REPLICATING A MODEL OF AVOIDANCES ACROSS CONTINENTS Bahattin Tolga Oztan and Douglas R. White.
Asset Pricing Models: Their uses and their limitations - Bahattin
Transcript of Asset Pricing Models: Their uses and their limitations - Bahattin
![Page 1: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/1.jpg)
CHAPTER 9
The Capital Asset Pricing Model
![Page 2: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/2.jpg)
It is the equilibrium model that underlies all
modern financial theory
Derived using principles of diversification with
simplified assumptions
Markowitz, Sharpe, Lintner and Mossin are
researchers credited with its development
CAPITAL ASSET PRICING MODEL (CAPM)
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 2
![Page 3: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/3.jpg)
Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
There are homogeneous expectations
ASSUMPTIONS: INVESTORS
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 3
![Page 4: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/4.jpg)
Information is costless and available to all
investors
No taxes and transaction costs
Risk-free rate available to all
Investors are rational mean-variance optimizers
ASSUMPTIONS: ASSETS
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 4
![Page 5: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/5.jpg)
All investors will hold the same portfolio for risky
assets – market portfolio, which contains all securities
and the proportion of each security is its market value
as a percentage of total market value held by all investors
includes all traded assets
suppose not: then price… -> included
is on the efficient frontier
asset weights: for each $ in risky assets, how much is in IBM?
for stock i: market cap of stock i / market cap of all stocks
RESULTING EQUILIBRIUM CONDITIONS
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 5
iii
iii
PN
PNw
![Page 6: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/6.jpg)
Risk premium on the market depends on the
average risk aversion of all market participants
Risk premium on an individual security is a
function of its covariance with the market
RESULTING EQUILIBRIUM CONDITIONS
CONTINUED
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 6
![Page 7: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/7.jpg)
FIGURE 9.1 THE EFFICIENT FRONTIER AND
THE CAPITAL MARKET LINE
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 7
![Page 8: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/8.jpg)
MARKET RISK PREMIUM
The risk premium on the market portfolio will be
proportional to its risk and the degree of risk
aversion of the investor:
2
2
( )
where is the variance of the market portolio and
is the average degree of risk aversion across investors
M f M
M
E r r A
A
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 8
![Page 9: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/9.jpg)
The risk premium on individual securities is a
function of the individual security’s contribution
to the risk of the market portfolio
An individual security’s risk premium is a function
of the covariance of returns with the assets that
make up the market portfolio
RETURN AND RISK FOR INDIVIDUAL
SECURITIES
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 9
![Page 10: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/10.jpg)
USING GE TEXT EXAMPLE
Covariance of GE return with the market
portfolio:
Therefore, the reward-to-risk ratio for
investments in GE would be:
1 1
( , ) , ( , )n n
GE M GE k k k k GE
k k
Cov r r Cov r w r w Cov r r
( ) ( )GE's contribution to risk premium
GE's contribution to variance ( , ) ( , )
GE GE f GE f
GE GE M GE M
w E r r E r r
w Cov r r Cov r r
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 10
![Page 11: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/11.jpg)
USING GE TEXT EXAMPLE CONTINUED
Reward-to-risk ratio for investment in market
portfolio:
Reward-to-risk ratios of GE and the market
portfolio:
And the risk premium for GE:
2
( )Market risk premium
Market variance
M f
M
E r r
2
( ) ( ( )
( , )
GE f M f
GE M M
E r r E r r
Cov r r
2
( , )( ) ( )GE M
GE f M f
M
Cov r rE r r E r r
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 11
![Page 12: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/12.jpg)
EXPECTED RETURN-BETA RELATIONSHIP
CAPM holds for the overall portfolio because:
This also holds for the market portfolio:
P
( ) ( ) andP k k
k
k k
k
E r w E r
w
( ) ( )M f M M fE r r E r r
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 12
![Page 13: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/13.jpg)
FIGURE 9.2 THE SECURITY MARKET LINE
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 13
![Page 14: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/14.jpg)
FIGURE 9.3 THE SML AND A POSITIVE-ALPHA
STOCK
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 14
![Page 15: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/15.jpg)
THE INDEX MODEL AND REALIZED RETURNS
To move from expected to realized returns—use
the index model in excess return form:
The index model beta coefficient turns out to be
the same beta as that of the CAPM expected
return-beta relationship
i i i M iR R e
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 15
![Page 16: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/16.jpg)
FIGURE 9.4 ESTIMATES OF INDIVIDUAL
MUTUAL FUND ALPHAS, 1972-1991
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 16
![Page 17: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/17.jpg)
THE CAPM AND REALITY
Is the condition of zero alphas for all stocks as
implied by the CAPM met
Not perfect but one of the best available
Is the CAPM testable
Proxies must be used for the market portfolio
CAPM is still considered the best available
description of security pricing and is widely
accepted
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 17
![Page 18: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/18.jpg)
ECONOMETRICS AND THE EXPECTED
RETURN-BETA RELATIONSHIP
It is important to consider the econometric
technique used for the model estimated
Statistical bias is easily introduced
Miller and Scholes paper demonstrated how
econometric problems could lead one to
reject the CAPM even if it were perfectly valid
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 18
![Page 19: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/19.jpg)
EXTENSIONS OF THE CAPM
Zero-Beta Model
Helps to explain positive alphas on low beta
stocks and negative alphas on high beta stocks
Consideration of labor income and non-traded
assets
Merton’s Multiperiod Model and hedge portfolios
Incorporation of the effects of changes in the
real rate of interest and inflation
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 19
![Page 20: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/20.jpg)
EXTENSIONS OF THE CAPM CONTINUED
A consumption-based CAPM
Models by Rubinstein, Lucas, and Breeden
Investor must allocate current wealth between today’s consumption and investment for the
future
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 20
![Page 21: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/21.jpg)
LIQUIDITY AND THE CAPM
Liquidity
Illiquidity Premium
Research supports a premium for illiquidity.
Amihud and Mendelson
Acharya and Pedersen
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 21
![Page 22: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/22.jpg)
FIGURE 9.5 THE RELATIONSHIP BETWEEN
ILLIQUIDITY AND AVERAGE RETURNS
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 22
![Page 23: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/23.jpg)
THREE ELEMENTS OF LIQUIDITY
Sensitivity of security’s illiquidity to market
illiquidity:
Sensitivity of stock’s return to market illiquidity:
Sensitivity of the security illiquidity to the market
rate of return:
1
( , )
( )
i ML
M M
Cov C C
Var R C
3
( , )
( )
i ML
M M
Cov C R
Var R C
2
( , )
( )
i ML
M M
Cov R C
Var R C
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 23
![Page 24: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/24.jpg)
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 1
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Question:
The market price of a stock is $40.
Its expected rate of return is 13%.
The risk-free rate is 7%
The market risk premium is 8%.
Suppose its covariance w/ the market portfolio doubles (other variables are unchanged)?
Do you have enough information to find what will be the new price of the stock?
Assume that the stock is expected to pay a constant dividend in perpetuity.
1 /16 /2010 24
![Page 25: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/25.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Answer:
If the covariance of the security doubles, then so will its beta and its risk premium.
The current risk premium is 6% = 13% - 7%
the new risk premium would be twice as high: 12%
the new discount rate for the security would be 19% = 12% + 7%
If the stock pays a level perpetual dividend, then we know from the original data that:
Price = Dividend/Discount rate => $40 = D/0.13 => D = $5.20.
At the new discount rate of 19%, the stock would be worth only:
$5.20/0.19 = $27.37.
1 /16 /2010 25
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 2
![Page 26: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/26.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Question:
Consider the following table, which gives a security analyst’s expected return on two
stocks for two particular market returns:
Market Return Aggressive Stock Defensive Stock
-------------------------------------------------------------------------------------------
5% 2% 3.5%
20% 32% 14%
-------------------------------------------------------------------------------------------
What hurdle rate should be used by the management of the aggressive firm for a project
with the risk characteristics of the defensive firm’s stock?
The risk-free rate is 8%.
1 /16 /2010 26
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 3
![Page 27: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/27.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Answer:
The hurdle rate is determined by the project beta, 0.70, not by the firm’s beta.
The correct discount rate is 11.15%, the fair rate of return on Stock D (defensive). Why?
(a) The beta is the sensitivity of the stock return to the market return movements.
Then beta is the change in the stock return per change in the market return. Therefore:
A = (2 - 32)/(5 - 20) = 2.00
D = (3.5 - 14)/(5 - 20) = 0.70
(d) The defensive stock has a fair expected return of:
E(RD) = 8% + 0.7(12.5% - 8%) = 11.5%,
1 /16 /2010 27
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 4
![Page 28: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/28.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Question:
Two investment advisors are comparing performance.
One averaged a 19% rate of return and the other a 16% rate of return.
However, the beta of the first investor was 1.5, whereas that of the second was 1.
(a) Can you tell which investor was a better predictor of individual stocks (aside from the
issue of general movements in the market)?
(b) If the T-bill rate were 6% and the market return during the period were 14%, which
investor would be the superior stock selector?
(c) What if the T-bill rate were 3% and the market return were 15%?
1 /16 /2010 28
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 5
![Page 29: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/29.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Answer:
(a) We know that:
R1 = 19%, R2 = 16%, 1 = 1.5, and 1 = 1.
To tell which investor was a better predictor of individual stocks, we should look at their
abnormal return, which is the ex-post (alpha)
that is, the abnormal return is the difference between
the actual return
and the return predicted by the SML.
Without information about the parameters of this equation (risk-free rate and the market
rate of return) we cannot tell which investor is more accurate.
1 /16 /2010 29
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 6
![Page 30: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/30.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Answer:
(b) If Rf = 6% and Rm = 14%, then (using the notation of alpha for the abnormal return):
1 = 19% - [6% + 1.5(14% - 6%)] = 19% - 18% = 1%
2 = 16% - [6% + 1(14% - 6%)] = 16% - 14% = 2%.
Here, the second investor has the larger abnormal return
and thus he appears to be a more accurate predictor.
By making better predictions,
the second investor appears to have tilted his portfolio toward underpriced stocks.
1 /16 /2010 30
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 7
![Page 31: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/31.jpg)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Answer:
(c) If Rf = 3% and Rm = 15%, then
1 = 19% - [3% + 1.5(15% - 3%)] = 19% - 21% = -2%
2 = 16% - [3% + 1(15% - 3%)] = 16% - 15% = 1%.
1 /16 /2010
CAPM: EXAMPLES OF PRACTICAL
PROBLEMS 8
![Page 32: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/32.jpg)
INDEX MODEL VS. CAPM
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Risk CAPM (theoretical, unobservable portfolio)
Index model (observable, “proxy” portfolio)
)(
),(
2M
Mii
R
RRCov
),(),( MiMiiMi ReRCovRRCov
)(0)(0 22MiMi RR
)(
),(
2M
Mii
R
RRCov
1 /16 /2010 32
![Page 33: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/33.jpg)
INDEX MODEL VS. CAPM 2
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Beta Relationship
CAPM (no expected excess return for any security)
Index model (average realized alpha is 0)
Fig 10.3
)][(][ fMifi rrErrE
ifMiifi errrr )(
)][(][ fMiifi rrErrE
1 /16 /2010 33
![Page 34: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/34.jpg)
MARKET MODEL
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Idea
use realized excess returns
Equivalence
CAPM + Market model = Index model
])[(][ MMiii rErrEr
)][(][ fMifi rrErrE
ifMiifi errrr )(
1 /16 /2010 34
![Page 35: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/35.jpg)
SUMMARY
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
CAPM
Factor model
Index model
Market model ])[(][ MMiii rErrEr
)][(][ fMifi rrErrE
ifMiifi errrr )(
iiii eFrEr ][
1 /16 /2010 35
![Page 36: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/36.jpg)
CHAPTER 10
Arbitrage Pricing Theory and Multifactor Models of Risk and Return
![Page 37: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/37.jpg)
SINGLE FACTOR MODEL
Returns on a security come from two sources
Common macro-economic factor
Firm specific events
Possible common macro-economic factors
Gross Domestic Product Growth
Interest Rates
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 37
![Page 38: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/38.jpg)
SINGLE FACTOR MODEL EQUATION
ri = Return for security I
= Factor sensitivity or factor loading or factor
beta
F = Surprise in macro-economic factor
(F could be positive, negative or zero)
ei = Firm specific events
( )i i i ir E r F e
i
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 38
![Page 39: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/39.jpg)
MULTIFACTOR MODELS 1
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Necessity
CAPM
not practical
Index model
practical
unique factor is unsatisfactory
example: Table 10.2 (very small R2
)
Solution
multiple factors
1 /16 /2010 39
![Page 40: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/40.jpg)
MULTI-FACTOR MODELS 2
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Factors in practice
business cycles factors
examples (Chen Roll Ross)
industrial production % change
expected inflation % change
unanticipated inflation % change
LT corporate over LT gvt. bonds
LT gvt. bonds over T-bills
interpretation
residual variance = firm specific risk
1 /16 /2010 40
![Page 41: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/41.jpg)
MULTI-FACTOR MODELS 3
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Factors in practice
firm characteristics (Fama and French)
firm size
difference in return
between firms with low vs. high equity market value
proxy for business cycle sensitivity?
market to book
difference in return
between firms with low vs. high BTM ratio
proxy for bankruptcy risk?
1 /16 /2010 41
![Page 42: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/42.jpg)
MULTIFACTOR MODELS 4
Use more than one factor in addition to market
return
Examples include gross domestic product,
expected inflation, interest rates etc.
Estimate a beta or factor loading for each
factor using multiple regression.
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 42
![Page 43: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/43.jpg)
MULTIFACTOR MODEL EQUATION
ri = E(ri) + GDP GDP + IR IR + ei
ri = Return for security I
GDP= Factor sensitivity for GDP
IR = Factor sensitivity for Interest Rate
ei = Firm specific events
i
i
i
i
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 43
![Page 44: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/44.jpg)
MULTIFACTOR SML MODELS
E(r) = rf + GDPRPGDP + IRRPIR
GDP = Factor sensitivity for GDP
RPGDP = Risk premium for GDP
IR = Factor sensitivity for Interest Rate
RPIR = Risk premium for Interest Rate
i i
i
i
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 44
![Page 45: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/45.jpg)
ARBITRAGE PRICING THEORY (APT)
BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS
Nature of arbitrage
APT
well-diversified portfolios
individual assets
APT vs. CAPM
APT vs. Index models
single factor
multi-factor
1 /16 /2010 45
![Page 46: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/46.jpg)
ARBITRAGE PRICING THEORY
Arbitrage - arises if an investor can construct a
zero investment portfolio with a sure profit
Since no investment is required, an investor can
create large positions to secure large levels of
profit
In efficient markets, profitable arbitrage
opportunities will quickly disappear
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 46
![Page 47: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/47.jpg)
APT & WELL-DIVERSIFIED PORTFOLIOS
rP = E (rP) + PF + eP
F = some factor
For a well-diversified portfolio:
eP approaches zero
Similar to CAPM,
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 47
![Page 48: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/48.jpg)
FIGURE 10.1 RETURNS AS A FUNCTION OF
THE SYSTEMATIC FACTOR
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 48
![Page 49: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/49.jpg)
FIGURE 10.2 RETURNS AS A FUNCTION OF
THE SYSTEMATIC FACTOR: AN ARBITRAGE
OPPORTUNITY
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 49
![Page 50: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/50.jpg)
FIGURE 10.3 AN ARBITRAGE OPPORTUNITY
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 50
![Page 51: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/51.jpg)
FIGURE 10.4 THE SECURITY MARKET LINE
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 51
![Page 52: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/52.jpg)
APT applies to well diversified portfolios and not
necessarily to individual stocks
With APT it is possible for some individual stocks
to be mispriced - not lie on the SML
APT is more general in that it gets to an
expected return and beta relationship without
the assumption of the market portfolio
APT can be extended to multifactor models
APT AND CAPM COMPARED
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 52
![Page 53: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/53.jpg)
MULTIFACTOR APT
Use of more than a single factor
Requires formation of factor portfolios
What factors?
Factors that are important to performance of
the general economy
Fama-French Three Factor Model
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 53
![Page 54: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/54.jpg)
TWO-FACTOR MODEL
The multifactor APR is similar to the one-factor case
But need to think in terms of a factor portfolio
Well-diversified
Beta of 1 for one factor
Beta of 0 for any other
1 1 2 2( )i i i i ir E r F F e
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 54
![Page 55: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/55.jpg)
EXAMPLE OF THE MULTIFACTOR APPROACH
Work of Chen, Roll, and Ross
Chose a set of factors based on the ability of
the factors to paint a broad picture of the
macro-economy
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 55
![Page 56: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/56.jpg)
ANOTHER EXAMPLE:
FAMA-FRENCH THREE-FACTOR MODEL
The factors chosen are variables that on past evidence seem to predict
average returns well and may capture the risk premiums
Where:
SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess
of the return on a portfolio of large stocks
HML = High Minus Low, i.e., the return of a portfolio of stocks with a high
book to-market ratio in excess of the return on a portfolio of stocks with a
low book-to-market ratio
it i iM Mt iSMB t iHML t itr R SMB HML e
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 56
![Page 57: Asset Pricing Models: Their uses and their limitations - Bahattin](https://reader031.fdocuments.net/reader031/viewer/2022021212/620659bf8c2f7b173006f06f/html5/thumbnails/57.jpg)
THE MULTIFACTOR CAPM AND THE APM
A multi-index CAPM will inherit its risk factors
from sources of risk that a broad group of
investors deem important enough to hedge
The APT is largely silent on where to look for
priced sources of risk
BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 57