CHAPTER 8

AN INTRODUCTION TO ASSET PRICING MODELS

I.Capital Market Theory: An Overview
A.Background for Capital Market Theory

1.Assumptions of Capital Market Theory

a.All investors are Markowitz efficient investors who want to target points on the efficient frontier

b.You can borrow or lend any amount of money at the RFR

c.Homogeneous expectations

d.Same one period time horizon

e.Investments infinitely divisible

f.No taxes or transactions costs involved in buying or selling assets

g.No inflation or change in the interest rates

h.Capital markets are in equilibrium

2.Development of Capital Market Theory

  • Concept of risk-free asset (asset with zero variance). Such an asset would have zero correlation with all other risky assets
B.Risk-Free Asset

1.Standard Deviation of the Expected Return of a Risk-Free Asset is zero

2.Covariance of the Risk-Free Asset with any Risky Asset or Portfolio of Assets will always equal zero

3.Combining a Risk-Free Asset and a Risky Portfolio

a.Expected return for a portfolio that includes a risk-free asset is the weighted average of the two returns

b.Standard Deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio

c.The Risk-Return Combination – the graph of possible returns and risks looks like a straight line (see Exhibit 8.1)

d.Risk-return Possibilities with Leverage – extends the range of portfolio possibilities (see Exhibit 8.2)

C.The Market Portfolio

1.What Assets are Included? – all risky assets are included

2.Systematic and Unsystematic Risk – since the market portfolio includes all risky assets, it is a completely diversified portfolio. Only systematic risk remains in the market portfolio

3.How to Measure of Diversification

4.Diversification and the Elimination of Unsystematic Risk – about 30-40 stocks need to be included in the portfolio to achieve maximum diversification benefit

5.The CML and the Separation Theorem – Investment decision versus financing decision (see Exhibit 8.4)

6.A Risk Measure for the CML – The only important consideration for risky assets is their covariance with the market portfolio

II.The Capital Asset Pricing Model (CAPM): Expected Return and Risk

A.The Security Market Line (see Exhibit 8.5)

1.Beta – standardized measure of systematic risk (see Exhibit 8.6)

2.Determining the Expected Rate of Return for a Risky Asset – determined by the risk-free rate plus a risk premium for the individual asset

3.Identifying Undervalued and Overvalued Assets (see Exhibits 8.7, 8.8, and 8.9)

4.Calculating Systematic Risk: The Characteristic Line (see Exhibit 8.10)

a.The impact of the time interval

  • The return time interval makes a difference, and its impact increases as the firm’s size declines

b.The effect of the market proxy

  • The choice of the indicator series used as the market proxy makes a difference

5.Example Computations of a Characteristic Line (see Exhibits 8.11, 8.12, and 8.13)

III.Relaxing the Assumptions

  1. Differential Borrowing and Lending Rates – the ability of investors to borrow unlimited amounts at the T-bill rate is questionable (see Exhibit 8.14)
  2. Zero Beta Model – does not require a risk-free asset (see Exhibit 8.15)
  3. Transaction Costs – with transactions costs, the SML will be a band of securities, rather than a straight line (see Exhibit 8.16)
  4. Heterogeneous Expectations and Planning Periods – will have an impact on the CML and SML
  5. Taxes – could cause major differences in the CML and SML among investors

IV.Empirical Tests of the CAPM

A.Stability of Beta - betas for individual stocks are not stable, but portfolio betas are stable
  1. Comparability of Published Estimates of Beta – differences exist. Hence, consider the return interval used and the firm’s relative size

V.Relationship Between Systematic Risk and Return

A.Effect of Skewness on Relationship – investors prefer stocks with high positive skewness that provide an opportunity for very large returns
  1. Effect of Size, P/E, and Leverage – size and P/E have an inverse impact on returns after considering the CAPM. Financial leverage also helps explain the cross-section of average returns
  2. Effect of Book-to-Market Value – Fama and French questioned the relationship between returns and beta in their seminal 1992 study. They found the BV/MV ratio to be a key determinant of returns
  3. Summary of CAPM Risk-Return Empirical Results – the relationship between beta and rates of return is a moot point
VI.The Market Portfolio: Theory versus Practice
  • There is a controversy over the market portfolio. Hence, proxies are used
  • There is no unanimity about which proxy to use
  • An incorrect market proxy will affect both the beta risk measures and the position and slope of the SML that is used to evaluate portfolio performance

VII.What is Next?

  • Alternative asset pricing models

8 - 1