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Applications of the CAPM & APT

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?. Example 1: risk arbitrage. “Pfizer Makes Rival Bid For Warner-Lambert”

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Applications of the CAPM & APT

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  1. Applications of theCAPM & 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(rn) - rf = rf + n[E(rm) - rf]

  6. Under the CAPM • Each stock’s return follows: rn(t) - rf = rf + n[rm(t) - rf] + en(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, ...

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