1. Applications of the CAPM & APT How can you control risk when managing a long-short portfolio? How can you assess the risk profile of a portfolio with 100+ stocks?

2. Example 1: risk arbitrage “Pfizer Makes Rival Bid For Warner- Lambert” Pfizer said it would offer 2.5 Pfizer shares for each share of Warner-Lambert outstanding. Today’s prices: PFE = $35, WLA = $90 Risk arbitrage: For each 2.5 shares of WLA long, short one share of PFE.

3. Example 2: an arbitrary pair Long IBM Short eBay? Dollar for dollar?

4. Example 3: Long-Short Fund Suppose you want –To buy 100 stocks with low P/E ratios –To short 100 stocks with high P/E ratios, $ for $ What about risk exposure to systematic vs unsystematic?

5. The CAPM The risk premium for a stock is a function of its contribution to the risk of the market portfolio A stock’s risk premium is a function of its covariance with the market portfolio. E(r n ) - r f = r f +  n  [E(r m ) - r f ]

6. Under the CAPM Each stock’s return follows: r n(t) - r f = r f +  n  [r m (t) - r f ] + e n(t) Thus, there is just one source of systematic risk

7. Implications for Market-Neutral Funds Make the total beta of the Long Portfolio equal the total beta of the Short Portfolio Show me an example? Any problems?

8. The APT Multiple factors constitute “systematic risks”, not just the market portfolio! Show me the equation, please!

9. What factors? Factors include, in addition to market portfolio, –Industrial production growth –Interest rates –Term premium or yield curve slope –Default premium = BBB corporate bond yield - Treasury bond yield –Size factor –Book/market factor Estimate a beta for each factor using multiple regression

10. Now, how do I do market-neutral? You want to make total factor beta of the Long Portfolio = total factor beta of the Short Portfolio, for every known factor!

11. Problems and Concerns? How many factors are too few? Let the R-square speak! But, ultimately, it is difficult to make the Long & the Short sides exactly match.

12. Risk Management Keep a profile of your portfolio’s exposure to every known risk factor: –Macroeconomic factors: interest rate, inflation, … –Industry factors: oil, retail, semiconductor, …. Barra, Northfield,...