Session5&6.Risk & Return(2) FFL SMU
Transcript of Session5&6.Risk & Return(2) FFL SMU
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Risk, Return, and
Portfolio Management
• Measures of Risk and Return
• Portfolio Construction and
Management
• Capital Markets and Pricing of Risk
• Optimal Portfolio Choice
• Capital Asset Pricing Model
Value = + + + FCF1 FCF2 FCF∞
(1 + WACC)1 (1 + WACC)∞ (1 + WACC)2
Free cash flow (FCF)
Market interest rates
Firm’s business risk Market risk aversion
Firm’s debt/equity mix Cost of debt
Cost of equity
Weighted average cost of capital
(WACC)
Net operating profit after taxes
Required investments in operating capital
−
=
Determinants of Intrinsic Value: The Cost of Equity
...
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What is investment risk?
• Two types of investment risk
– Stand-alone risk
– Portfolio risk
• Investment risk is related to the probability of
earning a low or negative actual return.
• The greater the chance of lower than
expected, or negative returns, the riskier the
investment.
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Probability Distributions
• A listing of all possible outcomes, and the
probability of each occurrence.
• Can be shown graphically.
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Expected Rate of Return
Rate of
Return (%) 100 15 0 -70
Firm X
Firm Y
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Selected Realized Returns, 1926-2010
Source: Based on Ibbotson Stocks, Bonds, Bills, and Inflation: 2011
Classic Yearbook (Chicago: Morningstar, Inc., 2011), p. 32.
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Value of $100 Invested at the End of 1925 in U.S.
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What are investment returns?
• Investment returns measure the financial results
of an investment.
• Returns may be historical or prospective
(anticipated).
• Returns can be expressed in:
– Dollar terms.
– Percentage terms.
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An investment costs $1,000 and is sold after
1 year for $1,100.
Dollar return:
Percentage return:
$ Received - $ Invested
$1,100 - $1,000 = $100.
$ Return/$ Invested
$100/$1,000 = 0.10 = 10%.
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How Does One Measure Returns?
• Realized (Historical) Returns
– The return that actually occurs over a particular time
period.
Rate Gain Capital YieldDividend
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t
tt
t
t
t
ttt
P
PP
P
Div
P
PDivR
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Hypothetical Investment Alternatives
Economy Prob. T-Bills HT Coll USR MP
Recession 0.1 5.5% -27.0% 27.0% 6.0% -17.0%
Below avg 0.2 5.5% -7.0% 13.0% -14.0% -3.0%
Average 0.4 5.5% 15.0% 0.0% 3.0% 10.0%
Above avg 0.2 5.5% 30.0% -11.0% 41.0% 25.0%
Boom 0.1 5.5% 45.0% -21.0% 26.0% 38.0%
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Why is the T-bill return independent of the economy?
Do T-bills promise a completely risk-free return?
• T-bills will return the promised 5.5%, regardless of
the economy.
• No, T-bills do not provide a completely risk-free
return, as they are still exposed to inflation.
Although, very little unexpected inflation is likely to
occur over such a short period of time.
• T-bills are also risky in terms of reinvestment risk.
• T-bills are risk-free in the default sense of the word.
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How do the returns of High Tech and
Collections behave in relation to the market?
• High Tech: Moves with the economy, and
has a positive correlation. This is typical.
• Collections: Is countercyclical with the
economy, and has a negative correlation.
This is unusual.
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Calculating the Expected Return
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12.4%
(0.1)(45%)(0.2)(30%)
(0.4)(15%)(0.2)(-7%)-27%))(1.0(ˆ
r̂
return of rate Expectedˆ
N
1i
r
rP
r
ii
Summary of Expected Returns
Expected Return
High Tech 12.4%
Market 10.5%
US Rubber 9.8%
T-bills 5.5%
Collections 1.0%
High Tech has the highest expected return, and appears
to be the best investment alternative, but is it really?
Have we failed to account for risk?
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Calculating Standard Deviation
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N
1ii
2
2
P)r̂r(
Variance
deviation Standard
Standard Deviation for Each Investment
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%0.0
)1.0()5.55.5(
)2.0()5.55.5()4.0()5.55.5(
)2.0()5.55.5()1.0()5.55.5(
)ˆ(
bills-T
2/1
2
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bills-T
1
2
N
i
iPrr
σM = 15.2% σUSR = 18.8%
σColl = 13.2% σHT = 20%
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Comparing Standard Deviations
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USR
Prob. T-bills
HT
0 5.5 9.8 12.4 Rate of Return (%)
Comments on Standard Deviation as a
Measure of Risk
• Standard deviation (σi) measures total, or
stand-alone, risk.
• The larger σi is, the lower the probability that
actual returns will be close to expected
returns.
• Larger σi is associated with a wider
probability distribution of returns.
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Comparing Risk and Return
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Security Expected Return, Risk,
T - bills 5 .5% 0.0% High Tech 12.4 20.0 Collections* 1.0 13.2 US Rubber* 9.8 18.8 Market 10.5 1 5.2
*Seems out of place.
r̂
Coefficient of Variation (CV)
• A standardized measure of dispersion about
the expected value, that shows the risk per
unit of return.
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r̂return Expected
deviation StandardCV
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Illustrating the CV as a Measure of Relative Risk
σA = σB , but A is riskier because of a larger probability
of losses. In other words, the same amount of risk (as
measured by σ) for smaller returns.
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0
A B
Rate of Return (%)
Prob.
Risk Rankings by Coefficient of Variation
CV
T-bills 0.0
High Tech 1.6
Collections 13.2
US Rubber 1.9
Market 1.4
• Collections has the highest degree of risk per unit of
return.
• High Tech, despite having the highest standard
deviation of returns, has a relatively average CV.
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Investor Attitude Towards Risk
• Risk aversion: assumes investors dislike
risk and require higher rates of return to
encourage them to hold riskier securities.
• Risk premium: the difference between the
return on a risky asset and a riskless asset,
which serves as compensation for investors
to hold riskier securities.
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Portfolio Construction: Risk and Return
• Assume a two-stock portfolio is created with
$50,000 invested in both High Tech and
Collections.
• A portfolio’s expected return is a weighted
average of the returns of the portfolio’s
component assets.
• Standard deviation is a little more tricky and
requires that a new probability distribution for
the portfolio returns be constructed.
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Calculating Portfolio Expected Return
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%7.6%)0.1(5.0%)4.12(5.0ˆ
ˆˆ
:average weighteda is ˆ
1
p
N
i
iip
p
r
rwr
r
An Alternative Method for Determining
Portfolio Expected Return
Economy Prob HT Coll Port
Recession 0.1 -27.0% 27.0% 0.0%
Below avg 0.2 -7.0% 13.0% 3.0%
Average 0.4 15.0% 0.0% 7.5%
Above avg 0.2 30.0% -11.0% 9.5%
Boom 0.1 45.0% -21.0% 12.0%
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6.7% (12.0%) 0.10 (9.5%) 0.20
(7.5%) 0.40 (3.0%) 0.20 (0.0%) 0.10 r̂p
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Calculating Portfolio Standard Deviation and CV
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51.0%7.6
%4.3
%4.3
6.7) - (12.0 0.10
6.7) - (9.5 0.20
6.7) - (7.5 0.40
6.7) - (3.0 0.20
6.7) - (0.0 0.10 21
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p
p
CV
Comments on Portfolio Risk Measures
• σp = 3.4% is much lower than the σi of either
stock (σHT = 20.0%; σColl = 13.2%).
• σp = 3.4% is lower than the weighted
average of High Tech and Collections’ σ
(16.6%).
• Therefore, the portfolio provides the average
return of component stocks, but lower than
the average risk.
• Why? Negative correlation between stocks.
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General Comments about Risk
• σ 35% for an average stock.
• Most stocks are positively (though not
perfectly) correlated with the market (i.e., ρ
between 0 and 1).
• Combining stocks in a portfolio generally
lowers risk.
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Correlation
• The degree to which the stocks face common
risks and their prices move together.
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Returns Distribution for Two Perfectly
Negatively Correlated Stocks (ρ = -1.0)
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Returns Distribution for Two Perfectly
Positively Correlated Stocks (ρ = 1.0)
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Stock M
0
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-10
Stock M’
0
15
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-10
Portfolio MM’
0
15
25
-10
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Partial Correlation, ρ = +0.35
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Creating a Portfolio: Beginning with One Stock and
Adding Randomly Selected Stocks to Portfolio
• σp decreases as stocks are added, because
they would not be perfectly correlated with the
existing portfolio.
• Expected return of the portfolio would remain
relatively constant.
• Eventually the diversification benefits of
adding more stocks dissipates (after about 40
stocks), and for large stock portfolios, σp
tends to converge to 20%.
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Diversification in Stock Portfolios
# Stocks in Portfolio 10 20 30 40 2,000+
Diversifiable Risk
Market Risk
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Firm Specific Risk, p
p (%)
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Breaking Down Sources of Risk
Stand-alone or total risk
= Market risk + Diversifiable risk
• Market risk: portion of a security’s stand-
alone risk that cannot be eliminated through
diversification. Measured by beta.
• Diversifiable risk: portion of a security’s
stand-alone risk that can be eliminated
through proper diversification.
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Failure to Diversify
• If an investor chooses to hold a one-stock
portfolio (doesn’t diversify), would the investor
be compensated for the extra risk they bear? – NO!
– Stand-alone risk is not important to a well-
diversified investor.
– Rational, risk-averse investors are concerned with
σp, which is based upon market risk.
– There can be only one price (the market return) for
a given security.
– No compensation should be earned for holding
unnecessary, diversifiable, risk.
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The Capital Asset Pricing Model (CAPM)
William F. Sharpe
b. 1934
Nobel Laureate, 1990
The risk premium for
any security is
proportional to its beta
with the market
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Capital Asset Pricing Model (CAPM)
• Model linking risk and required returns. CAPM
suggests that there is a Security Market Line
(SML) that states that a stock’s required return
equals the risk-free return plus a risk premium
that reflects the stock’s risk after diversification.
ri = rRF + (rM – rRF)βi
ri = rRF + (RPM)βi
• Primary conclusion: The relevant riskiness of a
stock is its contribution to the riskiness of a well-
diversified portfolio.
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Beta
• Measures a stock’s market risk, and shows a
stock’s volatility relative to the market.
• Indicates how risky a stock is if the stock is
held in a well-diversified portfolio.
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Comments on Beta
• If beta = 1.0, the security is just as risky as
the average stock.
• If beta > 1.0, the security is riskier than
average.
• If beta < 1.0, the security is less risky than
average.
• Most stocks have betas in the range of 0.5 to
1.5.
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How is Beta Interpreted?
EXCESS RETURN
ON STOCK
EXCESS RETURN
ON MARKET PORTFOLIO
Beta < 1
(defensive)
Beta = 1
Beta > 1
(aggressive)
Each characteristic
line has a
different slope.
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Capital Asset Pricing Model (CAPM)
• CAPM allows us to find the required returns for a given level of risk.
• SML shows relationship between risk (measured by asset’s covariance with market) and its required return.
• Risk measure for market is market’s covariance with itself, i.e., its variance, Var (RM).
• For any risky asset, required return = RF + risk premium which is based on the covariance of the asset with the market.
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Estimating the Required Rate of Return
• Estimating the required return takes two steps:
1. Measure the investment’s systematic risk, β
2. Determine the risk premium required to compensate
for that amount of systematic risk
• Systematic risk depends on the beta of the
security.
– Beta: a measure of the sensitivity of a stock’s returns
relative to the market returns.
R Rit i i Mt
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Estimating the Required Return (cont’d)
rj = rF + βj(rM - rF)
M = 1.0
Systematic Risk (Beta)
rF
rM
Req
uir
ed
Retu
rn
Risk
Premium
SML • Market Risk Premium
– Historical average
excess return of the
market over rF
– Researchers
generally report
estimates of 4–8%
for the future equity
risk premium.
– SML: Security Mkt Line
)(
),(
)(
),( )(
market h thecommon wit is that of Volatility
i
Mkt
Mkti
Mkt
i
MktiiMkt
iRVar
RRCov
RSD
RRCorrRSD
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Example on Required Return
• Estimate the required rate of return for a stock
with a beta of 1.14 when the risk-free rate is 8%
and an expected market return of 14%.
rF=8%
rM=14%
M = 1.0
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Can the beta of a security be negative?
• Yes, if the correlation between Stock i and
the market is negative (i.e., ρi,m < 0).
• If the correlation is negative, the regression
line would slope downward, and the beta
would be negative.
• However, a negative beta is highly unlikely.
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Calculating Betas
• Well-diversified investors are primarily concerned
with how a stock is expected to move relative to the
market in the future.
• Without a crystal ball to predict the future, analysts
are forced to rely on historical data. A typical
approach to estimate beta is to run a regression of
the security’s past returns against the past returns of
the market.
• The slope of the regression line is defined as the
beta coefficient for the security.
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Illustrating the Calculation of Beta
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.
.
.
ri
_
rM -5 0 5 10 15 20
20
15
10
5
-5
-10
Regression line:
ri = -2.59 + 1.44 rM ̂ ̂
Year rM ri
1 15% 18%
2 -5 -10
3 12 16
Beta Coefficients for High Tech, Collections,
and T-Bills
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rM
ri
-20 0 20 40
40 20
-20
HT: b = 1.32
T-bills: b = 0
Coll: b = -0.87
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Web Sites for Beta
• http://finance.yahoo.com
– Enter the ticker symbol for a “Stock Quote”, such as
IBM or Dell, then click GO.
– When the quote comes up, select Key Statistics from
panel on left.
– Can also download historical prices to compute returns.
• www.valueline.com
– Enter a ticker symbol at the top of the page.
• Most stocks have betas in the range of 0.5 to 1.5.
Comparing Expected Returns and Beta Coefficients
Security Expected Return Beta
High Tech 12.4% 1.32
Market 10.5 1.00
US Rubber 9.8 0.88
T-Bills 5.5 0.00
Collections 1.0 -0.87
Riskier securities have higher returns, so the rank
order is OK.
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The Security Market Line (SML): Calculating
Required Rates of Return
SML: ri = rRF + (rM – rRF)βi
ri = rRF + (RPM)βi
• If the expected return on the market is
10.5% and the risk free rate is 5.5%, the
market risk premium is
RPM = rM rRF = 10.5% 5.5% = 5.0%.
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What is the market risk premium?
• Additional return over the risk-free rate
needed to compensate investors for
assuming an average amount of risk.
• Its size depends on the perceived risk of the
stock market and investors’ degree of risk
aversion.
• Varies from year to year, but most estimates
suggest that it ranges between 4% and 8%
per year.
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Calculating Required Rates of Return
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rHT = 5.5% + (5.0%)(1.32) = 5.5% + 6.6% = 12.10%
rM = 5.5% + (5.0%)(1.00) = 10.50%
rUSR = 5.5% +(5.0%)(0.88) = 9.90%
rT-bill = 5.5% + (5.0)(0.00) = 5.50%
rColl = 5.5% + (5.0%)(-0.87) = 1.15%
r
High Tech 12.4% 12.1% Undervalued
Market 10.5 10.5 Fairly valued
US Rubber 9.8 9.9 Overvalued
T-bills 5.5 5.5 Fairly valued
Collections 1.0 1.15 Overvalued
Expected vs. Required Returns
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r̂
)rr̂(
)rr̂(
)rr̂(
)rr̂(
)rr̂(
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Illustrating the Security Market Line
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. .
Coll
. HT
T-bills
. USR
SML
rM = 10.5
rRF = 5.5
-1 0 1 2
.
SML: ri = 5.5% + (5.0%)βi
ri (%)
Risk, bi
.
An Example:
Equally-Weighted Two-Stock Portfolio
• Create a portfolio with 50% invested in High
Tech and 50% invested in Collections.
• The beta of a portfolio is the weighted
average of each of the stock’s betas.
βP = wHTβHT + wCollβColl
βP = 0.5(1.32) + 0.5(-0.87)
βP = 0.225
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Calculating Portfolio Required Returns
• The required return of a portfolio is the weighted average of each of the stock’s required returns.
rP = wHTrHT + wCollrColl
rP = 0.5(12.10%) + 0.5(1.15%)
rP = 6.625% • Or, using the portfolio’s beta, CAPM can be
used to solve for expected return.
rP = rRF + (RPM)βP
rP = 5.5% + (5.0%)(0.225)
rP = 6.625%
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Computing a Portfolio’s Variance and Volatility
• Variance of a Two-Stock Portfolio
),(2 )( )( )( 21212
2
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2
1 rrCovwwrVarwrVarwrVar P
Exercise: Portfolio application problem
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Portfolio Application Problem
• F&N (F) has an expected return of 10% and a
standard deviation of 20%; CapitaLand (C) has an
expected return of 16% and a standard deviation
of 40%. If the correlation between F&N and
CapitaLand is 0.4, what are the expected return
and standard deviation for a portfolio comprised of
30% in F&N and 70% in CapitaLand?
Factors That Change the SML
• What if investors raise inflation expectations
by 3%, what would happen to the SML?
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SML1
ri (%) SML2
0 0.5 1.0 1.5
13.5
10.5 8.5
5.5
ΔI = 3%
Risk, bi
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Factors That Change the SML
• What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML?
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SML1
ri (%) SML2
0 0.5 1.0 1.5
ΔRPM = 3%
Risk, bi
13.5
10.5
5.5
Verifying the CAPM Empirically
• The CAPM has not been verified completely.
• Statistical tests have problems that make
verification almost impossible.
• Some argue that there are additional risk
factors, other than the market risk premium,
that must be considered.
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More Thoughts on the CAPM
• Investors seem to be concerned with both
market risk and total risk. Therefore, the SML
may not produce a correct estimate of ri.
ri = rRF + (rM – rRF)bi + ???
• CAPM/SML concepts are based upon
expectations, but betas are calculated using
historical data. A company’s historical data
may not reflect investors’ expectations about
future riskiness.
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Questions and Answers