1 Chapter 4

2 Market Indices for USA and Latin America, Market Indices for USA and Latin America,

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

4 Specification of the Model

5 Estimation of Model: Brazil

6 Eq. 1 : Pre-filtering of Data

7 Partial Derivatives for Brazil

8

9 Estimated Weights and T-Statistics Brazil Brazil

10 Chile Model

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

12 Partial Derivatives for Chile

13

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

15 Mexico Model

16 Linear, Polynomial, and NN Esitamtes: Mexico Mexico

17 Partial Derivatives for Mexico

18

19 Weights and T-Statistics for Mexico

20 Chapter 5

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

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

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

24 Eq:3 :Gaussian Probability Distribution

25 Eq.4: Bandwidth Parameter

26 Eq.5: Gaussian Kernel Estimator

27 Eq.6: Delta Vector

28 Eq.7: Epanechnikov Kernel Estimator

29 Figura 1:. Log-Normal Time Series

30 Figura 2: Histogram of Log-Normal Random Variable

31 Figure 3:Density Estimation of Log- Normal Random Variable dist Gaussiana Estimador Kernel

32 Figura 4: Realization of Two Log- Normal Random Variables

33 Table 1: Risk Measure of x and y

34 Table 2: Measures of Returns, MSCI Indices

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

36 Figura 5:Density Function for Optimal Portfolio Returns, USA and Latin America x 10

37 Table 4: Optimal Portfolio Weights, USA and Asia

38 Density Function for USA and Asia Portfolios x 10

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

40 Figure 7: Density Function, USA-Asia-Latin America x 10 -3

41 Chapter VI

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 Eq.1: Definition of Means

44 Eq.2: Variance of Two Groups

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

46 Eq.4: Discriminant Vector

47 Eq.5: Logit Model.

48 Eq.6: Likelihood Function for Logit Model

49 Eq 7: Partial Derivative of Logit Model

50 Eq 8 :Probit Model

51 Eq 9: Likelihood Function for Probit Model

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

53 Eq 11: Neural Network Binary Choice Model

54 Eq 12: Partial Derivative for Neural Network Model

55 Figura 1: MSCI Index for Brazil

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

57 Figure 2: Latin American and US Stock Market Indices Figure 2: Latin American and US Stock Market Indices /15/90 12/16/9111/15/9310/16/95 ARGENTINA BRASIL CHILE MEXICO USA

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

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

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

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

62 Figure 3: Bank Insolvency Model: Partial Derivatives Logit and Probit Models Figure 3: Bank Insolvency Model: Partial Derivatives Logit and Probit Models Number of Variable Logit Probit

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