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

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

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

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.

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

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

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)

9.3 The market model and beta estimation Example 9-1

9.3 The market model and beta estimation Table 9-1 Average Return ( ) Variance (2i) Covariance [COV (Ri, Rm)] JNJ .0042 .00162 .000407 MRK .0021 .00610 .000974 PG .0105 .00124 .000244 Market .0043 .00126

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

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

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

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.

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

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

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

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

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

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

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.

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.

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).

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.

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

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

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

Appendix 9B. Arbitrage Pricing Model

Appendix 8B. Arbitrage Pricing Model