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