1. Financial Analysis, Planning and Forecasting Theory and Application
Chapter 9
Risk and Return Trade-off Analysis By
Cheng F. Lee
Rutgers University, USA
John Lee
Center for PBBEF Research, USA

2. Outline
9.1 Introduction
9.2 Capital Market Line, Efficient-market hypothesis, and capital asset pricing model
9.3 The market model and beta estimation
9.4 Empirical evidence for the risk-return relationship
9.5 Why beta is important in financial management
9.6 Systematic risk determination
9.7 Some applications and implications of the capital asset pricing model
9.8 Liquidity and CAPM
9.9 APT
9.10 Summary
Appendix 9A. Mathematical derivation of CAPM
Appendix 9B. Arbitrage Pricing Model

3. Lending, borrowing, and the market portfolio The capital market line
9.2 Capital Market Line, Efficient-market hypothesis, and capital asset pricing model
Lending, borrowing, and the market portfolio
The capital market line
The efficient-market hypothesis
- Weak-form efficient-market hypothesis
- Semistrong-form efficient-market hypothesis
- Strong-form efficient-market hypothesis
The capital asset pricing model

4. 9.2 Capital Market Line, Efficient-market hypothesis, and capital asset pricing model
Figure 9.1 The Capital Market Line
From Figure 9.1, we can derive the capital market line as follows.
Step 1. Since
therefore,
then we can obtain Eq. 9.2.

5. 9.2 Capital Market Line, Efficient-market hypothesis, and capital asset pricing model
(9.3)
(9.4)
Figure 9.2 The Capital Asset Pricing Model (SML)
Derivation of Equation (9.4) can be found in Appendix 8A

6. 9.2 Capital Market Line, Efficient-market hypothesis, and capital asset pricing model
(9.5)
(9.6)

7. 9.3 The market model and beta estimation
Ri, t = αi + i Rm, t + εi, t (9.7)
Ri, t – Rf, t = αi + i (Rm, t – Rf, t) + εi, t (9.8)
(9.9)

8. 9.3 The market model and beta estimation
Example 9-1

9. 9.3 The market model and beta estimation
Table 9-1
Average Return ( )
Variance (2i)
Covariance [COV (Ri, Rm)]
JNJ
.0042
.00162
MRK
.0021
.00610 PG
.0105
.00124
Market
.0043
.00126

10. 9.3 The market model and beta estimation
Figure 9-3 Mean-Variance Comparison
MRK
JNJ
Market PG

11. 9.3 The market model and beta estimation
Figure 9-4 SML Comparison PG
JNJ
MRK
Market

12. 9.4 Empirical evidence for the risk-return relationship
E(Ri) – Rf = [E(Rm) – Rf] i (9.10)
(9.5)
(9.11)

13. 9.5 Why beta is important in financial management
The use of beta is of great importance to the financial manager because it is a key component in the estimation of the cost of capital. A firm’s expected cost of capital can be derived from E(Ri), where E(Ri) = Rf + βi [E (Rm) – Rf]. This assumes that the manager has access to the other parameters, such as the risk-free rate and the market rate of return. (This is explored in more detail in chapter 12.)
Ri, t = αi + βi Rm, t + єi, t (9.7)
Beta is also an important variable because of its usefulness in security analysis. In this type of analysis, beta is used to measure a security’s response to a change in the market and so can be used to structure portfolios that have certain risk characteristics.

14. 9.6 Systematic risk determination
Business risk
Financial risk
Other financial variables
Capital labor ratio
Fixed costs and variable costs
Market-based versus accounting-based beta forecasting

15. 9.6 Systematic risk determination
Business risk and financial risk
Other Financial Variables

16. 9.6 Systematic risk determination
(9.12)
Capital labor ratio
Q=f(K, L) (9.13)
(9.14)

17. 9.7 Some applications and implications of the capital asset pricing model
Table 9-2 Regression Results for the Accounting Beta
Coefficients
t Values
Intercept ( )
Financial leverage ( )
Dividend payout ( )
Sales beta( )
Operating income beta ( )
.911
.704
-.175
.03
.011
11.92
5.31
-3.50
3.02
2.18

18. 9.7 Some applications and implications of the capital asset pricing model
(9.15)
(9.16)
(9.17)

19. 9.7 Some applications and implications of the capital asset pricing model
FIGURE 9-5
Capital Budgeting and Business Strategy Matrix

20. 9.8 Liquidity and Capital Asset Pricing Model
Acharya and Pedersen (2005) proposed the following model for liquidity considering the impact of liquidity risk on security pricing
The overall risk of a security account for three kinds of liquidity risk defined as follows
First, measures the sensitivity of security illiquidity to market illiquidity. In general, investors demand higher premium for holding an illiquid security when the overall market liquidity is low. Further, measures the sensitivity of security’s return to market illiquidity. Investors are willing to accept a lower average return on security that will provide higher returns when market illiquidity is higher. Finally measures the sensitivity of security illiquidity to the market rate of return. In general, investors are willing to accept a lower average return on security that can be sold more easily.

21. 9.9 Arbitrage Pricing Theory
Ross (1976, 1977) has derived a generalized capital asset pricing relationship called arbitrage pricing theory (APT). To derive the APT, Ross assumed the expected rate of return on ith security be explained by k independent influences (or factors) as
Using Equation 9-18, Ross has shown that the risk premium of jth security can be defined as
By comparing Equation 9-19 with the CAPM equation, we can conclude that the APT is a generalized capital asset pricing model. Therefore, it is one of the important models for students of finance to understand. This model is generally discussed in upper-level financial management or investment courses.

22. 9.10 Intertemporal CAPM
Merton (1973,1992) derived an Intertemporal CAPM which allows the change of investment opportunity set as defined in Eq. (9.21). This Intertemporal CAPM will reduce to the one-period CAPM defined in Eq. (9.4).

23. 9.8 Summary
In Chapter 9 we have discussed the basic concepts of risk and diversification and how they pertain to the CAPM, as well as the procedure for deriving the CAPM itself. It was shown that the CAPM is an extension of the capital market line theory. The possible uses of the CAPM in financial analysis and planning were also indicated.
The concept of beta and its importance to the financial manager were introduced. Beta represents the firm’s systematic risk and is a comparative measure between a firm’s security or portfolio risk in comparison with the market risk. Systematic risk was further discussed by investigating the relationship between the beta coefficient and other important financial variables.

24. Appendix 9A. Mathematical derivation of the capital asset pricing model

25. Appendix 9A. Mathematical derivation of the capital asset pricing model
CML Slop:

26. Appendix 9A. Mathematical derivation of the capital asset pricing model
FIGURE 9-A1 The Opportunity Set Provided by Combinations of
Risky Asset / and Market Portfolio, M

27. Appendix 9B. Arbitrage Pricing Model

28. Appendix 8B. Arbitrage Pricing Model