he'll make a majorinvestment. He's narrowed his search to two firms, EvanstonWater Inc. (a public utility) and Astro Tech Corp. (a new high-tech company).

Public utilities are low-risk stocks because they are regulatedmonopolies

High tech firms are high-risk because new technical ideas cansucceed tremendously, fail completely or end up in-between

Harold has studied the history and prospects of both firms and

their industries, and with the help of his broker has made adiscrete estimate of the probability distribution of returns foreach stock as follows:

Examp

le


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Evaluate Harold's options in terms of statistical concepts of risk andreturn.

Examp

le

0.151300.0514

0.20300.1512

0.30150.6010

0.2000.1580.15-100%0.056%

P(kA)kAP(kE)kE

Astro

Tech

EvanstonWater


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A: First calculate the expected return for each stock--the mean for eachdistribution.

Examp

le

15.0%10.0%

130

30

15

0-100%

kA

0.7

1.8

6.0

1.20.3%

kE* P(kE)

19.50.150.0514

6.00.200.1512

4.50.300.6010

0.00.200.158-15.0%0.150.056%

kA* P(kA)P(kA)P(kE)kE

Astro TechEvanston Water


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Examp

le

1.7%SD kE =

2.8Var kE =

0.80.0516414

0.60.154212

0.00.6000100.60.154-28

0.80.0516-4%6%

(kE )2 x P(kE)P(kE)(kE )

2(kE )kE Ek Ek Ek

A: Next, calculate the variance and standard deviation of the stocks'returns.


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Examp

le

63.7SD kA =

4,058Var kA =

1,9840.1513,225115130

450.202251530

00.300015

450.20225-150

1,9840.1513,225-115%-100%

(kA )2 x P(kA)P(kA)(kA )

2(kA )kA Ak Ak Ak

E AE A

E A

1.7 63.7CV = = = 0.17 CV = = = 4.25

10.0 15.0k k

A: Finally, calculate the coefficient of variation for each stock's return.


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A: If Harold only considers expected return, hell certainly choose Astro.However, with Evanston his investment is relatively safe while withAstro there is a substantial chance hell lose everything.

No one but Harold can make the decision as to which investment heshould choose. It depends on his degree of risk aversion.

Examp

le


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Decomposing RiskSystematic (Market)and Unsystematic (Business-Specific) Risk

Fundamental truth of the investment world The returns on securities tend to move up and down

together Not exactly together or proportionately

Events and Conditions Causing Movement inReturns Some things influence all stocks (market risk)

Political news, inflation, interest rates, war, etc. Some things influence only particular firms (business-

specific risk) Earnings reports, unexpected death of key executive, etc.

Some things affect all companies within an industry A labor dispute, shortage of a raw material


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Comparison of IBM, Boeing and the S&P500

0

20

40

6080100

120

140

10/10/2000

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12/10/2000

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2/10/2001

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Date

Stock

Price

02004006008001000

120014001600

IBM Boeing S&P500

IndexV

alue

Market

reopens afterWorld Trade

Centercollapses.


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Movement in Return as Risk The total movement in a stock's return is the total risk

inherent in the stock

Separating Movement/Risk into Two Parts A stock's risk can be separated into systematic or

market risk and unsystematic or business-specificrisk


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Portfolios

A portfolio is an investor's total stock holding Risk and Return for a Portfolio

Each stock in a portfolio has its own expected returnand its own risk

Portfolios have their own risks and returns The return on a portfolio is a weighted average of the returns

of the individual stocks in the portfolio

The risk is the variance or standard deviation of theprobability distribution of the portfolio's return

Not the same as the weighted average of the standarddeviations or variances of the individual stocks within theportfolio


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Portfolios

The Goal of the Investor/Portfolio Owner Goal of investors: to capture the high

average returns of equities while avoiding as

much risk as possible Generally done by constructing diversifiedportfolios to minimize portfolio risk for a givenreturn

Investors are concerned with how stocksimpact portfolio performance, not with thestocks' stand-alone characteristics


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DiversificationHow Portfolio Risk IsAffected When Stocks Are Added

Diversification means adding different (diverse)stocks to a portfolio Can reduce (but not eliminate) risk in a portfolio

Business-Specific Risk and Diversification Business-specific risk is a series of essentiallyrandom events that push the returns of individualstocks up or down

Their effects simply cancel when added together over a

substantial number of stocks Is essentially random and can be diversified away

For this to work, the stocks within the portfolio must be fromfundamentally different industries


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Systematic (Market) Risk and Diversification If the returns of all stocks move up and down more or less

together, it's not possible to reduce risk completely Systematic risk can be reduced but never entirely eliminated

The Portfolio If we have a portfolio that is as diversified as the market, itsreturn will move in tandem with the market

The Impact on Portfolio Risk of Adding New Stocks If we add a stock to the portfolio which has returns perfectly

positively correlated with the portfolio, it will generally add risk tothe diversified portfolio If we add a stock that is perfectly negatively correlated with the

portfolio, it will decrease the risk of the portfolio


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The Risk of the New Additions By Themselves and inPortfolios Stocks with equal stand-alone risk can have opposite risk

impacts on a portfolio because of the timing of the variation intheir returns

A stock's risk in a portfolio sense is its market risk

Choosing Stocks to Diversify for Market Risk How do we diversify to reduce market risk in a portfolio

Theoretically it's simple: just add stocks that move countercyclically with the market

Unfortunately it's difficult to find stocks that move in that direction

However numerous stocks exist that have returns that are less thanpositively correlated with the market

Adding these stocks to the portfolio will generally reduce risksomewhat, but will not eliminate it


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The Importance of Market Risk Modern portfolio theory is based on the

assumption that investors focus on portfolios

rather than on individual stocks How stocks affect portfolios depends only on

market risk

For the small investor with a limited portfolio,these concepts do not apply

Measuring Market Risk The


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Measuring Market RiskTheConcept of Beta Market risk is a crucial concept in investing, so we need a

way to measure it for individual stocks A stock's beta measures its market risk

It measures the variation of a stock's return which accompaniesthe market's variation in return

Developing Beta Beta is developed by determining the historical relationship

between a stock's return and the return on a market index, suchas the S&P500

The stock's characteristic line reflects the average relationship

between its return and the market Beta is the slope of the characteristic line

Projecting Returns with Beta Knowing a stock's beta enables us to estimate changes in its

return given changes in the market's return



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Measuring Market RiskTheConcept of Beta

Characteristic Line for IBM

y = 1.3037x + 0.0009

-0.2

-0.15

-0.1

-0.050

0.05

0.1

0.15

-0.06 -0.04 -0.02 0 0.02 0.04 0.06

Return on S&P500

ReturnonIBM

Characteristic linedetermined usingdata from Slide 31.

IBMsbeta



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Measuring Market RiskTheConcept of Beta

Q: Conroy Corp. has a beta of 1.8 and is currently earning itsowners a return of 14%. The stock market in general isreacting negatively to a new crisis in the Middle East thatthreatens world oil supplies. Experts estimate that the returnon an average stock will drop from 12% to 8% because ofinvestor concerns over the economic impact of a potential oilshortage as well as the threat of a limited war. Estimate thechange in the return on Conroy shares and its new price.

A: Beta represents the past average change in Conroys return relative tochanges in the markets return.

The new return can be estimated as

kConroy = 14% - 7.2% = 6.8%

Examp

le

Conroy Conroy

Conroy

M

Conroy

k kb or 1.8

k 4%k = 7.2%

= =



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Measuring Market RiskTheConcept of Beta Betas are developed from historical data

May not be accurate if a fundamental change in the businessenvironment occurs

Small investors should remember that beta doesn'tmeasure total risk

A beta > (


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Using BetaThe Capital AssetPricing Model (CAPM)

The CAPM helps us determine how stock pricesare set in the market Developed in 1950s and 1960s by Harry Markowitz

and William Sharpe The CAPM's Approach

People won't invest unless a stock's expected returnis at least equal to their required return

The CAPM attempts to explain how investors'required returns are determined

Using Beta The Capital Asset


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Using BetaThe Capital AssetPricing Model (CAPM) Rates of Return, The Risk-Free Rate and Risk

Premiums The risk-free rate (kRF ) is a rate for which there is no

chance of receiving less than what is expected

Returns on federally insured bank accounts and short-termTreasury debt are examples of risk-free investments

Investing in any other investment is a risky venture;thus investors will require a return greater than therisk-free rate

Investors want to be compensated for the extra risk taken viaa rate known as the risk premium (KRP )

The CAPM purports to explain how the risk premium in requiredrates of return are formed

The Security Market Line (SML) is the heart of the CAPM

The Security Market Line


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The Security Market Line(SML)

The SML proposes that required rates of returnare determined by:

The Market Risk Premium Is a reflection of the investment community's level of risk aversion

It is the risk premium for an investment in the market as a whole

The Risk Premium for Stock X The beta for Stock X times the risk premium of the market

Says that the risk premium for a stock is determined only by thestock's relationship with the market as measured by beta

( )X RF M RF XMarket Risk

Premium

Stock X's Risk Premium

k k k k b= + 1 4 2 4 3

1 4 4 2 4 43



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The Security Market Line(SML)

The SML as a Portrayal of the Securities Market The standard equation of a straight line is

y = mx + b

Where: y is the vertical axis variable; x is the horizontal axis

variable; m is the slope of the line and b is the y intercept

The SML can be viewed as a straight line:

{ { ( ) {X RF M RF Xy = b + xm

k k k k b= + 1 4 2 4 3

The slope of the SML plotted in risk-return space reflectsthe general level of risk aversion

The vertical intercept of the SML represents investment inshort-term government securities



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The Security Market Line(SML) The SML as a Line of Market Equilibrium

If, for every stock, its expected return equals itsrequired return, the SML represents equilibrium

Suppose that a stock's expected return now becomes

less than its required return Investors would no longer desire that stock and owners of

the stock would sell while potential buyers would no longerbe interested

The stock price would drop because supply would exceed

demand Since the stock price is dropping, its expected return isincreasing, driving it back toward equilibrium

The SML represents a condition of stable equilibrium



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The Security Market Line(SML) Valuation Using Risk-Return Concepts

The SML allows us to calculate the minimum requiredrate of return for a stock

This return can then be used in the Gordon model to

determine an intrinsic value for a stock The Impact of Management Decisions on Stock

Prices Since managers can influence a stock's beta and

future growth rates, management's decisions impactthe price of the stock

The Security Market Line (SML)


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The Security Market Line (SML)Example

Q: The Kelvin Company paid an annual dividend of $1.50 recently, and isexpected to grow at 7% into the indefinite future. Short-term treasurybills are currently yielding 6%, and an average stock yields its owner10%. Kelvin stock is relatively volatile. Its return tends to move inresponse to political and economic changes about twice as much asdoes the return on the average stock. What should Kelvin sell fortoday?

A: The required rate of return using the SML is:

kKelvin = 6 + (10 6)2.0 = 14%

Plugging this required rate of return along with the growth rate of 7%into the Gordon model gives us the estimated price:

Examp

le

( ) ( )00

D 1 g $1.5 1.07P $22.93

k g .14 .07

+= = =



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Q: The Kelvin Company has an exciting new opportunity. The firm hasidentified a new field into which it can expand using technology italready possesses. The venture promises to increase the firm's growthrate to 9% from the current 7%. However, the project is new andunproven, so there's a chance it will fail and cause a considerable loss.As a result, there's some concern that the stock market won't react

favorably to the additional risk. Management estimates thatundertaking the venture will raise the firm's beta to 2.3 from its currentlevel of 2.0. Should Kelvin undertake the new project if the firmscurrent stock price is $22.93?

A: The objective of the firms management should be to maximize

shareholder wealth. If growth is expected to increase, this will have apositive impact on stock price; however, if an increase in beta isexpected, stockholders will demand a higher rate of return which willcause an offsetting drop in the stock price. The expected price of thestock given both the increase in the growth rate and the increase in thefirms beta must be calculated.

Examp

le



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The new required rate of return will be:

kKelvin = 6 + (10 6)2.3 = 15.2%

Plugging this new required rate of return along with the higher growthrate of 9% into the Gordon model gives us the new estimated price:

Thus, the venture looks like a good idea.

Exa

mp

le

( ) ( )00

D 1 g $1.5 1.09P $26.37

k g .152 .09

+= = =


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Adjustments to Changing Market Conditions The response to a change in the risk-free rate

If all else remains the same, a change in the risk-free ratecauses a parallel shift in the SML

The slope of the SML remains the same which means KMmust increase by the amount of the change in kRF

The response to a change in risk aversion Changes in attitudes toward risk are reflected by rotations of

the SML around its vertical intercept

The Validity and Acceptance of


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The Validity and Acceptance ofthe CAPM and SML

CAPM is an abstraction of reality designed tohelp make predictions Its simplicity has lead to its popularity

It relates risk and return in an easy-to-understand concept

However, CAPM is not universally accepted Continuing debate exists as to its relevance and

usefulness

Fama and French found no historical relationship betweenthe returns on stocks and their betas

Chapter 08 Risk & Return

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