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Investment Analysis and Portfolio Management By Reilly and BrownChapter No. 9 An Introduction to Asset Pricing Models
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Saif [email protected]
[email protected]+923216633271
Lecture Presentation Software to accompany
Investment Analysis and Portfolio Management
Sixth Editionby
Frank K. Reilly & Keith C. Brown
Chapter 9
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Chapter 9 - An Introduction to Asset Pricing Models
Questions to be answered:
• What are the assumptions of the capital asset pricing model?
• What is a risk-free asset and what are its risk-return characteristics?
• What is the covariance and correlation between the risk-free asset and a risky asset or portfolio of risky assets?
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Chapter 9 - An Introduction to Asset Pricing Models
• What is the expected return when you combine the risk-free asset and a portfolio of risky assets?
• What is the standard deviation when you combine the risk-free asset and a portfolio of risky assets?
• When you combine the risk-free asset and a portfolio of risky assets on the Markowitz efficient frontier, what does the set of possible portfolios look like?
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Chapter 9 - An Introduction to Asset Pricing Models
• Given the initial set of portfolio possibilities with a risk-free asset, what happens when you add financial leverage (that is, borrow)?
• What is the market portfolio, what assets are included in this portfolio, and what are the relative weights for the alternative assets included?
• What is the capital market line (CML)?
• What do we mean by complete diversification?
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Chapter 9 - An Introduction to Asset Pricing Models
• How do we measure diversification for an individual portfolio?
• What are systematic and unsystematic risk?
• Given the capital market line (CML), what is the separation theorem?
• Given the CML, what is the relevant risk measure for an individual risky asset?
• What is the security market line (SML) and how does it differ from the CML?
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Chapter 9 - An Introduction to Asset Pricing Models
• What is beta and why is it referred to as a standardized measure of systematic risk?
• How can you use the SML to determine the expected (required) rate of return for a risky asset?
• Using the SML, what do we mean by an undervalued and overvalued security, and how do we determine whether an asset is undervalued or overvalued?
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Chapter 9 - An Introduction to Asset Pricing Models
• What is an asset’s characteristic line and how do you compute the characteristic line for an asset?
• What is the impact on the characteristic line when you compute it using different return intervals (e.g., weekly versus monthly) and when you employ different proxies (i.e., benchmarks) for the market portfolio (e.g., the S&P 500 versus a global stock index)?
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Chapter 9 - An Introduction to Asset Pricing Models
• What is the arbitrage pricing theory (APT) and how does it differ from the CAPM in terms of assumptions?
• How does the APT differ from the CAPM in terms of risk measure?
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Capital Market Theory: An Overview
• Capital market theory extends portfolio theory and develops a model for pricing all risky assets
• Capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset
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Assumptions of Capital Market Theory
1. All investors are Markowitz efficient investors who want to target points on the efficient frontier. – The exact location on the efficient frontier and,
therefore, the specific portfolio selected, will depend on the individual investor’s risk-return utility function.
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Assumptions of Capital Market Theory
2. Investors can borrow or lend any amount of money at the risk-free rate of return (RFR). – Clearly it is always possible to lend money at the
nominal risk-free rate by buying risk-free securities such as government T-bils. It is not always possible to borrow at this risk-free rate, but we will see that assuming a higher borrowing rate does not change the general results.
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Assumptions of Capital Market Theory
3. All investors have homogeneous expectations; that is, they estimate identical probability distributions for future rates of return.– Again, this assumption can be relaxed. As long
as the differences in expectations are not vast, their effects are minor.
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Assumptions of Capital Market Theory
4. All investors have the same one-period time horizon such as one-month, six months, or one year. – The model will be developed for a single
hypothetical period, and its results could be affected by a different assumption. A difference in the time horizon would require investors to derive risk measures and risk-free assets that are consistent with their time horizons.
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Assumptions of Capital Market Theory
5. All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio. – This assumption allows us to discuss
investment alternatives as continuous curves. Changing it would have little impact on the theory.
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Assumptions of Capital Market Theory
6. There are no taxes or transaction costs involved in buying or selling assets. – This is a reasonable assumption in many
instances. Neither pension funds nor religious groups have to pay taxes, and the transaction costs for most financial institutions are less than 1 percent on most financial instruments. Again, relaxing this assumption modifies the results, but does not change the basic thrust.
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Assumptions of Capital Market Theory
7. There is no inflation or any change in interest rates, or inflation is fully anticipated.– This is a reasonable initial assumption, and it
can be modified.
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Assumptions of Capital Market Theory
8. Capital markets are in equilibrium.– This means that we begin with all investments
properly priced in line with their risk levels.
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Assumptions of Capital Market Theory
• Some of these assumptions are unrealistic
• Relaxing many of these assumptions would have only minor influence on the model and would not change its main implications or conclusions.
• Judge a theory on how well it explains and helps predict behavior, not on its assumptions.
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Risk-Free Asset
• An asset with zero variance
• Zero correlation with all other risky assets
• Provides the risk-free rate of return (RFR)
• Will lie on the vertical axis of a portfolio graph
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Risk-Free Asset
Covariance between two sets of returns is
n
1ijjiiij )]/nE(R-)][RE(R-[RCov
Because the returns for the risk free asset are certain,
0RF Thus Ri = E(Ri), and Ri - E(Ri) = 0
Consequently, the covariance of the risk-free asset with any risky asset or portfolio will always equal zero. Similarly the correlation between any risky asset and the risk-free asset would be zero.
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Combining a Risk-Free Asset with a Risky Portfolio
Expected return
the weighted average of the two returns
))E(RW-(1(RFR)W)E(R iRFRFport
This is a linear relationship
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Combining a Risk-Free Asset with a Risky Portfolio
Standard deviation
The expected variance for a two-asset portfolio is
211,22122
22
21
21
2port rww2ww)E(
Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this formula would become
iRFiRF iRF,RFRF22
RF22
RF2port )rw-(1w2)w1(w)E(
Since we know that the variance of the risk-free asset is zero and the correlation between the risk-free asset and any risky asset i is zero we can adjust the formula
22RF
2port )w1()E( i
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Combining a Risk-Free Asset with a Risky Portfolio
Given the variance formula22
RF2port )w1()E( i
22RFport )w1()E( i the standard deviation is
i)w1( RF
Therefore, the standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio.
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Combining a Risk-Free Asset with a Risky Portfolio
Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets.
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Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier
)E( port
)E(R port Figure 9.1
RFR
M
C
AB
D
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Risk-Return Possibilities with Leverage
To attain a higher expected return than is available at point M (in exchange for accepting higher risk)
Either invest along the efficient frontier beyond point M, such as point D
Or, add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M
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Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier
)E( port
)E(R port
Figure 9.2
RFR
M
CML
Borrowing
Lending
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The Market Portfolio
Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line
Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML
Therefore this portfolio must include ALL RISKY ASSETS
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The Market Portfolio
Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value
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The Market Portfolio
Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away
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Systematic Risk
Only systematic risk remains in the market portfolio
Systematic risk is the variability in all risky assets caused by macroeconomic variables
Systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time
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Examples of Macroeconomic Factors Affecting Systematic Risk
• Variability in growth of money supply
• Interest rate volatility
• Variability in
industrial production
corporate earnings
and cash flow
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How to Measure Diversification
All portfolios on the CML are perfectly positively correlated with each other and with the completely diversified market Portfolio M
A completely diversified portfolio would have a correlation with the market portfolio of +1.00
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Diversification and the Elimination of Unsystematic RiskThe purpose of diversification is to reduce the
standard deviation of the total portfolio
This assumes that imperfect correlations exist among securities
As you add securities, you expect the average covariance for the portfolio to decline
How many securities must you add to obtain a completely diversified portfolio?
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Diversification and the Elimination of Unsystematic Risk
Observe what happens as you increase the sample size of the portfolio by adding securities that have some positive correlation
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Number of Stocks in a Portfolio and the Standard Deviation of Portfolio Return
Figure 9.3Standard Deviation of Return
Number of Stocks in the Portfolio
Standard Deviation of the Market Portfolio (systematic risk)
Systematic Risk
Total Risk
Unsystematic (diversifiable) Risk
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The CML and the Separation Theorem
The CML leads all investors to invest in the M portfolio
Individual investors should differ in position on the CML depending on risk preferences
How an investor gets to a point on the CML is based on financing decisions
Risk averse investors will lend part of the portfolio at the risk-free rate and invest the remainder in the market portfolio
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The CML and the Separation Theorem
Investors preferring more risk might borrow funds at the RFR and invest everything in the market portfolio
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The CML and the Separation Theorem
The decision of both investors is to invest in portfolio M along the CML
(the investment decision)
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The CML and the Separation Theorem
The decision to borrow or lend to obtain a point on the CML is a separate decision based on risk preferences
(financing decision)
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The CML and the Separation Theorem
Tobin refers to this separation of the investment decision from the financing decision the separation theorem
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A Risk Measure for the CML
Covariance with the M portfolio is the systematic risk of an asset
The Markowitz portfolio model considers the average covariance with all other assets in the portfolio
The only relevant portfolio is the M portfolio
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A Risk Measure for the CML
Together, this means the only important consideration is the asset’s covariance with the market portfolio
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A Risk Measure for the CML
Because all individual risky assets are part of the M portfolio, an asset’s rate of return in relation to the return for the M portfolio may be described using the following linear model:
Miiiit RbaRwhere:
Rit = return for asset i during period t
ai = constant term for asset i
bi = slope coefficient for asset i
RMt = return for the M portfolio during period t
= random error term
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Variance of Returns for a Risky Asset
)Rba(Var)Var(R Miiiit )(Var)Rb(Var)a(Var Miii
)(Var)Rb(Var0 Mii
risk icunsystemator portfoliomarket the
torelatednot return residual theis )(Var
risk systematicor return market to
related varianceis )Rb(Var that Note Mii
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The Capital Asset Pricing Model: Expected Return and Risk
• The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier
• An asset’s covariance with the market portfolio is the relevant risk measure
• This can be used to determine an appropriate expected rate of return on a risky asset - the capital asset pricing model (CAPM)
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The Capital Asset Pricing Model: Expected Return and Risk
• CAPM indicates what should be the expected or required rates of return on risky assets
• This helps to value an asset by providing an appropriate discount rate to use in dividend valuation models
• You can compare an estimated rate of return to the required rate of return implied by CAPM - over/ under valued ?
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The Security Market Line (SML)
• The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Covi,m)
• This is shown as the risk measure
• The return for the market portfolio should be consistent with its own risk, which is the covariance of the market with itself - or its variance:
2m
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Graph of Security Market Line (SML)
)E(R i
Figure 9.5
RFR
imCov2m
mR
SML
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The Security Market Line (SML)The equation for the risk-return line is
)Cov(RFR-R
RFR)E(R Mi,2M
Mi
RFR)-R(Cov
RFR M2M
Mi,
2M
Mi,Cov
We then define as beta
RFR)-(RRFR)E(R Mi i
)( i
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Graph of SML with Normalized Systematic Risk
)E(R i
Figure 9.6
)Beta(Cov 2Mim/0.1
mR
SML
0
Negative Beta
RFR
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Determining the Expected Rate of Return for a Risky Asset
The expected rate of return of a risk asset is determined by the RFR plus a risk premium for the individual asset
The risk premium is determined by the systematic risk of the asset (beta) and the prevailing market risk premium (RM-RFR)
RFR)-(RRFR)E(R Mi i
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Determining the Expected Rate of Return for a Risky Asset
Assume: RFR = 6% (0.06)
RM = 12% (0.12)
Implied market risk premium = 6% (0.06)
Stock Beta
A 0.70B 1.00C 1.15D 1.40E -0.30
RFR)-(RRFR)E(R Mi i
E(RA) = 0.06 + 0.70 (0.12-0.06) = 0.102 = 10.2%
E(RB) = 0.06 + 1.00 (0.12-0.06) = 0.120 = 12.0%
E(RC) = 0.06 + 1.15 (0.12-0.06) = 0.129 = 12.9%
E(RD) = 0.06 + 1.40 (0.12-0.06) = 0.144 = 14.4%
E(RE) = 0.06 + -0.30 (0.12-0.06) = 0.042 = 4.2%
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Determining the Expected Rate of Return for a Risky Asset
In equilibrium, all assets and all portfolios of assets should plot on the SML
Any security with an estimated return that plots above the SML is underpriced
Any security with an estimated return that plots below the SML is overpriced
A superior investor must derive value estimates for assets that are consistently superior to the consensus market evaluation to earn better risk-adjusted rates of return than the average investor
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Identifying Undervalued and Overvalued Assets
Compare the required rate of return to the expected rate of return for a specific risky asset using the SML over a specific investment horizon to determine if it is an appropriate investment
Independent estimates of return for the securities provide price and dividend outlooks
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Price, Dividend, and Rate of Return Estimates
Stock (Pi) Expected Price (Pt+1) (Dt+1) of Return (Percent)
A 25 27 0.50 10.0 %B 40 42 0.50 6.2C 33 39 1.00 21.2D 64 65 1.10 3.3E 50 54 0.00 8.0
Current Price Expected Dividend Expected Future Rate
Table 9.1
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Comparison of Required Rate of Return to Estimated Rate of Return
Stock Beta E(Ri) Estimated Return Minus E(Ri) Evaluation
A 0.70 10.2% 10.0 -0.2 Properly ValuedB 1.00 12.0% 6.2 -5.8 OvervaluedC 1.15 12.9% 21.2 8.3 UndervaluedD 1.40 14.4% 3.3 -11.1 OvervaluedE -0.30 4.2% 8.0 3.8 Undervalued
Required Return Estimated Return
Table 9.2
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Plot of Estimated Returnson SML Graph
Figure 9.7)E(R i
Beta0.1
mRSML
0 .20 .40 .60 .80 1.20 1.40 1.60 1.80-.40 -.20
.22 .20 .18 .16 .14 .12 Rm .10 .08 .06 .04 .02
AB
C
D
E
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Calculating Systematic Risk: The Characteristic Line
The systematic risk input of an individual asset is derived from a regression model, referred to as the asset’s characteristic line with the model portfolio:
tM,iiti, RRwhere: Ri,t = the rate of return for asset i during period tRM,t = the rate of return for the market portfolio M during t
miii R-R
2M
Mi,Cov
i
error term random the
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Scatter Plot of Rates of ReturnFigure 9.8
RM
RiThe characteristic line is the regression line of the best fit through a scatter plot of rates of return
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The Impact of the Time IntervalNumber of observations and time interval used in
regression vary
Value Line Investment Services (VL) uses weekly rates of return over five years
Merrill Lynch, Pierce, Fenner & Smith (ML) uses monthly return over five years
There is no “correct” interval for analysis
Weak relationship between VL & ML betas due to difference in intervals used
Interval effect impacts smaller firms more
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The Effect of the Market ProxyThe market portfolio of all risky assets must
be represented in computing an asset’s characteristic line
Standard & Poor’s 500 Composite Index is most often used– Large proportion of the total market value of
U.S. stocks– Value weighted series
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Weaknesses of Using S&P 500as the Market Proxy
– Includes only U.S. stocks – The theoretical market portfolio should include
U.S. and non-U.S. stocks and bonds, real estate, coins, stamps, art, antiques, and any other marketable risky asset from around the world
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Comparing Market ProxiesCalculating Beta for Coca-Cola using Morgan
Stanley (M-S) World Equity Index and S&P 500 as market proxies results in a 1.27 beta when compared with the M-S index, but a 1.01 beta compared to the S&P 500
The difference is exaggerated by the small sample size (12 months) used, but selecting the market proxy can make a significant difference
Here are the computations from page 303:
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Computation of Beta of Coca-Colawith Selected Indexes Table 9.3
Return S&P 500 M-S World Coca-ColaS&P M-S S&P M-S Coca- RS&P - E(RS&P) RM-S - E(RM-S) RKO - E(RKO)
Date 500 World 500 World Cola ( 1 ) ( 2 ) ( 3 ) ( 4 )a ( 5 )b
Dec-97 970.43 933.60Jan-98 980.28 961.50 1.02 2.99 (2.91) -1.16 1.08 -3.40 3.94 -3.69Feb-98 1049.34 1025.30 7.04 6.64 5.98 4.87 4.73 5.49 26.73 25.96Mar-98 1101.75 1067.40 4.99 4.11 8.47 2.82 2.20 7.97 22.49 17.55Apr-98 1111.75 1059.30 0.91 -0.76 1.93 -1.27 -2.66 1.43 -1.81 -3.82May-98 1090.82 1061.80 -1.88 0.24 3.29 -4.06 -1.67 2.80 -11.35 -4.67Jun-98 1133.84 1085.70 3.94 2.25 9.09 1.77 0.35 8.59 15.21 2.98Jul-98 1120.67 1082.70 -1.16 -0.28 (5.85) -3.34 -2.18 -6.35 21.17 13.84Aug-98 957.98 937.10 -14.52 -13.45 (19.10) -16.69 -15.35 -19.60 327.10 300.87Sep-98 1017.01 952.40 6.16 1.63 (11.52) 3.99 -0.27 -12.01 -47.91 3.27Oct-98 1098.67 1032.20 8.03 8.38 17.25 5.86 6.47 16.75 98.07 108.43Nov-98 1163.63 1097.60 5.91 6.34 3.70 3.74 4.43 3.20 11.97 14.19Dec-98 1229.23 1150.00 5.64 4.77 (4.37) 3.46 2.87 -4.87 -16.87 -13.97
2.17 1.90 0.50 Total = 448.74 460.93Standard Deviation 6.18 5.63 9.87
CovKO ,S&P= 448.74/ 12 = 37.39 VarS&P = St.Dev.S&P2
= 38.19 BetaKO,S&P= 0.98 AlphaKO ,S&P= -1.63
CovKO ,M-S= 460.93/ 12 = 38.41 VarM-S = St.Dev.M-S2
= 31.70 BetaKO,M-S= 1.21 AlphaKO ,M-S= -1.81
Correlation coef.KO ,S&P= 0.61 Correlation coef.KO ,M-S= 0.69
aColumn (4) is equal to column (1) multiplied by column (3) bColumn (5) is equal to column (2) multiplied by column (3)
Index
Average
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Arbitrage Pricing Theory (APT)
• CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
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Assumptions of Arbitrage Pricing Theory (APT)
1. Capital markets are perfectly competitive
2. Investors always prefer more wealth to less wealth with certainty
3. The stochastic process generating asset returns can be presented as K factor model (to be described)
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Assumptions of CAPMThat Were Not Required by APTAPT does not assume
• A market portfolio that contains all risky assets, and is mean-variance efficient
• Normally distributed security returns • Quadratic utility function
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Arbitrage Pricing Theory (APT)
For i = 1 to N where:
= return on asset i during a specified time period
ikikiiiitt bbbER ...21
Ri
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Arbitrage Pricing Theory (APT)
For i = 1 to N where:
= return on asset i during a specified time period
= expected return for asset i
ikikiiiitt bbbER ...21
Ri
Ei
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Arbitrage Pricing Theory (APT)
For i = 1 to N where:
= return on asset i during a specified time period
= expected return for asset i
= reaction in asset i’s returns to movements in a common factor
ikikiiiitt bbbER ...21
Ri
Ei
bik
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Arbitrage Pricing Theory (APT)
For i = 1 to N where:
= return on asset i during a specified time period
= expected return for asset i
= reaction in asset i’s returns to movements in a common factor
= a common factor with a zero mean that influences the returns on all assets
ikikiiiitt bbbER ...21
Ri
Ei
bik
k
SAIF ULLAH, [email protected], +923216633271
Arbitrage Pricing Theory (APT)
For i = 1 to N where:
= return on asset i during a specified time period
= expected return for asset i
= reaction in asset i’s returns to movements in a common factor
= a common factor with a zero mean that influences the returns on all assets
= a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero
ikikiiiitt bbbER ...21
Ri
Ei
bik
ki
SAIF ULLAH, [email protected], +923216633271
Arbitrage Pricing Theory (APT)
For i = 1 to N where:
= return on asset i during a specified time period
= expected return for asset i
= reaction in asset i’s returns to movements in a common factor
= a common factor with a zero mean that influences the returns on all assets
= a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero
= number of assets
ikikiiiitt bbbER ...21
Ri
Ei
bik
ki
N
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
k
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:– Inflation
k
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:– Inflation– Growth in GNP
k
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:– Inflation– Growth in GNP– Major political upheavals
k
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:– Inflation– Growth in GNP– Major political upheavals– Changes in interest rates
k
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:– Inflation– Growth in GNP– Major political upheavals– Changes in interest rates– And many more….
k
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Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:– Inflation– Growth in GNP– Major political upheavals– Changes in interest rates– And many more….
Contrast with CAPM insistence that only beta is relevant
k
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Arbitrage Pricing Theory (APT)Bik determine how each asset reacts to this
common factor
Each asset may be affected by growth in GNP, but the effects will differ
In application of the theory, the factors are not identified
Similar to the CAPM, the unique effects are independent and will be diversified away in a large portfolio
i
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Arbitrage Pricing Theory (APT)
• APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is zero when the unique effects are diversified away
• The expected return on any asset i (Ei) can be expressed as:
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Arbitrage Pricing Theory (APT)
where:
= the expected return on an asset with zero systematic risk where
ikkiii bbbE ...22110
0
01 EEi
00 E1 = the risk premium related to each of the common
factors - for example the risk premium related to interest rate risk
bi = the pricing relationship between the risk premium and asset i - that is how responsive asset i is to this common factor K
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Example of Two Stocks and a Two-Factor Model= changes in the rate of inflation. The risk premium
related to this factor is 1 percent for every 1 percent change in the rate
1)01.( 1
= percent growth in real GNP. The average risk premium related to this factor is 2 percent for every 1 percent change in the rate
= the rate of return on a zero-systematic-risk asset (zero beta: boj=0) is 3 percent
2)02.( 2
)03.( 3 3
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Example of Two Stocks and a Two-Factor Model= the response of asset X to changes in the rate of
inflation is 0.501xb
)50.( 1 xb
= the response of asset Y to changes in the rate of inflation is 2.00 )50.( 1 yb1yb
= the response of asset X to changes in the growth rate of real GNP is 1.50
= the response of asset Y to changes in the growth rate of real GNP is 1.75
2xb
2yb)50.1( 2 xb
)75.1( 2 yb
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Example of Two Stocks and a Two-Factor Model
= .03 + (.01)bi1 + (.02)bi2 Ex = .03 + (.01)(0.50) + (.02)(1.50)
= .065 = 6.5%
Ey = .03 + (.01)(2.00) + (.02)(1.75)
= .085 = 8.5%
22110 iii bbE
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Empirical Tests of the APT• Studies by Roll and Ross and by Chen
support APT by explaining different rates of return with some better results than CAPM
• Reinganum’s study did not explain small-firm results
• Dhrymes and Shanken question the usefulness of APT because it was not possible to identify the factors
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Summary
• When you combine the risk-free asset with any risky asset on the Markowitz efficient frontier, you derive a set of straight-line portfolio possibilities
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Summary
• The dominant line is tangent to the efficient frontier– Referred to as the capital market line
(CML)
– All investors should target points along this line depending on their risk preferences
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Summary• All investors want to invest in the risky
portfolio, so this market portfolio must contain all risky assets– The investment decision and financing decision
can be separated
– Everyone wants to invest in the market portfolio
– Investors finance based on risk preferences
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Summary• The relevant risk measure for an
individual risky asset is its systematic risk or covariance with the market portfolio– Once you have determined this Beta
measure and a security market line, you can determine the required return on a security based on its systematic risk
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Summary
• Assuming security markets are not always completely efficient, you can identify undervalued and overvalued securities by comparing your estimate of the rate of return on an investment to its required rate of return
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Summary
• The Arbitrage Pricing Theory (APT) model makes simpler assumptions, and is more intuitive, but test results are mixed at this point
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The InternetInvestments Online
www.valueline.com
www.barra.com
www.stanford.edu/~wfsharpe.com
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End of Chapter 9–An Introduction to Asset Pricing Models
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Future topicsChapter 10
• Extensions of Capital Asset Pricing Model
• Relaxation of Assumptions– Effect on SML and CML
• Empirical Tests of the Theory