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Asset Management

Asset Management. Lecture 6. Outline for today. Treynor Black Model M2 measure of performance Sensitivity to return assumption Tracking error. Treynor Black Model. The optimization of a risky portfolio using a single-index model is know as the Treynor Black model (or diagonal model ).

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Asset Management

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  1. Asset Management Lecture 6

  2. Outline for today • Treynor Black Model • M2 measure of performance • Sensitivity to return assumption • Tracking error

  3. Treynor Black Model • The optimization of a risky portfolio using a single-index model is know as the Treynor Black model (or diagonal model)

  4. Optimizing procedure

  5. Treynor Black Model

  6. Table 27.1 active portfolio management with 6 assets

  7. Table 27.1 active portfolio management with 6 assets

  8. Table 27.1 active portfolio management with 6 assets

  9. Table 27.1 active portfolio management with 6 assets

  10. Table 27.1 active portfolio management with 6 assets

  11. Table 27.1 active portfolio management with 6 assets

  12. Table 27.1 active portfolio management with 6 assets

  13. Table 27.1 active portfolio management with 6 assets

  14. Table 27.1 active portfolio management with 6 assets

  15. Table 27.1 active portfolio management with 6 assets

  16. Table 27.1 active portfolio management with 6 assets

  17. Table 27.1 active portfolio management with 6 assets

  18. M2Measure Developed by Modigliani and Modigliani Create an adjusted portfolio P* with T-bills and the managed portfolio P so that SD[r(P*)]= SD[r(M)] Example: Volatility of r(P)=1.5*volatility of r(M) P*=2/3P+1/3T With the same SD, you can now compare the performance

  19. M2Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 30/42 = .714 in P (1-.714) or .286 in T-bills r(P*)=(.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed

  20. M2Measure: Example E(r) M P M2 P* T σ σ(M) σ(P)

  21. M2Measure: Example E(r) P* M2 P M T σ σ(M) σ(P)

  22. M2Measure • Simplification for calculation

  23. Table 27.1 active portfolio management with 6 assets

  24. Target price and alpha on June 1, 2006

  25. The Optimal Risky Portfolio with the Analysts’ New Forecasts

  26. The Optimal Risky Portfolio (WA< 1)

  27. Drawback of the model • Extreme sensitivity to expected return assumptions • The results often run against investor intuition • Such quantitative optimization processes are rarely employed by managers • What about putting some constraints to this model?

  28. Tracking error • Portfolios are often compared against a benchmark • Tracking error • Benchmark Risk: SD of Tracking error

  29. The Optimal Risky Portfolio with the Analysts’ New Forecasts

  30. Tracking error • Set weight in the active portfolio to meet the desired benchmark risk • For a unit investment in the active portfolio • For our example: • For a desired benchmark risk • Assume that the desired benchmark risk is 0.0385 • Wa(Te)=0.0385/0.0885 • Wa(Te)=0.43

  31. Constrained benchmark risk

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