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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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Portfolio TheoryExample
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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Portfolio TheoryExample
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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Portfolio TheoryExample
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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Portfolio TheoryExample
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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Portfolio TheoryExample
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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Portfolio TheoryExample
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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Portfolio TheoryExample
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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Decomposing RiskSystematic (Market)and Unsystematic (Business-Specific) Risk
Comparison of IBM, Boeing and the S&P500
0
20
40
6080100
120
140
10/10/2000
11/10/2000
12/10/2000
1/10/2001
2/10/2001
3/10/2001
4/10/2001
5/10/2001
6/10/2001
7/10/2001
8/10/2001
9/10/2001
10/10/2001
Date
Stock
Price
02004006008001000
120014001600
IBM Boeing S&P500
IndexV
alue
Market
reopens afterWorld Trade
Centercollapses.
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Decomposing RiskSystematic (Market)and Unsystematic (Business-Specific) Risk
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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DiversificationHow Portfolio Risk IsAffected When Stocks Are Added
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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DiversificationHow Portfolio Risk IsAffected When Stocks Are Added
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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DiversificationHow Portfolio Risk IsAffected When Stocks Are Added
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
Measuring Market Risk The
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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
Measuring Market Risk The
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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%
= =
Measuring Market Risk The
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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
The Security Market Line
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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
The Security Market Line
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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
The Security Market Line
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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
+= = =
The Security Market Line (SML)
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The Security Market Line (SML)Example
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
The Security Market Line (SML)
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The Security Market Line (SML)Example
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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The Security Market Line
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