Portfolio Theory - CAPM
-
Upload
andy-quach -
Category
Documents
-
view
222 -
download
0
Transcript of Portfolio Theory - CAPM
-
7/30/2019 Portfolio Theory - CAPM
1/85
Portfolio Theory
Capital Asset Pricing Model
-
7/30/2019 Portfolio Theory - CAPM
2/85
Chapter 5: Portfolio Theory &
Asset Pricing Model
Dont put all your eggs in one basket.- Ancient Chinese Proverb
-
7/30/2019 Portfolio Theory - CAPM
3/85
-
7/30/2019 Portfolio Theory - CAPM
4/85
Modern portfolio theory
How to reduce risk (diversification) How to pricerisk (beta)
Asset pricing model (CAPM)
We will Cover
-
7/30/2019 Portfolio Theory - CAPM
5/85
Required
rate of
return =
Risk-free
rate ofreturn
Since Treasurys are essentially, free of defaultrisk, the rate of return on a Treasury security is
considered the rate of return.
What is the Required Return
for a Treasury Security?
-
7/30/2019 Portfolio Theory - CAPM
6/85
Required
rate ofreturn
=
Risk-free
rate ofreturn +
Risk
Premium
How large of a risk premium should we
require to buy a corporate security?
For a corporate stock or bond, what
is the required rate of return?
-
7/30/2019 Portfolio Theory - CAPM
7/85
Expected Return - the return that an
investor expects to earn on an asset,
given its price, growth potential, etc.
Required Return - the return that an
investor requires on an asset given itsrisk.
Returns
-
7/30/2019 Portfolio Theory - CAPM
8/85
Returns may be historical orprospective (anticipated).
Returns can be expressed in:
Dollar terms.
Percentage terms.
Returns
-
7/30/2019 Portfolio Theory - CAPM
9/85
The possibility that an actual return will
differ from our expected return.
Uncertainty in the distribution of
possible outcomes.
What is Risk?
-
7/30/2019 Portfolio Theory - CAPM
10/85
Uncertainty in the distribution of possible outcomes.
Assume normal distribution
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
-10 -5 0 5 10 15 20 25 30
Company B
return
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
4 8 12
Company A
return
What is Risk?
-
7/30/2019 Portfolio Theory - CAPM
11/85
To get a general idea of a stocks
price variability, we could look at
the stocks price range over the pastyear.
A more scientific approach is to
examine the stocks STANDARD
DEVIATION of returns.
How do we Measure Risk?
-
7/30/2019 Portfolio Theory - CAPM
12/85
Standard deviation is a measure of the
dispersion of possible outcomes. The greater the standard deviation, thegreater the uncertainty, and therefore , thegreater the RISK.
Coefficient of variation (CV) is a relativerisk measure of stand-alone risk.
How do we Measure Risk?
-
7/30/2019 Portfolio Theory - CAPM
13/85
Combining several securities in a
portfolio can actually reduce overall
risk.
How does this work?
Portfolios
-
7/30/2019 Portfolio Theory - CAPM
14/85
rate
ofreturn
time
Given stock A & B, the returns on these
stocks do not move together over time(they are not perfectly correlated)
-
7/30/2019 Portfolio Theory - CAPM
15/85
rate
ofreturn
time
rA
Given stock A & B, the returns on these
stocks do not move together over time
(they are not perfectly correlated)
-
7/30/2019 Portfolio Theory - CAPM
16/85
rate
ofreturn
time
rA
rB
Given stock A & B, the returns on these
stocks do not move together over time
(they are not perfectly correlated)
-
7/30/2019 Portfolio Theory - CAPM
17/85
rate
ofreturn
time
rp
rA
rB
Given stock A & B, the returns on these
stocks do not move together over time(they are not perfectly correlated
-
7/30/2019 Portfolio Theory - CAPM
18/85
rate
ofreturn
time
rp
rA
rB
What has happened to the variability
of returns for the portfolio?
-
7/30/2019 Portfolio Theory - CAPM
19/85
Calculation of Return and Risk for a Portfolio
of Stocks
Expected return on a portfolio is the weighted
average of individual stock returns:
n
iiiP
REwRE
1
)()(
If the portfolio has two stocks, the portfolio mean is:
)()()(2211
REwREwREP
where w1 = weight for stock 1
w2 = weight for stock 2 &
w1 + w2 = 1
Note: the weights can be negative short selling.
-
7/30/2019 Portfolio Theory - CAPM
20/85
Calculation of Risk for a Portfolio of Stocks
Standard deviation on a portfolio of N-assets:
If the portfolio has two stocks, the portfolio standard
deviation is:
where w1 = weight for stock 1
w2 = weight for stock 2 & w1 + w2 = 1.0
N
i
N
jij
ijjiii
N
i
port Covwww1 ,1
22
1
BAABAA
2
B
2
A
2
A
2
Ap r)w1(w2)w1(w
-
7/30/2019 Portfolio Theory - CAPM
21/85
Portfolio return is the weighted average of individualstocks rates of return
Portfolio risk depends on the weighted average of: Variance of each stock
More importantly, covariance between individual stocks
Which dominates (or more important?)
N # of Variance # of COV
2 2 23 3 6
N N N2-1
ReCap:
-
7/30/2019 Portfolio Theory - CAPM
22/85
Investing in more than one security toreduce risk.
If two stocks are perfectly positively
correlated, diversification has noeffect on risk.
If two stocks are perfectly negatively
correlated, the portfolio is perfectlydiversified.
Diversification
-
7/30/2019 Portfolio Theory - CAPM
23/85
If you owned a share of every stock
traded on the NYSE and NASDAQ,
would you be diversified?
YES!
Would you have eliminated all of yourrisk?
NO! Common stock portfolios still
have risk. (Remember the October1987 stock market crash?)
-
7/30/2019 Portfolio Theory - CAPM
24/85
Some risk can be diversifiedaway and some can not
Market Riskis also calledNondiversifiable risk, systematic risk.This type of risk can not be
diversified away. Firm-Specific riskis also called
diversifiable risk, unsystematic risk.
This type of risk can be reducedthrough diversification.
-
7/30/2019 Portfolio Theory - CAPM
25/85
Unexpected changes in interest rates.
Unexpected changes in cash flows due to
tax rate changes, foreign competition, andthe overall business cycle.
Market Risk
-
7/30/2019 Portfolio Theory - CAPM
26/85
A companys labor force goes on strike.
A companys top management dies in a
plane crash. A huge oil tank bursts and floods a
companys production area.
Firm-Specific Risk
-
7/30/2019 Portfolio Theory - CAPM
27/85
portfolio
risk
number of stocks
As you add stocks to your
portfolio, firm-specific risk isreduced.
-
7/30/2019 Portfolio Theory - CAPM
28/85
portfolio
risk
number of stocks
Market risk
As you add stocks to your
portfolio, firm-specific risk isreduced.
-
7/30/2019 Portfolio Theory - CAPM
29/85
-
7/30/2019 Portfolio Theory - CAPM
30/85
Large
0 15
Prob.
2
1
1 35% ; Large 20%.
Return
-
7/30/2019 Portfolio Theory - CAPM
31/85
As more stocks are added, each new stock has asmaller risk-reducing impact on the portfolio.
p falls very slowly after about 40 stocks areincluded. The lower limit for p is about 20% =M .
By forming well-diversified portfolios, investors
can eliminate about half the riskiness of owning asingle stock.
Foundation of Modern Portfolio Theory
Conclusion
-
7/30/2019 Portfolio Theory - CAPM
32/85
Developed by Harry Markowitz in 1958.
Based on diversification effect: If we combine
stocks into portfolios, depending upon thecorrelation between stocks in the portfolio andthe weighting of each stock, some portfolios willdominate others, e.g. some portfolios will have
higher rates of return given the same risk(standard deviation) or some portfolios will havelower standard deviations given the same return.These portfolios will form the EFFICIENTFRONTIER.
Modern Portfolio Theory
-
7/30/2019 Portfolio Theory - CAPM
33/85
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 no taxesand no transactions costs.
All investors are price takers, that is, investors buying andselling wont influence stock prices.
Quantitiesof all assets are given and fixed.
What are the assumptions
of the MPT and Asset Pricing Models
-
7/30/2019 Portfolio Theory - CAPM
34/85
ExpectedPortfolioReturn, r
p
Risk, p
Efficient Set
Feasible Set
Feasible and Efficient Portfolios
with Risky Assets
-
7/30/2019 Portfolio Theory - CAPM
35/85
The feasible set of portfolios represents all
portfolios that can be constructed from a givenset of stocks.
An efficient portfolio is one that offers:
the most return for a given amount of risk, or
the least risk for a give amount of return.
The collection of efficient portfolios is calledthe efficient set or efficient frontier.
-
7/30/2019 Portfolio Theory - CAPM
36/85
IB2 IB1
IA2IA1
Optimal PortfolioInvestor A
Optimal Portfolio
Investor B
Risk p
ExpectedReturn, rp
Optimal Portfolios
-
7/30/2019 Portfolio Theory - CAPM
37/85
Indifference curvesreflect an investorsattitude toward risk as reflected in his orher risk/return tradeoff function. Theydiffer among investors because of
differences in risk aversion.An investors optimal portfoliois defined
by the tangency point between theefficient set and the investors
indifference curve.
-
7/30/2019 Portfolio Theory - CAPM
38/85
IB2 IB1
IA2IA1
Optimal PortfolioInvestor A
Optimal Portfolio
Investor B
Risk p
ExpectedReturn, rp
Optimal Portfolios
-
7/30/2019 Portfolio Theory - CAPM
39/85
When a risk-free asset is added to thefeasible set, investors can create portfoliosthat combine this asset with a portfolio ofrisky assets.
The straight line connecting rfwith M, thetangency point between the line and the oldefficient set, becomes the new efficientfrontier.
What impact does rF have on
the efficient frontier?
-
7/30/2019 Portfolio Theory - CAPM
40/85
M
Z
.Arf
M Risk, p
Efficient Set with a Risk-Free Asset
The Capital MarketLine (CML):
New EfficientFrontier
.
.B
rM
ExpectedReturn, rp
Optimal Portfolio Choice With a
-
7/30/2019 Portfolio Theory - CAPM
41/85
Optimal Portfolio Choice With a
Risk-Free Asset
G
Standard deviation
Expected
return M
C
rF
E
Capital market line
-
7/30/2019 Portfolio Theory - CAPM
42/85
The Capital Market Line (CML)is all linearcombinations of the risk-free asset andPortfolio M.
Portfolios below the CML are inferior.
The CML defines the new efficient frontier.
All investors will choose a portfolio on the
CML. Optimal portfolio choice is M and
combinations of risk-free asset and MTobins Separation Theorem
What is the Capital Market Line?
-
7/30/2019 Portfolio Theory - CAPM
43/85
rf
MRisk, p
I1I2
CML
P = OptimalPortfolio
.P
.M
rP
rM
P
ExpectedReturn, rp
-
7/30/2019 Portfolio Theory - CAPM
44/85
What is the implication of CAPM andmodern portfolio theory on individualsecurities?
From modern portfolio theory, welearned: diversification reduces riskOnly systematic risk is important
From capital market line, we learnedthe efficient portfolio is the marketportfolio M
Capital Asset Pricing Model
Security Market Line (SML)
-
7/30/2019 Portfolio Theory - CAPM
45/85
Yes. For example:
Interest rate changes affect all firms, but
which would be more affected:
a) Retail food chain
b) Commercial bank
Do some firms have more
market risk than others?
-
7/30/2019 Portfolio Theory - CAPM
46/85
Yes. For example:
Interest rate changes affect all firms, but
which would be more affected:
a) Retail food chain
b) Commercial bank
Do some firms have more
market risk than others?
-
7/30/2019 Portfolio Theory - CAPM
47/85
Note
As we know, the market compensates
investors for accepting risk - but only
for market risk. Firm-specific risk can
and should be diversified away.
So - we need to be able to measure
market risk.
-
7/30/2019 Portfolio Theory - CAPM
48/85
Beta: a measure of market risk.
Specifically, it is a measure of how an
individual stocks returns vary withmarket returns.
Its a measure of the sensitivity of an
individual stocks returns to changes in
the market.
This is why we have BETA.
-
7/30/2019 Portfolio Theory - CAPM
49/85
A firm that has a beta = 1 has average market
risk. The stock is no more or less volatile than
the market.
A firm with a beta > 1 is more volatile than the
market (ex: computer firms)
Aggressive stocks
A firm with a beta < 1 is less volatile than the
market (ex: utilities). Defensive stocks.
The markets beta is 1
-
7/30/2019 Portfolio Theory - CAPM
50/85
Run a regression line ofpast returns on
Stock iversus returns on the market.
The regression line is called thecharacteristic line.
The slope coefficient of the characteristic
line is defined as the beta coefficient.
How are betas calculated?
-
7/30/2019 Portfolio Theory - CAPM
51/85
Method of Calculation
Analysts use a computer with statistical or
spreadsheet software to perform the regression.
At least 3 years of monthly returns or 1
years of weekly returns are used.
Many analysts use 5 years of monthly
returns.
Most stocks have betas in the range of 0.5 to
1.5.
C l l ti B t
-
7/30/2019 Portfolio Theory - CAPM
52/85
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500
returns
. . . .
. . . .. . . .
. . . .
. . . .
. . . .
. . . .. . . .
. . .
. . . .
. . . .
Calculating Beta
C l l ti B t
-
7/30/2019 Portfolio Theory - CAPM
53/85
-5-15 5 10 15
-15
-10
-10
-5
5
10
15
XYZ Co. returns
S&P 500
returns
. . . .
. . . .. . . .
. . . .
. . . .
. . . .
. . . .. . . .
. . .
. . . .
. . . .
Beta = slope
= 1.20
This is the
characteristic line
of XYZ stock
Calculating Beta
-
7/30/2019 Portfolio Theory - CAPM
54/85
Interpreting Regression Results
The R2measures the percent of a stocksvariance that is explained by the market.The typical R2 is:
0.3 for an individual stock over 0.9 for a well diversified portfolio
The 95% confidence interval shows therange in which we are 95% sure that the
true value of beta lies. The typical range is: from about 0.5 to 1.5 for an individual stock
from about .92 to 1.08 for a well diversified portfolio
-
7/30/2019 Portfolio Theory - CAPM
55/85
Beta Equation [11.17], p 351
Mathematically, beta is calculated as:
)(
),(2
M
Mii
R
RRCOV
-
7/30/2019 Portfolio Theory - CAPM
56/85
We know how to measure risk, using
standard deviation for overall risk and beta
for market risk.
We know how to reduce overall risk to only
market risk through diversification.
We need to know how to price risk so we will
know how much extra return we should
require for accepting extra risk.
Summary:
-
7/30/2019 Portfolio Theory - CAPM
57/85
The return on an investment
required by an investor given theinvestments risk.
What is the Required Rate of
Return?
-
7/30/2019 Portfolio Theory - CAPM
58/85
Required
rate of
return
=
Risk-free
rate of
return+
Risk
Premium
-
7/30/2019 Portfolio Theory - CAPM
59/85
Required
rate of
return
=
Risk-free
rate of
return+
Risk
Premium
Market
Risk
-
7/30/2019 Portfolio Theory - CAPM
60/85
Required
rate of
return
=
Risk-free
rate of
return+
Risk
Premium
Market
Risk
Firm-specific
Risk
i
-
7/30/2019 Portfolio Theory - CAPM
61/85
= +
Required
rate of
return
Risk-free
rate of
return
Risk
Premium
Market
Risk
Firm-specific
Risk
can be diversified
away
Required
-
7/30/2019 Portfolio Theory - CAPM
62/85
Required
rate of
return
Beta
Lets try to graph this
relationship!
Required
-
7/30/2019 Portfolio Theory - CAPM
63/85
Required
rate of
return
Risk-free
rate ofreturn
(6%)
Beta
12% .
1
Required
-
7/30/2019 Portfolio Theory - CAPM
64/85
q
rate of
return
Risk-free
rate ofreturn
(6%)
Beta
12% .
1
security
marketline
(SML)
-
7/30/2019 Portfolio Theory - CAPM
65/85
This linear relationship between risk
and required return is known asthe Capital Asset Pricing Model
(CAPM)
The CAPM is an equilibrium model thatspecifies the relationship between riskandrequired rate of returnfor assets held in well-diversified portfolios.
It is based on the premise that only one factoraffects risk - the market portfolio.
-
7/30/2019 Portfolio Theory - CAPM
66/85
Basic Messages of CAPM
If you want to earn higher returns, you must
be prepared to bear higher risk.
If you are not fully diversified, you are
bearing risk without being compensated.
Required
SML
-
7/30/2019 Portfolio Theory - CAPM
67/85
rate of
return
Risk-free
rate ofreturn
(6%)
Beta
12% .
1
SML
0
Is there a riskless
(zero beta) security?
Required
SML
-
7/30/2019 Portfolio Theory - CAPM
68/85
rate of
return
Beta
12% .
1
SML
0
Is there a riskless
(zero beta) security?
Treasury
securities are
as close to riskless
as possible.Risk-free
rate ofreturn
(6%)
Required
SMLWh d s th S&P 500
-
7/30/2019 Portfolio Theory - CAPM
69/85
rate of
return
Beta
12% .
1
SMLWhere does the S&P 500
fall on the SML?
Risk-free
rate ofreturn
(6%)
0
Required
SMLWhere does the S&P 500
-
7/30/2019 Portfolio Theory - CAPM
70/85
rate of
return
Beta
12% .
1
SWhere does the S&P 500
fall on the SML?
The S&P 500 isa good
approximation
for the market
Risk-free
rate ofreturn
(6%)
0 Required
SML
-
7/30/2019 Portfolio Theory - CAPM
71/85
rate of
return
Beta
12% .
1
UtilityStocks
Risk-free
rate ofreturn
(6%)
0 Required
SMLHigh-tech
-
7/30/2019 Portfolio Theory - CAPM
72/85
rate of
return
Beta
12% .
1
High tech
stocks
Risk-free
rate ofreturn
(6%)
0
-
7/30/2019 Portfolio Theory - CAPM
73/85
E(Ri) = RF +
Beta,Risk-freeRate
[E(RMRF)]
Capital Asset Pricing Model
SML [Equation 11.9, p 351]
Cov(Ri,RM)
M
Equity(Market) RiskPremium
-
7/30/2019 Portfolio Theory - CAPM
74/85
Suppose the Treasury bond rate is
6%, the average return on the S&P
500 index is 12%, and Walt Disneyhas a beta of 1.2.
According to the CAPM, what should
be the required rate of return onDisney stock?
Example:
-
7/30/2019 Portfolio Theory - CAPM
75/85
=
According to the CAPM, Disney stock
should be priced to give a 13.2% return. If the expected return > 13.2%
Underpriced, good investment
If the expected return < 13.2%
Overpriced, bad investment
If the expected return = 13.2%
Properly priced, good investment
E(RDisney) = RF+ [E(RM) RF] Disney
Required
f
SMLTheoretically every
-
7/30/2019 Portfolio Theory - CAPM
76/85
rate of
return
Beta
12% .
10
Theoretically, every
security should lie
on the SML
Risk-free
rate ofreturn
(6%)
Required
f
SMLTheoretically every
-
7/30/2019 Portfolio Theory - CAPM
77/85
rate of
return
Beta
12% .
10
Theoretically, every
security should lie
on the SML
If every stock
is on the SML,investors are being fully
compensated for risk.Risk-free
rate ofreturn
(6%)
Required
f
SMLIf a security is above
-
7/30/2019 Portfolio Theory - CAPM
78/85
rate of
return
Beta
12% .
10
If a security is above
the SML, it is
underpriced.
Risk-free
rate ofreturn
(6%)
Required
t f
SMLIf a security is above
-
7/30/2019 Portfolio Theory - CAPM
79/85
rate of
return
Beta
12% .
10
If a security is above
the SML, it is
underpriced.
If a security isbelow the SML, it
is overpriced.Risk-free
rate ofreturn
(6%)
The Global Efficient Set
-
7/30/2019 Portfolio Theory - CAPM
80/85
The Global Efficient Set
B
Standard deviation
Expected
return
A
Efficient frontier-
US and foreign stocks
C
DEfficient frontier-
US stocks only
Gl b l Di ifi i Eff
-
7/30/2019 Portfolio Theory - CAPM
81/85
portfolio
risk
number of stocks
Domestic Portfolio
International Portfolio
Global Diversification Effect
Gl b l Di ifi i
-
7/30/2019 Portfolio Theory - CAPM
82/85
Global Diversification
Expands the set of securities available toinvestors.
If security returns are not perfectly
synchronized, investors can achieve greaterrisk reduction through global diversificationrather than limiting their choices in thedomestic markets.
Global diversification pushes out the efficientfrontier.
In Class Problem #6
-
7/30/2019 Portfolio Theory - CAPM
83/85
You are given the following information on the returns for market portfolio, Mand the returns on common stock A:
Probability RM RA RF.25 .20 .25 .06
.25 -.05 -.15 .06
.25 .30 .55 .06
.25 -.05 -.15 .06
A. Determine beta for stock A.
B. Using SML criterion to determine whether you would invest in the stock.
To answer this, you have to plot the expected SML. Mark your axis clearlyand make sure you plot the risk-free rate, beta, and expected returns andrequired returns properly on the graph.
C. Which asset is more risky, the common stock A or the market portfolio, M?In systematic risk? In total risk? Explain.
In Class Problem #6
In Class Problem #7
-
7/30/2019 Portfolio Theory - CAPM
84/85
Combine CAPM and Dividend Growth
Model:
Use CAPM to calculate required rate of
return
Use dividend growth model to calculate the
value of the stock
In Class Problem #7
In Class Problem #7
-
7/30/2019 Portfolio Theory - CAPM
85/85
The risk-free rate of return is 11 percent; the required rate of return on
the market is 14 percent; and UHM Companys stock has a betacoefficient of 1.5.
If the dividend expected during the coming year, D1, is $2.25, and if g =a constant 5%, at what price should UHMs stock sell?
Now, suppose the Federal Reserve Board increases the moneysupply, causing the risk-free rate to drop to 9 percent and marketreturn to fall to 12 percent. What would this do to the price of thestock?
Now, suppose UHM has a change in management. The new groupinstitutes policies that increase the expected constant growth rate to
6 percent. Also, the new management stabilizes sales and profits,and thus causes the beta coefficient to decline from 1.5 to 1.3.Assume that RF and RM are equal to the values in part B. After allthese changes, what is UHMs new equilibrium price? (Note: D1goes to $2.27).
In Class Problem #7