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Stochasticity of Correlations

Stochasticity of Correlations. Xiaoyang Zhuang Economics 201FS Duke University 2/23/2010. Motivation. The Problem In a crisis, “correlations go to 1.” For portfolio managers, converging correlations throw off diversification and hedging strategies. Two O ptimal S olutions

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Stochasticity of Correlations

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  1. Stochasticity of Correlations XiaoyangZhuang Economics 201FS Duke University 2/23/2010

  2. Motivation • The Problem • In a crisis, “correlations go to 1.” • For portfolio managers, converging correlations throw off diversification and hedging strategies. • Two Optimal Solutions • 1. Predict when crises occur. • 2. Dynamically rebalance portfolio as crisis unfolds. • Two Possible Approaches • 1. Empirically observe the characteristics of an unfolding crisis. • 2. Account for correlation as stochastic processes in the original portfolio optimization problem: • min(α)σ2 = αVαsubject toαTe = 1, αT = P • (Buraschi, Porchia, and Trojani, 2010, J. Finance)

  3. Long-Run vs. Crisis Correlations Long-Run Correlations: 1/1/2000 – 12/30/2010 Crisis Correlations: 6/1/20 – 12/30/2010

  4. Roadmap • Discuss the five stocks used in the data analysis and explain why they were selected • For each pair of stocks, we will examine the • Price series • Correlations series (as implied by the stock and portfolio realized variances): • Pearson Correlations • Future directions

  5. About the Stocks Alcoa (AA) The world’s leading producer of aluminum. DuPont (DD) A diversified scientific company with innovations in “agriculture, nutrition, electronics, communications, safety and protection, home and construction, transportation and apparel.” Ford (F) An multinational car company. JPMorgan & Chase (JPM) A diversified financial services company. Wal-Mart (WMT) A multinational company operating a chain of discount department stores and warehouse stores. April 9, 1997 – December 23, 2010 (3420 days) These stocks were selected because They belong to companies in diverse industries. (To examine the effectiveness of diversification.) 2. They did not exhibit long-term directional trends in the last decade. (To isolate firm-level behavior from macroeconomic trends.) NOTE: For each stock, most of the price variation was within $20 of the mean.

  6. Alcoa and DuPont: Price Series

  7. Alcoa and DuPont: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  8. Alcoa and DuPont: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  9. Alcoa and Ford: Price Series

  10. Alcoa and Ford : Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  11. Alcoa and Ford : Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  12. Alcoa and JPMorgan Chase: Price Series

  13. Alcoa and JPMorgan Chase: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  14. Alcoa and JPM: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  15. Alcoa and Wal-Mart: Price Series

  16. Alcoa and Wal-Mart: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  17. Alcoa and WMT: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  18. DuPont and Ford: Price Series

  19. DuPont and Ford: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  20. DuPont and Ford: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  21. DuPont and JPMorgan Chase: Price Series

  22. DuPont and JPMorgan Chase: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  23. DuPont and JPM: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  24. Ford and JPMorgan Chase: Price Series

  25. Ford and JPMorgan Chase: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  26. Ford and JPM: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  27. Ford and Wal-Mart: Price Series

  28. Ford and Wal-Mart: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  29. Ford and WMT: Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  30. JPMorgan Chase and Wal-Mart: Price Series

  31. JPMorgan Chase and Wal-Mart: Implied Correlation • Calculations • Variances (on the right-hand side of the equation) were estimated using the five-minute Realized Volatility estimator.

  32. JPM and WMT : Overlapping Pearson Correlation • Calculations • Pearson correlations are calculated in four-month intervals • If A and B are adjacent intervals, A and B overlap 119/120 days

  33. Future Directions Empirical directions Explore the literature in more detail to find refinements to correlation estimates. “Covariance Estimation,” (Boudt, Cornelissen and Croux, 2010, working paper) “Estimating Covariation: Epps Effect, Microstructure” (Zhang, 2008, J. Econometrics) Explore the differences between realized correlation and the implied correlations we’ve found here. Explore the relationship between correlation and trading volume. Explore the notion of correlation co-jumps. Theoretical direction Explore theoretical frameworks for dynamic portfolio optimization (Buraschi, Porchia, and Trojani, 2010, J. Finance)

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