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8-1
CHAPTER 8
Risk and Rates of Return
 Stand-alone risk
 Portfolio risk
 Risk & return: CAPM / SML
8-2
Investment returns
The rate of return on an investment can be
calculated as follows:
(Amount received – Amount invested)
Return = ________________________
Amount invested
For example, if $1,000 is invested and $1,100 is
returned after one year, the rate of return for this
investment is:
($1,100 - $1,000) / $1,000 = 10%.
8-3
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.
8-4
Probability distributions
 A listing of all possible outcomes, and the
probability of each occurrence.
 Can be shown graphically.
Expected Rate of Return
Rate of
Return (%)
100
15
0
-70
Firm X
Firm Y
8-5
Selected Realized Returns,
1926 – 2004
Average Standard
Return Deviation
Small-company stocks 17.5% 33.1%
Large-company stocks 12.4 20.3
L-T corporate bonds 6.2 8.6
L-T government bonds 5.8 9.3
U.S. Treasury bills 3.8 3.1
Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation
Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), p28.
8-6
Investment alternatives
Economy Prob. T-Bill 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%
8-7
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 rate
risk.
 T-bills are risk-free in the default sense of the
word.
8-8
How do the returns of HT and Coll.
behave in relation to the market?
 HT – Moves with the economy, and has
a positive correlation. This is typical.
 Coll. – Is countercyclical with the
economy, and has a negative
correlation. This is unusual.
8-9
Calculating the expected return
12.4%
(0.1)
(45%)
(0.2)
(30%)
(0.4)
(15%)
(0.2)
(-7%)
(0.1)
(-27%)
r
P
r
r
return
of
rate
expected
r
HT
^
N
1
i
i
i
^
^










8-10
Summary of expected returns
Expected return
HT 12.4%
Market 10.5%
USR 9.8%
T-bill 5.5%
Coll. 1.0%
HT has the highest expected return, and appears
to be the best investment alternative, but is it
really? Have we failed to account for risk?
8-11
Calculating standard deviation
deviation
Standard


2
Variance 



i
2
N
1
i
i P
)
r
(r
σ 


 ˆ
8-12
Standard deviation for each investment
15.2%
18.8%
20.0%
13.2%
0.0%
(0.1)
5.5)
-
(5.5
(0.2)
5.5)
-
(5.5
(0.4)
5.5)
-
(5.5
(0.2)
5.5)
-
(5.5
(0.1)
5.5)
-
(5.5
P
)
r
(r
M
USR
HT
C oll
bills
T
2
2
2
2
2
bills
T
N
1
i
i
2
^
i

































2
1
8-13
Comparing standard deviations
USR
Prob.
T - bill
HT
0 5.5 9.8 12.4 Rate of Return (%)
8-14
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
closer to expected returns.
 Larger σi is associated with a wider
probability distribution of returns.
8-15
Comparing risk and return
Security Expected
return, r
Risk, σ
T-bills 5.5% 0.0%
HT 12.4% 20.0%
Coll* 1.0% 13.2%
USR* 9.8% 18.8%
Market 10.5% 15.2%
* Seem out of place.
^
8-16
Coefficient of Variation (CV)
A standardized measure of dispersion about
the expected value, that shows the risk per
unit of return.
r
return
Expected
deviation
Standard
CV
ˆ



8-17
Risk rankings,
by coefficient of variation
CV
T-bill 0.0
HT 1.6
Coll. 13.2
USR 1.9
Market 1.4
 Collections has the highest degree of risk per unit
of return.
 HT, despite having the highest standard deviation
of returns, has a relatively average CV.
8-18
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.
0
A B
Rate of Return (%)
Prob.
8-19
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.
8-20
Portfolio construction:
Risk and return
 Assume a two-stock portfolio is created with
$50,000 invested in both HT 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 devised.
8-21
Calculating portfolio expected return
6.7%
(1.0%)
0.5
(12.4%)
0.5
r
r
w
r
:
average
weighted
a
is
r
p
^
N
1
i
i
^
i
p
^
p
^



 

8-22
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%
6.7%
(12.0%)
0.10
(9.5%)
0.20
(7.5%)
0.40
(3.0%)
0.20
(0.0%)
0.10
rp
^






8-23
Calculating portfolio standard
deviation and CV
0.51
6.7%
3.4%
CV
3.4%
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
p
2
1
2
2
2
2
2
p



























8-24
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 HT and Coll.’s σ (16.6%).
 Therefore, the portfolio provides the
average return of component stocks, but
lower than the average risk.
 Why? Negative correlation between stocks.
8-25
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.
8-26
Returns distribution for two perfectly
negatively correlated stocks (ρ = -1.0)
-10
15 15
25 25
25
15
0
-10
Stock W
0
Stock M
-10
0
Portfolio WM
8-27
Returns distribution for two perfectly
positively correlated stocks (ρ = 1.0)
Stock M
0
15
25
-10
Stock M’
0
15
25
-10
Portfolio MM’
0
15
25
-10
8-28
Creating a portfolio:
Beginning with one stock and adding
randomly selected stocks to portfolio
 σp decreases as stocks 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
10 stocks), and for large stock portfolios, σp
tends to converge to  20%.
8-29
Illustrating diversification effects of
a stock portfolio
# Stocks in Portfolio
10 20 30 40 2,000+
Diversifiable Risk
Market Risk
20
0
Stand-Alone Risk, p
p (%)
35
8-30
Breaking down sources of risk
Stand-alone 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.
8-31
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.
8-32
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) bi
 Primary conclusion: The relevant riskiness of a
stock is its contribution to the riskiness of a well-
diversified portfolio.
8-33
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.
8-34
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.
8-35
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.
8-36
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.
8-37
Illustrating the calculation of beta
.
.
.
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
8-38
Beta coefficients for
HT, Coll, and T-Bills
ri
_
kM
_
-20 0 20 40
40
20
-20
HT: b = 1.30
T-bills: b = 0
Coll: b = -0.87
8-39
Comparing expected returns
and beta coefficients
Security Expected Return Beta
HT 12.4% 1.32
Market 10.5 1.00
USR 9.8 0.88
T-Bills 5.5 0.00
Coll. 1.0 -0.87
Riskier securities have higher returns, so the
rank order is OK.
8-40
The Security Market Line (SML):
Calculating required rates of return
SML: ri = rRF + (rM – rRF) bi
ri = rRF + (RPM) bi
 Assume the yield curve is flat and that
rRF = 5.5% and RPM = 5.0%.
8-41
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.
8-42
Calculating required rates of return
 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%
8-43
Expected vs. Required returns
r)
r
(
Overvalued
1.2
1.0
Coll.
r)
r
(
ued
Fairly val
5.5
5.5
bills
-
T
r)
r
(
Overvalued
9.9
9.8
USR
r)
r
(
ued
Fairly val
10.5
10.5
Market
r)
r
(
d
Undervalue
12.1%
12.4%
HT
r
r
^
^
^
^
^
^





8-44
Illustrating the
Security Market Line
.
.
Coll.
.
HT
T-bills
.
USR
SML
rM = 10.5
rRF = 5.5
-1 0 1 2
.
SML: ri = 5.5% + (5.0%) bi
ri (%)
Risk, bi
8-45
An example:
Equally-weighted two-stock portfolio
 Create a portfolio with 50% invested in
HT and 50% invested in Collections.
 The beta of a portfolio is the weighted
average of each of the stock’s betas.
bP = wHT bHT + wColl bColl
bP = 0.5 (1.32) + 0.5 (-0.87)
bP = 0.225
8-46
Calculating portfolio required returns
 The required return of a portfolio is the weighted
average of each of the stock’s required returns.
rP = wHT rHT + wColl rColl
rP = 0.5 (12.10%) + 0.5 (1.15%)
rP = 6.63%
 Or, using the portfolio’s beta, CAPM can be used
to solve for expected return.
rP = rRF + (RPM) bP
rP = 5.5% + (5.0%) (0.225)
rP = 6.63%
8-47
Factors that change the SML
 What if investors raise inflation expectations
by 3%, what would happen to the SML?
SML1
ri (%)
SML2
0 0.5 1.0 1.5
13.5
10.5
8.5
5.5
D I = 3%
Risk, bi
8-48
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?
SML1
ri (%) SML2
0 0.5 1.0 1.5
13.5
10.5
5.5
D RPM = 3%
Risk, bi
8-49
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.
8-50
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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risk return.ppt

  • 1. 8-1 CHAPTER 8 Risk and Rates of Return  Stand-alone risk  Portfolio risk  Risk & return: CAPM / SML
  • 2. 8-2 Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.
  • 3. 8-3 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.
  • 4. 8-4 Probability distributions  A listing of all possible outcomes, and the probability of each occurrence.  Can be shown graphically. Expected Rate of Return Rate of Return (%) 100 15 0 -70 Firm X Firm Y
  • 5. 8-5 Selected Realized Returns, 1926 – 2004 Average Standard Return Deviation Small-company stocks 17.5% 33.1% Large-company stocks 12.4 20.3 L-T corporate bonds 6.2 8.6 L-T government bonds 5.8 9.3 U.S. Treasury bills 3.8 3.1 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2005 Yearbook (Chicago: Ibbotson Associates, 2005), p28.
  • 6. 8-6 Investment alternatives Economy Prob. T-Bill 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%
  • 7. 8-7 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 rate risk.  T-bills are risk-free in the default sense of the word.
  • 8. 8-8 How do the returns of HT and Coll. behave in relation to the market?  HT – Moves with the economy, and has a positive correlation. This is typical.  Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual.
  • 9. 8-9 Calculating the expected return 12.4% (0.1) (45%) (0.2) (30%) (0.4) (15%) (0.2) (-7%) (0.1) (-27%) r P r r return of rate expected r HT ^ N 1 i i i ^ ^          
  • 10. 8-10 Summary of expected returns Expected return HT 12.4% Market 10.5% USR 9.8% T-bill 5.5% Coll. 1.0% HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?
  • 11. 8-11 Calculating standard deviation deviation Standard   2 Variance     i 2 N 1 i i P ) r (r σ     ˆ
  • 12. 8-12 Standard deviation for each investment 15.2% 18.8% 20.0% 13.2% 0.0% (0.1) 5.5) - (5.5 (0.2) 5.5) - (5.5 (0.4) 5.5) - (5.5 (0.2) 5.5) - (5.5 (0.1) 5.5) - (5.5 P ) r (r M USR HT C oll bills T 2 2 2 2 2 bills T N 1 i i 2 ^ i                                  2 1
  • 13. 8-13 Comparing standard deviations USR Prob. T - bill HT 0 5.5 9.8 12.4 Rate of Return (%)
  • 14. 8-14 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 closer to expected returns.  Larger σi is associated with a wider probability distribution of returns.
  • 15. 8-15 Comparing risk and return Security Expected return, r Risk, σ T-bills 5.5% 0.0% HT 12.4% 20.0% Coll* 1.0% 13.2% USR* 9.8% 18.8% Market 10.5% 15.2% * Seem out of place. ^
  • 16. 8-16 Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return. r return Expected deviation Standard CV ˆ   
  • 17. 8-17 Risk rankings, by coefficient of variation CV T-bill 0.0 HT 1.6 Coll. 13.2 USR 1.9 Market 1.4  Collections has the highest degree of risk per unit of return.  HT, despite having the highest standard deviation of returns, has a relatively average CV.
  • 18. 8-18 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. 0 A B Rate of Return (%) Prob.
  • 19. 8-19 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.
  • 20. 8-20 Portfolio construction: Risk and return  Assume a two-stock portfolio is created with $50,000 invested in both HT 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 devised.
  • 21. 8-21 Calculating portfolio expected return 6.7% (1.0%) 0.5 (12.4%) 0.5 r r w r : average weighted a is r p ^ N 1 i i ^ i p ^ p ^      
  • 22. 8-22 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% 6.7% (12.0%) 0.10 (9.5%) 0.20 (7.5%) 0.40 (3.0%) 0.20 (0.0%) 0.10 rp ^      
  • 23. 8-23 Calculating portfolio standard deviation and CV 0.51 6.7% 3.4% CV 3.4% 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 p 2 1 2 2 2 2 2 p                           
  • 24. 8-24 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 HT and Coll.’s σ (16.6%).  Therefore, the portfolio provides the average return of component stocks, but lower than the average risk.  Why? Negative correlation between stocks.
  • 25. 8-25 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.
  • 26. 8-26 Returns distribution for two perfectly negatively correlated stocks (ρ = -1.0) -10 15 15 25 25 25 15 0 -10 Stock W 0 Stock M -10 0 Portfolio WM
  • 27. 8-27 Returns distribution for two perfectly positively correlated stocks (ρ = 1.0) Stock M 0 15 25 -10 Stock M’ 0 15 25 -10 Portfolio MM’ 0 15 25 -10
  • 28. 8-28 Creating a portfolio: Beginning with one stock and adding randomly selected stocks to portfolio  σp decreases as stocks 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 10 stocks), and for large stock portfolios, σp tends to converge to  20%.
  • 29. 8-29 Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Diversifiable Risk Market Risk 20 0 Stand-Alone Risk, p p (%) 35
  • 30. 8-30 Breaking down sources of risk Stand-alone 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.
  • 31. 8-31 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.
  • 32. 8-32 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) bi  Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well- diversified portfolio.
  • 33. 8-33 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.
  • 34. 8-34 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.
  • 35. 8-35 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.
  • 36. 8-36 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.
  • 37. 8-37 Illustrating the calculation of beta . . . 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
  • 38. 8-38 Beta coefficients for HT, Coll, and T-Bills ri _ kM _ -20 0 20 40 40 20 -20 HT: b = 1.30 T-bills: b = 0 Coll: b = -0.87
  • 39. 8-39 Comparing expected returns and beta coefficients Security Expected Return Beta HT 12.4% 1.32 Market 10.5 1.00 USR 9.8 0.88 T-Bills 5.5 0.00 Coll. 1.0 -0.87 Riskier securities have higher returns, so the rank order is OK.
  • 40. 8-40 The Security Market Line (SML): Calculating required rates of return SML: ri = rRF + (rM – rRF) bi ri = rRF + (RPM) bi  Assume the yield curve is flat and that rRF = 5.5% and RPM = 5.0%.
  • 41. 8-41 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.
  • 42. 8-42 Calculating required rates of return  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%
  • 43. 8-43 Expected vs. Required returns r) r ( Overvalued 1.2 1.0 Coll. r) r ( ued Fairly val 5.5 5.5 bills - T r) r ( Overvalued 9.9 9.8 USR r) r ( ued Fairly val 10.5 10.5 Market r) r ( d Undervalue 12.1% 12.4% HT r r ^ ^ ^ ^ ^ ^     
  • 44. 8-44 Illustrating the Security Market Line . . Coll. . HT T-bills . USR SML rM = 10.5 rRF = 5.5 -1 0 1 2 . SML: ri = 5.5% + (5.0%) bi ri (%) Risk, bi
  • 45. 8-45 An example: Equally-weighted two-stock portfolio  Create a portfolio with 50% invested in HT and 50% invested in Collections.  The beta of a portfolio is the weighted average of each of the stock’s betas. bP = wHT bHT + wColl bColl bP = 0.5 (1.32) + 0.5 (-0.87) bP = 0.225
  • 46. 8-46 Calculating portfolio required returns  The required return of a portfolio is the weighted average of each of the stock’s required returns. rP = wHT rHT + wColl rColl rP = 0.5 (12.10%) + 0.5 (1.15%) rP = 6.63%  Or, using the portfolio’s beta, CAPM can be used to solve for expected return. rP = rRF + (RPM) bP rP = 5.5% + (5.0%) (0.225) rP = 6.63%
  • 47. 8-47 Factors that change the SML  What if investors raise inflation expectations by 3%, what would happen to the SML? SML1 ri (%) SML2 0 0.5 1.0 1.5 13.5 10.5 8.5 5.5 D I = 3% Risk, bi
  • 48. 8-48 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? SML1 ri (%) SML2 0 0.5 1.0 1.5 13.5 10.5 5.5 D RPM = 3% Risk, bi
  • 49. 8-49 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.
  • 50. 8-50 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.