InvestmentsCopyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Chapter 8
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Chapter Summary
Objective: To discuss the nature and illustrate the use of arbitrage. To introduce the index model and the APT.
The Single Index Model
The Arbitrage Pricing Theory
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Easier for security analysts to specialize
Drawback:
the simple dichotomy rules out important risk sources (such as industry events)
The Single Index Model
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
ßi = index of a security’s particular return to the factor
F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns
Single Factor Model
Assumption: a broad market index like the S&P500 is the common factor
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Single Index Model
ai = stock’s expected return if market’s excess return is zero
bi(rM-ri) = the component of return due to market movements
ei = the component of return due to unexpected firm-specific events
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Market or systematic risk: risk related to the macro economic factor or market index
Unsystematic or firm specific risk: risk not related to the macro factor or market index
Total risk = Systematic + Unsystematic
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Regression Results
R-SQR = 0.575
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
a has a different interpretation: a + rf (1-b)
Merill Lynch’s ‘adjusted b’
Forecasting beta as a function of past beta
Forecasting beta as a function of firm size, growth, leverage etc.
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Multifactor Models
Estimate a beta for each factor using multiple regression
Chen, Roll and Ross
Returns a function of several macroeconomic and bond market variables instead of market returns
Fama and French
Returns a function of size and book-to-market value as well as market returns
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Summary Reminder
Objective: To discuss the nature and illustrate the use of arbitrage. To introduce the index model and the APT.
The Single Index Model
The Arbitrage Pricing Theory
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Arbitrage Pricing Theory
Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit
Since no investment is required, an investor can create large positions to secure large levels of profit
In efficient markets, profitable arbitrage opportunities will quickly disappear
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Arbitrage Example
(pp. 293-295)
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Arbitrage Portfolio
25.83
6.40
0.94
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Arbitrage Action and Returns
Action: Short 3 shares of D and buy 1 of A, B & C to form portfolio P
Returns: You earn a higher rate on the investment than you pay on the short sale
E(r)
s
P
D
25.83
22.25
6.40
8.58
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
APT & Well-Diversified
For a well-diversified portfolio eP approaches zero
The result is similar to CAPM
Bodie Kane Marcus Perrakis Ryan INVESTMENTS, Fourth Canadian Edition
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Disequilibrium Example
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Disequilibrium Example
Short Portfolio C
Use funds to construct an equivalent risk higher return Portfolio D
D is comprised of A & Risk-Free Asset
Arbitrage profit of 1%
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
Copyright © McGraw-Hill Ryerson Limited, 2003
Slide 8-*
APT applies to well diversified portfolios and not necessarily to individual stocks
With APT it is possible for some individual stocks to be mispriced - not lie on the SML
APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio
APT can be extended to multifactor models
APT and CAPM Compared