# Risk Return and Capital Asset Pricing Model by obr30388

VIEWS: 6 PAGES: 15

• pg 1
```									ee8190f5-f13e-4629-9378-6f657810a299.xls                                                                                   Model
Ch 03 Mini Case                                                                                            3/8/2001

Chapter 3. Mini Case

Situation
To begin, briefly review the Chapter 2 Mini Case. Then, extend your knowledge of risk and return by

CAPM
The Capital Asset Pricing Model is an equilibrium model that specifies the relationship between risk and
required rate of return for assets held in well diversified portfolios.

Assumptions
Investors all think in terms of a single holding period.
All investors have identical expectations.
Investors can borrow or lend unlimited amounts at the risk free rate.
All assets are perfectly divisible.
There are not taxes and transaction costs.
All investors are price takers, that is, investors buying and selling will not influence stock prices.
Quantities of all assets are given and fixed.

FEASIBLE AND EFFICIENT PORTFOLIOS
The feasible set of portfolios represent all portfolios that can be constructed from a given set of stocks.
An efficient portfolio is one that offers: the most return for a given amount of risk or the least risk for a
given amount of return.

Expected
Portfolio             Efficient Set
Return, kp

Feasible Set

Risk, sp
Feasible and Efficient Portfolios
.

OPTIMAL PORTFOLIOS
An investor's optimal portfolio is defined by the tangency point between the efficient set and the investor's
indifference curve. The inderference curve reflect an investor's attitude toward risk as reflected in his or

Expected
IB2 I
Return, kp                                B1

Michael C. Ehrhardt                                             Page 1                                                  7/19/2011
Expected
ee8190f5-f13e-4629-9378-6f657810a299.xls                                                                              Model
IB2 I
Return, kp                              B1

Optimal Portfolio
IA2                                               Investor B
IA1

Optimal Portfolio
Investor A

Risk sp
Optimal Portfolios
.

EFFICIENT SET WITH A RISK-FREE ASSET
When a risk free asset is added to the feasible set, investors can create portfolios that combine this asset
with a portfolio of risky asset. The straight line connecting krf with M, the tangency point between the line
and the old efficiency set, becomes the new efficient frontier.

Efficient Set with a Risk-Free Asset

Expected                                   Z
Return, kp
.B
^
kM                  .
M

The Capital Market

kRF
A   .                           Line (CML):
New Efficient Set

sM                                     Risk, sp
.

OPTIMAL PORTFOLIO WITH A RISK-FREE ASSET
The optimal portfolio for any investor is the point of tangency between the CML and the investors indifference
curve.

Expected
Return, kp
CML
I2
I1

. .
^                          M
kM
^                 R
k
Michael C. Ehrhardt
R                                           Page 2                                               7/19/2011

R = Optimal
kRF                                   Portfolio
CML
I2
I1
ee8190f5-f13e-4629-9378-6f657810a299.xls
^
kM
^
k   R
M

.R
.                                                                                                  Model

R = Optimal
kRF                                                    Portfolio

sR          sM                                  Risk, sp
.

Capital Market Line
The capital market line is all linear combinations of the risk free asset and portfolio M.

khat=                               krf              +            (km-krf)/sm           x                  sp

Intercept                              Slope                         Risk Measure

The CML gives the risk and return relationship for efficient portfolios
The SML , also part of CAPM, gives the risk and return relationship for individual stocks.

SML =                                   ki                +             (RPm)               x                  b

Beta Calculation
Run a regression line of past returns on Stock I versus returns on the market

Year                   km               ki
1                    15%             18%
2                    -5%             -10%
3                    12%             16%

Beta Calculation

25%
20%
15%
Stock Return

10%                                               beta calculation

5%
Linear (beta
0%                                               calculation)
-10%     -5%-5% 0%            5%    10%      15%      20%
-10%                                        y = 1.4441x - 0.0259
R² = 0.9943
-15%
Market Return

R2 measures the percent of a stock's variance as explained by the market.

Relationship between stand alone, market, and diversifiable risk

Michael C. Ehrhardt                                                           Page 3                                                    7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                                                                                    Model

s2j =                 b2j *s2m                 +           s2ej

s2j =         stand alone risk of stock J
2       2
b j *s     m=       market risk of stock J
s2ej =        diversifiable risk of stock J

Test to verify CAPM
Beta stability test and tests based on the slope of the SML.

Test of the SML indicate a more-or-less linear relationship between realized return and market risk.
Slope is less than predicted
Irrelevance of diversifiable risk specified in the CAPM model can be questioned.
Betas of individual securities are not good estimators of future risk.
Betas of ten or more randomly selected stocks are reasonably stable.
Past betas are good estimates of future portfolio volitility.

Conclusions regarding CAPM
It is impossible to verify.
Recent studies have questioned its validity.
Investors seemed to be concerned with both market and stand alone risk. Therefore, the SML may not produce the correct estimate of kj.
CAPM/SML concepts are based on expectations, yeta betas are calculated using historical data.

CAPM and the Arbitrage Pricing Theory
The CAPM is a single factor model. The APT proposes that the relationship between risk and return is more complex and may be due
to multiple factos such as GDP, growth, expected inflation, tax rate changes, and dividend yield.

Required Return for stock I under the Fama-French-3-Factor Model
Fama and French propose three factors:
The excess market return, km-krf.
The return on, S, a portfolio of small firms minus the return on B, a portfolio of big firms. This return is called
ksmb, for S minus B.
The return on, H, a portfolio of firms with high book-to-market ratios minus the return on L, a portfolio of firms
with low book-to-market ratios. This return is called khml, for H minus L.

Required return for Stock I

ki =                  krf                   +         (km-krf) b         +              (ksmb) c          +

b= Sensitivity of stock I to the market
c= Sensitivity of stock I to the size factor
c= Sensitivity of stock I to the book-to-market factor

b=                                         0.9
krf =                                   6.8%
RPm =                                   6.3%
c=                                        -0.5
value for size factor =                 4.0%
d=                                        -0.3
book-to-market factor=                  5.0%

ki =                        8.97%

CAPM =                       12.47%

Michael C. Ehrhardt                                              Page 4                                                 7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls               Model

Michael C. Ehrhardt                        Page 5   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls               Model

Michael C. Ehrhardt                        Page 6   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls               Model

Michael C. Ehrhardt                        Page 7   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls               Model

Michael C. Ehrhardt                        Page 8   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls               Model

Michael C. Ehrhardt                        Page 9   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                Model

Michael C. Ehrhardt                        Page 10   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                Model

Michael C. Ehrhardt                        Page 11   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                Model

Michael C. Ehrhardt                        Page 12   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                Model

Michael C. Ehrhardt                        Page 13   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                Model

Michael C. Ehrhardt                        Page 14   7/19/2011
ee8190f5-f13e-4629-9378-6f657810a299.xls                                        Model

Excess Returns
on Wal-Mart,
kS-kRF
120%

110%

100%

90%

80%

70%

60%

50%

40%                         Excess Returns
on the Market, k M-kRF
30%

20%

10%

0%
-30%     -20%   -10%           0%       10%    20%          30%

Michael C. Ehrhardt                                          Page 15         7/19/2011

```
To top