1. Unit 5 - Portfolio Management
TECHNICAL ANALYSIS
Course Materials by
K.Rajeswari
Asst Professor
SNS college of technology
Unit 5 - Portfolio Management
Capital Asset Pricing Model

2. Capital Asset Pricing Model
Relates the required rate of return for any security with the market risk for the security as measured by beta
Focus on the equilibrium relationship between the risk and expected return on risky assets
Builds on Markowitz portfolio theory
Each investor is assumed to diversify his or her portfolio according to the Markowitz model, choosing a location on the efficient frontier that matches his/her return-risk preferences
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3. CAPM Assumptions All investors:
Use the same information to generate an efficient frontier (i.e., identical inputs: E(R), σ, ρ)
Have the same one- period time horizon
Can borrow or lend money at the risk-free rate of return
No transaction costs
No personal income (i.e., indifferent between dividends and capital gains) taxes
No inflation
No single investor can affect the price of a stock (i.e., price-takers)
Capital markets are in equilibrium
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4. CAPM Assumptions These assumptions appear unrealistic
The important issue is how well the theory predicts (describes) reality
The CAPM is robust since most of its assumptions can be relaxed without significant effects on the model
Not all of the CAPM assumptions are unrealistic:
Some institutional investors are tax-exempt
Significant reduction in transaction costs by using discount brokers and/or internet
For the one-period horizon of the model, inflation may be fully (or mostly) anticipated
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5. Market Portfolio Most important implication of the CAPM
All investors hold the same optimal portfolio of risky assets
As a result of the assumption that all investors have the same time horizon and homogenous expectations regarding the expected returns and risks for any given risky asset
The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
The portfolio of all risky assets is the optimal risky portfolio called the market portfolio
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6. Characteristics of the Market Portfolio (M)
All risky assets must be in portfolio, so it is completely diversified
Contains only systematic risk (cannot be eliminated)
All securities included in proportion to their market value
In theory, should contain all risky assets worldwide, both financial and real, in their proper proportions
Is found by determining which efficient portfolio offers the highest risk premium, given the existence of a risk- free asset
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7. The Equilibrium Risk-Return trade-off
The CAPM is an equilibrium model that encompasses two important relationships:
The capital market line (CML), specifies the equilibrium relationship between expected return and total risk for efficient portfolios
The security market line (SML), specifies the equilibrium relationship between expected return and systematic risk
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8. Capital Market Line Line from RF to L is capital market line (CML)
x = risk premium
= E(RM) - RF
y = risk = M
Slope = x/y = market price of risk for efficient portfolios
= [E(RM) - RF]/M
y-intercept = RF = price of forgone consumption L M
E(RM) x RF y M
Risk 6

9. Capital Market Line
Slope of the CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market
Relationship between risk and expected return for portfolio P (Equation for CML):
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10. Capital Market Line The following should be noted about the CML:
Only efficient portfolios consisting of the risk-free asset and portfolio M lie on the CML
It indicates the optimal expected returns associated with different portfolio risk levels
It must always be upwards sloping because the price of risk must always be positive
Although, it must be upward sloping ex ante (before the fact), it can be, and sometimes is, downward sloping ex post (after the fact). This merely indicates that the returns actually realized differed from those that were expected
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11. Security Market Line
CML Equation only applies to markets in equilibrium and efficient portfolios (i.e., cannot be used to assess the expected return on individual securities or inefficient portfolios)
The Security Market Line depicts the tradeoff between risk and expected return for individual securities
Under CAPM, all investors hold the risky portion of their portfolio in the market portfolio
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12. Security Market Line
The expected return on any risky asset is directly proportional to its covariance with the market portfolio
Equation for expected return for an individual stock similar to CML Equation
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13. Security Market Line Beta = 1.0 implies as risky as market
Securities A and B are more risky than the market
Beta > 1.0
Security C is less risky than the market
Beta < 1.0
SML
E(R) A
E(RM) B C RF
0.5
1.0
1.5
2.0
BetaM 10

14. Security Market Line
The SML represents the trade-off between systematic risk (β) and the expected return for all assets, whether individual securities, inefficient portfolios, or efficient portfolios
Beta measures systematic risk
Measures relative risk compared to the market portfolio of all stocks
Volatility of security i is different (higher or lower) than that of the market if β_i > 1 or β_i < 1 and is equal to that of the market if β_i = 1
β_i = 1 means that for every 1% change in the market’s return, on average security i’s returns change 1%
β_M = 1 and β_RF = 0
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15. Security Market Line
β is useful for comparing the relative systematic risk of different stocks and, in practice, is used by investors to judge a stock’s riskiness
βs may vary widely across companies in different industries and within a give industry
All securities should lie on the SML
The expected return on the security should be only that return needed to compensate for systematic risk
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16. SML and Asset Values Underpriced SML: Er = rf +  (Erm – rf)
Overpriced rf β
Underpriced  expected return > required return according to CAPM
 lie “above” SML
Overpriced  expected return < required return according to CAPM
 lie “below” SML
Correctly priced  expected return = required return according to CAPM
 lie along SML
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17. CAPM’s Expected Return-Beta Relationship
Required rate of return on an asset (ki) is composed of
risk-free rate (RF)
risk premium (βi [ E(RM) - RF ])
Market risk premium adjusted for specific security
ki = RF + βi [ E(RM) - RF ]
The greater the systematic risk, the greater the required return
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18. Estimating the SML
To use the SML, an investor needs estimates of the return on the risk-free asset, the expected return on the market index, and the β for an individual security
Treasury Bill rate used to estimate RF
Expected return for the market index in not observable
Estimated using past market returns and taking an expected value
Estimating individual security betas is difficult
β is only company-specific factor in CAPM
Requires asset-specific forecast
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19. Estimating Beta Market model
Relates the return on each stock to the return on the market, assuming a linear relationship with an intercept and slope
Rit =αi +βi RMt + eit
It is identical to the single-index model except that it does not make the assumption that the error terms of the different securities are uncorrelated
The Market Model produces an estimate of return for any stock
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20. Estimating Beta Characteristic line
A regression equation used to estimate β by regressing stock returns on market returns
Line fitted to total returns for a security relative to total returns for the market index
β is the slope of the characteristic line
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21. Test of CAPM Fama and French (1992)
Indicate that the CAPM’s sole risk factor, market risk β, posses no explanatory power in discriminating among the cross-sectional returns of US stocks
Common market equity (ME) and the ratio of book equity to market equity (BE/ME) combine to explain the cross-section of expected returns
Three-factor model (overall market factors, factors related to firm size, & BE/ME ratio)
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22. Test of CAPM Empirical SML is “flatter” than predicted SML
Fama and French (1992)
Market
Size
Book-to-market ratio
Roll’s Critique
True market portfolio is unobservable
Tests of CAPM are merely tests of the mean- variance efficiency of the chosen market proxy
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23. Arbitrage Pricing Theory(APT)
Based on the Law of One Price
Two otherwise identical assets cannot sell at different prices
Equilibrium prices adjust to eliminate all arbitrage opportunities
Unlike CAPM, APT does not assume
single-period investment horizon, absence of personal taxes, riskless borrowing or lending, mean-variance decisions
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24. Factors APT assumes returns generated by a factor model
Factor Characteristics
Each risk must have a pervasive influence on stock returns
Risk factors must influence expected return and have nonzero prices
Risk factors must be unpredictable to the market
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25. APT Model
Most important are the deviations of the factors from their expected values
The expected return-risk relationship for the APT can be described as:
E(Rit) =a0+bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +… +bin (risk premium for factor n)
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26. APT Model
Reduces to CAPM if there is only one factor and that factor is market risk
Roll and Ross (1980) Factors:
Changes in expected inflation
Unanticipated changes in inflation
Unanticipated changes in industrial production
Unanticipated changes in the default risk premium
Unanticipated changes in the term structure of interest rates
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27. Problems with APT Factors are not well specified ex ante
To implement the APT model, the factors that account for the differences among security returns are required
CAPM identifies market portfolio as single factor
Neither CAPM or APT has been proven superior
Both rely on unobservable expectations
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28. Thanks…
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