1. 1 Chapter 4

2. 2 Market Indices for USA and Latin America, 1988 - 1996 Market Indices for USA and Latin America, 1988 - 1996

3. 3 MSCI (Morgan Stanley) Indices: Summary Statistics and Correlations MSCI (Morgan Stanley) Indices: Summary Statistics and Correlations

4. 4 Specification of the Model

5. 5 Estimation of Model: Brazil

6. 6 Eq. 1 : Pre-filtering of Data

7. 7 Partial Derivatives for Brazil

8. 8

9. 9 Estimated Weights and T-Statistics Brazil Brazil

10. 10 Chile Model

11. 11 Linear, Polynomial, and NN Estimates Chilean Model Linear, Polynomial, and NN Estimates Chilean Model

12. 12 Partial Derivatives for Chile

13. 13

14. 14 Weights and T-Statistics for NN Model: Chile Chile

15. 15 Mexico Model

16. 16 Linear, Polynomial, and NN Esitamtes: Mexico Mexico

17. 17 Partial Derivatives for Mexico

18. 18

19. 19 Weights and T-Statistics for Mexico

20. 20 Chapter 5

21. 21 Eq.1:Problem of Optimal Portfolio Selection: Risk/Return Trade-Off Eq.1:Problem of Optimal Portfolio Selection: Risk/Return Trade-Off

22. 22 Eq.:Semi-VarianceEq.:Semi-Variance

23. 23 Downside Risk Estimation Risk is the area in the left tail of distribution T*: minimum acceptable return Returns Probability

24. 24 Eq:3 :Gaussian Probability Distribution

25. 25 Eq.4: Bandwidth Parameter

26. 26 Eq.5: Gaussian Kernel Estimator

27. 27 Eq.6: Delta Vector

28. 28 Eq.7: Epanechnikov Kernel Estimator

29. 29 Figura 1:. Log-Normal Time Series 102030405060708090100 0 2 4 6 8 10 12

30. 30 Figura 2: Histogram of Log-Normal Random Variable -202468101214 2 4 6 8 10 12 14 16 18 20

31. 31 Figure 3:Density Estimation of Log- Normal Random Variable 024681012 0.002 0.004 0.006 0.008 0.01 0.012 0.014 dist Gaussiana Estimador Kernel

32. 32 Figura 4: Realization of Two Log- Normal Random Variables 0102030405060708090100 2 4 6 8 10 12 14 16 18

33. 33 Table 1: Risk Measure of x and y

34. 34 Table 2: Measures of Returns, MSCI Indices

35. 35 Table 3: Optiomal Portfolio Weights, USA and Latin America

36. 36 Figura 5:Density Function for Optimal Portfolio Returns, USA and Latin America -0.08-0.06-0.04-0.0200.020.040.060.080.1 0 0.2 0.4 0.6 0.8 1 1.2 x 10

37. 37 Table 4: Optimal Portfolio Weights, USA and Asia

38. 38 Density Function for USA and Asia Portfolios -0.06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10

39. 39 Table 5: World Portfolio: USA, Asia, Latin America

40. 40 Figure 7: Density Function, USA-Asia-Latin America -0.08-0.06-0.04-0.0200.020.040.06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10 -3

41. 41 Chapter VI

42. 42 Discminant Analysis l We observe two groups, x1 and x2, which are sets of characteristics of members of two groups, 1 and 2 l How can we decide if a new set of characteristics should be classified in group 1 or 2? l We can use linear discriminant analysis l Logit Analysis l Probit Analysis l Neural Network Analysis

43. 43 Eq.1: Definition of Means

44. 44 Eq.2: Variance of Two Groups

45. 45 Eq.3:Quadratic Optimization Problem: Linear Discriminant Analysis Eq.3:Quadratic Optimization Problem: Linear Discriminant Analysis

46. 46 Eq.4: Discriminant Vector

47. 47 Eq.5: Logit Model.

48. 48 Eq.6: Likelihood Function for Logit Model

49. 49 Eq 7: Partial Derivative of Logit Model

50. 50 Eq 8 :Probit Model

51. 51 Eq 9: Likelihood Function for Probit Model

52. 52 Equação 10: Partial Derivative for Probit Model Equação 10: Partial Derivative for Probit Model

53. 53 Eq 11: Neural Network Binary Choice Model

54. 54 Eq 12: Partial Derivative for Neural Network Model

55. 55 Figura 1: MSCI Index for Brazil

56. 56 Table 1: Performance of Moving Average Trading Rule Table 1: Performance of Moving Average Trading Rule

57. 57 Figure 2: Latin American and US Stock Market Indices Figure 2: Latin American and US Stock Market Indices 0 500 1000 1500 2000 1/15/90 12/16/9111/15/9310/16/95 ARGENTINA BRASIL CHILE MEXICO USA

58. 58 Eq 13: Dependent Variable in Buy/Sell Model Eq 13: Dependent Variable in Buy/Sell Model

59. 59 Table 2: Performance of Trading Rules of Alternative Models Table 2: Performance of Trading Rules of Alternative Models

60. 60 Table 3: Consumer Credit Model: Estimates Table 3: Consumer Credit Model: Estimates

61. 61 Table 4: Analysis of Bank Insolvency in Texas Table 4: Analysis of Bank Insolvency in Texas

62. 62 Figure 3: Bank Insolvency Model: Partial Derivatives Logit and Probit Models Figure 3: Bank Insolvency Model: Partial Derivatives Logit and Probit Models -1.5 -0.5 0 0.5 1 1.5 157111315171921 Number of Variable Logit Probit

63. 63 Figure 4: Bank Insolvency Model-Partial Derivatives Neural Network Model Figure 4: Bank Insolvency Model-Partial Derivatives Neural Network Model -4E-10 -2E-10 0 2E-10 4E-10 6E-10 157111315171921 Number of Variable