2. Arbitrage Pricing Theory and Multifactor Models Arbitrage Opportunity and Profit Diversification and APT APT and CAPM Comparison Multifactor Models

3. Investments 122 Arbitrage Opportunity and Profit  Arbitrage  The opportunity of making riskless profit by exploiting relative mispricing of securities  E.g., IBM: $96 on NYSE and $96.15 on NASDAQ creates an arbitrage opportunity  Zero-Investment Portfolio  A portfolio of zero value by long and short the same amount of securities  E.g., Buy $10,000 of stock A and short $10,000 of stock B creates a zero-investment portfolio

4. Investments 123 Arbitrage Opportunity and Profit  Example: Two stocks A, B and a bond C.  If it rains tomorrow, A pays $1.3 and B pays $0.2  if it does not rain, A pays $0.3 and B pays $1.5  C pays $2 regardless.  Price today: P A = P B = $1, P C = $2  Find the arbitrage opportunity and profit from it  Solution  Short 1 share of A and B each to get $2  Use the proceeds to buy bond C  Total initial investment = $0  P/L = $0.5 if it rains, and P/L = $0.2 if it does not.

5. Investments 124 Diversification and APT  Well-diversified Portfolio  A portfolio sufficiently diversified such that non- systematic risk is negligible  Arbitrage Pricing Theory (APT)  A theory of risk-return relationships derived from no-arbitrage conditions in large capital market  Individual stock:  Well-diversified portfolio: R F is the factor return  No-arbitrage means: α P = 0

6. Investments 125 Diversification and APT  How does it work?  Factor portfolio:  If portfolio C has α P = 2%, β P = 0.5  Show me the money  Short $100 of the factor portfolio  Long $200 of portfolio C  Net payoff  Risk-free four bucks? I’ll take it anytime!

7. Investments 126 APT and CAPM Comparison  APT applies to well-diversified portfolios and not necessarily to individual stocks  It is possible for some individual stocks not to lie on the SML  APT is more general in that its factor does not have to be the market portfolio  Both models can be extended to multifactor setup

8. Investments 127 Multifactor Models  Possible to consider more than one benchmark factor!  Consider a two-factor model:  R i : excess return = r i – r f  R Mi : factor portfolios excess return = r Mi – r f  : return sensitivity to systematic factors - also called as “factor loadings” “factor betas”

9. Investments 128 Multifactor Models  Where do the factors come from?  Variables that reflect macroeconomic picture  E.g. industrial production, inflation, bond spreads  Variables that serve as proxies for exposure to systematic risk  E.g. Fama-French (1993) model approach

10. Investments 129 Fama-French (1993) Model  Three-factor model: Three-factor model  R i : stock excess return = r i – r f  R M : market excess return = r M – r f  SMB: “Small Minus Big” factor return SMB = 1/3 (Small Value + Small Neutral + Small Growth) - 1/3 (Big Value + Big Neutral + Big Growth)  HML: “High Minus Low” factor return HML =1/2 (Small Value + Big Value) - 1/2 (Small Growth + Big Growth)  : return sensitivity to factors

11. Investments 1210 Are All Risk Factors Covered Now?

12. Investments 1211 Wrap-up  What is arbitrage and how to do it?  What are the major differences between APT and CAPM?  Multifactor models – the way to go!