1. Capital Asset Pricing and Arbitrary Pricing Theory
CHAPTER 7

2. Risk and diversification
Market risk is the only risk left after diversification
Return that investors get in the market is rewarded for market risk only, not total risk
Hence market risk is relevant risk, and specific risk is irrelevant risk
In the market, higher beta gets higher return, not higher std gets higher return.

3. Example: std beta amount invested IBM 40% 0.95 2000 AT&T 20% 1.10 4000
What is the beta of market portfolio
Does IBM have more or less risk than the market
Which stock has more total risk
Which stock has more systematic risk
Which stock is expected to have higher return in the market
4. In the boom market, which stock do you choose
5. In the recession market, which stock do you choose
6. What is the beta of your portfolio

4. Capital Asset Pricing Model (CAPM)
How do investors know whether the return they get in the market is high enough to reward for the level of risk taken.

5. Capital Asset Pricing Model (CAPM)
CAPM gives the relationship between risk and return.
It gives the minimum return required by investors in order for them to buy stock
Example:
market risk premium = 0.08, Rf = 0.03
βx=1.25, βy=1.25
What is E(Rx), E(Ry), what is meaning of them?

6. Graph of Sample Calculations
E(r)
SML
.08
Rx=13%
Rm=11%
Ry=7.8% 3% ß .6
1.0
1.25 ß ß ß y m x

7. SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf
= market risk premium
SML = rf + b[E(rm) - rf]

8. Capital Asset Pricing Model (CAPM)
Remember earlier, we have
In CAPM, we have
What is the difference in meaning between the two expected return?

9. Capital Asset Pricing Model (CAPM)
When forecasted E(R) > required E(R), stock is undervalued or the price is too low
When forecasted E(R) < required E(R), stock is undervalued or the price is too high
In equilibrium, forecasted E(R) = required E(R)

10. Capital Asset Pricing Model (CAPM)
Example: E(Rm) = 14%, Rf = 6%
Stocks Beta E(R) (forecasted)
IBM %
ATT %
What is the market risk premium
what is the risk premium on IBM and ATT
According to CAPM, what is the required E(R) for IBM and ATT
Which stock is undervalued, which stock is overvalued

11. Determining the Expected Rate of Return for a Risky Asset
Let alpha (α) be the difference between the actual (forecasted) E(R) and the required E(R)
In equilibrium, all assets and all portfolios of assets should plot on the SML ( i.e., α = 0)
Any security with an estimated return that plots above the SML is underpriced (α > 0 )
Any security with an estimated return that plots below the SML is overpriced ( α < 0 )
Previous example:
αIBM= 17 – 15.6 = 1.4 > 0. Actual E(R) is above the SML
αATT= = -4 > 0. Actual E(R) is below the SML

12. Figure 7-2 The Security Market Line and Positive Alpha Stock

13. Chap. 7, Problem 19, p.236
Two investment advisers are comparing performance. One average a 19% return and the other a 16%. However, the beta of the first adviser was 1.5, while that of the second was 1.0.
Can you tell which adviser was better?
If the T-bill rate were 6%, and market return during the period were 14%, which would be better?
What if T-bill rate were 3% and market return 15%?

14. Estimating alpha and beta in practice (using index model)
alpha is the abnormal return = actual return – return predicted by CAPM
According to CAPM, alpha should be = 0
Beta is the systematic risk

15. Figure 7-4 Characteristic Line for GM

16. Characteristic Line for GM
All the points are actual values
Line is the predicted relationship
If there are a lot of specific risk, there will be a wide scatter of points around the line. Hence, using market risk only in this case does not produce a precise estimate of expected return
If the points are close to the line, there is only small specific risk. Using market risk can explain most of the company return.

17. Table 7-2 Security Characteristic Line for GM: Summary Output

18. Security Characteristic Line for GM: Summary Output
R-square:
ANOVA table
Total risk = systematic risk + unsystematic risk =
(100%) = % %
Alpha = > 0 (positive alpha, undervalued or overvalued?)
During the period Jan 99-Dec03: the risk-adjusted or abnormal return of GM = % or actual return is higher than CAPM predicted
Is this value statistically different from 0? Is this still consistent with CAPM
95% confidence interval ( to )
Beta =
Is beta statistically different from 0?

19. Implication of CAPM
CAPM is a benchmark about the fair (required) expected return on a risk asset. Investors calculate the return they actually earn based on their input and compare with the return they get from the CAPM
Compare the performance of the mutual fund: we use alpha or risk-adjusted return rather than regular return
Compute the cost of equity for capital budgeting

20. Does CAPM work in reality?
CAPM is only a theory
Assumptions
Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
No taxes, and transaction costs
Information is costless and available to all investors
Investors are rational mean-variance optimizers
Homogeneous expectations

21. Empirical test of CAPM
CAPM was introduced by Sharpe (1964) and later earned him a Nobel prize in 1990
It changes the world how we should perceive risk and the relationship between risk and return
However, it is only a theory, we need to test whether it works in practice
The test of CAPM falls into 2 categories
Stability of the beta
Slope of the SML

22. Empirical test of CAPM Stability of beta Slope of SML
betas of individual stocks are unstable
betas of a portfolio (> 10 stocks randomly selected) are reasonable stable
CAPM is a better concept for portfolio than for individual securities
Slope of SML
positive relationship between beta and return (consistent with CAPM)
Empirical slope is smaller than predicted (=market risk premium)
CAPM says that beta is the only source of risk, no specific risk, however, the empirical data show that there exists both risk (market and specific),

23. Current status of CAPM
CAPM is powerful at the conceptual level. It is a useful way to think about risk and return
Empirical data does not support CAPM fully but it is simple, logical, easy to use, so use CAPM with caution

24. Arbitrary pricing theory (APT)
CAPM is a single factor model. The market risk premium is the only factor
In CAPM, all the news, uncertainties affect the market, then the market affect the stock individually
In APT, there are n factors that can influence stock return so there will be n-sources of risk or n-channels of uncertainties
Empirical evidence support APT (more than 1 factor affect stock return), but unable to identify these factors.
So if the purpose is to get cost of capital only, then APT is appropriate
If we want to know sources of risk then APT is not useful

25. Fama-French three-factor model
Fama and French propose three factors:
The excess market return, rM-rRF.
the return on, S, a portfolio of small firms (where size is based on the market value of equity) minus the return on B, a portfolio of big firms. This return is called rSMB, for S minus B.
the return on, H, a portfolio of firms with high book-to-market ratios (using market equity and book equity) minus the return on L, a portfolio of firms with low book-to-market ratios. This return is called rHML, for H minus L.

26. Required Return for Stock i under the Fama-French 3-Factor Model
ri = rRF + (rM - rRF)bi + (rSMB)ci + (rHMB)di
bi = sensitivity of Stock i to the market return.
cj = sensitivity of Stock i to the size factor.
dj = sensitivity of Stock i to the book-to-market factor.
The model is widely used in research and practice