capital markets

1. CAPM & APT

2. 2
Capital Market Theory:
An Overview
Capital asset pricing model (CAPM) will
allow you to determine the required rate of
return for any risky asset

3. 3
Capital Asset Pricing Model (CAPM)
 Capital Asset Pricing Model (CAPM) is based on
observation that the returns on a financial asset
increase with the risk.
 CAPM concerns two types of risk namely
unsystematic and systematic risks. The central
principle of the CAPM is that, systematic risk, as
measured by beta, is the only factor affecting the
level of return.

4. 4
Introduction
The Capital Asset Pricing Model (CAPM)
is a theoretical description of the way in
which the market prices investment assets
• The CAPM is a positive theory

5. 5
Systematic and
Unsystematic Risk
Unsystematic risk can be diversified and is
irrelevant
Systematic risk cannot be diversified and is
relevant
• Measured by beta

6. Systematic and unsystematic risk
 Specifically:
Total risk = systematic risk + unsystematic risk
CAPM says:
(1)Unsystematic risk can be diversified away. It can be avoided by
diversifying at NO cost, the market will not reward the holder of
unsystematic risk at all.
(2)Systematic risk cannot be diversified away without cost.
investors need to be compensated by a certain risk premium for
bearing systematic risk

7. 7
Diversification and Beta
Beta measures systematic risk
• Investors differ in the extent to which they will
take risk, so they choose securities with different
betas
– E.g., an aggressive investor could choose a portfolio with
a beta of 2.0
– E.g., a conservative investor could choose a portfolio
with a beta of 0.5
A measure of the sensitivity of a stock’s return to
the returns on the market portfolio
βi = Cov(Ri, Rm)/Var(Rm)

8. Risk and return
 Investors need to be compensated by a certain risk premium for
bearing systematic risk
 The reward-to-risk ratio for any individual security in the
market is equal to the market reward-to-risk ratio, thus:
 The market reward-to-risk ratio is effectively the Market Risk
Premium which is defined as
 The market is defined as a portfolio of all wealth including
stocks.
 Rearranging the above equation and solve for the expected
return
]FR]M[E[R 

9. The CAPM formula
So E(Ri)=Rf + βi(E(Rm) – Rf)
Rf + Units × Price.
]R][E[R
)Var(R
)R,Cov(R
R]E[R FM
M
Mi
Fi 
]R][E[RR]E[R FMiFi  
Number of units of
systematic risk () Market Risk Premium
or the price per unit risk
or,

10. 10
Security Market Line
The graphical relationship between
expected return and beta is the security
market line (SML)
• The slope of the SML is the market price of
risk
• The slope of the SML changes periodically as
the risk-free rate and the market’s expected
return change

11. Sample Calculations for SML
E(rm) - rf = rf =
x = 1.25
E(rx) =
y = .6
E(ry) =
Equation of the SML
E(ri) = rf + i[E(rM) - rf]
0.03 + 1.25(.08) = .13 or 13%
0.03 + 0.6(0.08) = 0.078 or 7.8%
.08 .03
Return per unit of systematic risk = 8% & the return due to the Risk free return = 3%

12. E(r)
SML
ß
ßM
1.0
RM=11%
3%
Rx=13%
ßx
1.25
Ry=7.8%
ßy
0.6
.08
Graph of Sample Calculations
If the CAPM is correct, only β
risk matters in determining the
risk premium for a given slope
of the SML.

13. 13
SML and CAPM
If you show the security market line with
excess returns on the vertical axis, the
equation of the SML is the CAPM
• The intercept is zero
• The slope of the line is beta

14. 14
CAPM
The more risk you carry, the greater the
expected return:
( ) ( )
where ( ) expected return on security
risk-free rate of interest
beta of Security
( ) expected return on the market
i f i m f
i
f
i
m
E R R E R R
E R i
R
i
E R


    





15. 15
CAPM (cont’d)
The CAPM deals with expectations about
the future
Excess returns on a particular stock are
directly related to:
• The beta of the stock
• The expected excess return on the market

16. 16
CAPM (cont’d)
CAPM assumptions:
• Variance of return and mean return are all
investors care about
• Investors are price takers
– They cannot influence the market individually
• All investors have equal and costless access to
information
• There are no taxes or commission costs

17. 17
CAPM (cont’d)
CAPM assumptions (cont’d):
• Investors look only one period ahead
• Everyone is equally adept at analyzing
securities and interpreting the news

18. 18
Note on the
CAPM Assumptions
 Several assumptions are unrealistic:
• People pay taxes and commissions
• Many people look ahead more than one period
• Not all investors forecast the same distribution
 Theory is useful to the extent that it helps us learn
more about the way the world acts
• Empirical testing shows that the CAPM works
reasonably well

19. 19
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 0.70
B 1.00
C 1.15
D 1.40
E -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%

20. 20
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 6.2
C 33 39 1.00 21.2
D 64 65 1.10 3.3
E 50 54 0.00 8.0
Current Price Expected Dividend Expected Future Rate

21. 21
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 Valued
B 1.00 12.0% 6.2 -5.8 Overvalued
C 1.15 12.9% 21.2 8.3 Undervalued
D 1.40 14.4% 3.3 -11.1 Overvalued
E -0.30 4.2% 8.0 3.8 Undervalued
Required Return Estimated Return

22. 22
Arbitrage Pricing Theory
APT background
The APT model
Comparison of the CAPM and the APT

23. 23
Arbitrage Pricing Theory
 Arbitrage Pricing Theory was developed by Stephen Ross
(1976). His theory begins with an analysis of how investors
construct efficient portfolios and offers a new approach for
explaining the asset prices and states that the return on any
risky asset is a linear combination of various
macroeconomic factors that are not explained by this CAPM
theory.

24. Arbitrage Pricing Theory (APT)
 Arbitrage:
 Zero investment:
 Efficient markets:
Arises if an investor can construct
a zero investment portfolio with a
sure profit
Since no net investment outlay is
required, an Arbitrageurs can create
arbitrarily large positions to secure
large levels of profit
With efficient markets, profitable
arbitrage opportunities will quickly
disappear
7-24

25. 25
Arbitrage Pricing Theory
 Similar to CAPM it assumes that investors are fully
diversified and the systematic risk is an influencing factor in
the long run. However, unlike CAPM model APT specifies
a simple linear relationship between asset returns and the
associated factors because each share or portfolio may have
a different set of risk factors and a different degree of
sensitivity to each of them.

26. 26
APT Background (cont’d)
Not all analysts are concerned with the
same set of economic information
• A single market measure such as beta does not
capture all the information relevant to the price
of a stock

27. 27
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

28. 28
Arbitrage Pricing Theory - APT
Three major assumptions:
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 expressed as a linear function
of a set of K factors or indexes

29. 29
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 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
ikikiiiii bbbERi   ...21
Ri
Ei
bik
k
i
N

30. 30
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

31. 31
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

32. 32
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:

33. 33
Example-Portfolio beta and risk premium
 Consider the following
portfolio:
 A) Calculate the risk
premium on this portfolio
 B) Calculate the total
portfolio risk if Market risk
premium is 7.5%.
Asset Beta
Risk
prem.
Portfolio
Weight
X 1.2 9% 0.5
Y 0.8 6 0.3
Z 0.0 0 0.2
Port. 0.84  1.0

34. 34
Answer-Portfolio beta and risk premium
A) (9%) (0.5)=4.5
 (6%) (0.3)=1.8
 =6.3%
B) 0.84(7.5)=6.3%

35. 35
Example-risk premium
 Suppose the risk premium of the market portfolio
is 8%, with a st. dev. Of 22%.
 Calculate A) The Portifolio’s Beta and B) the risk
premium of the portfolio referring to a portfolio
invested 25% in x motor company with beta 0f
1.15 and 75% in y motor company with a beta of
1.25.

36. 36
Answer-risk premium
A) βy= 1.25, βx= 1.15
βp=wy βy+ wx βx
 =0.75(1.25)+0.25(1.15)=1.225
B) E(rp)-rf=βp[E(rm)-rf]
 =1.225(8%)=9.8%