SECURITIZA

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Chapter 4
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Market Indices for USA and Latin America, 1988 -
1996
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MSCI (Morgan Stanley) Indices Summary Statistics
and Correlations
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Specification of the Model
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Estimation of Model Brazil
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Eq. 1 Pre-filtering of Data
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Partial Derivatives for Brazil
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Estimated Weights and T-Statistics Brazil
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Chile Model
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Linear, Polynomial, and NN Estimates Chilean Model
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Partial Derivatives for Chile
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Weights and T-Statistics for NN Model Chile
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Mexico Model
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Linear, Polynomial, and NN Esitamtes Mexico
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Partial Derivatives for Mexico
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Weights and T-Statistics for Mexico
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Chapter 5
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Eq.1Problem of Optimal Portfolio Selection
Risk/Return Trade-Off
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Eq.Semi-Variance
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Downside Risk Estimation
Probability
Risk is the area in the left tail of distribution
Returns
T minimum acceptable return
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Eq3 Gaussian Probability Distribution
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Eq.4 Bandwidth Parameter
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Eq.5 Gaussian Kernel Estimator
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Eq.6 Delta Vector
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Eq.7 Epanechnikov Kernel Estimator
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Figura 1. Log-Normal Time Series
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Figura 2 Histogram of Log-NormalRandom Variable
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Figure 3Density Estimation of Log-Normal Random
Variable
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Figura 4 Realization of Two Log-Normal Random
Variables
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Table 1 Risk Measure of x and y
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Table 2 Measures of Returns, MSCI Indices
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Table 3 Optiomal Portfolio Weights,USA and
Latin America
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Figura 5Density Function for Optimal Portfolio
Returns, USA and Latin America
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Table 4 Optimal Portfolio Weights, USA and Asia
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Density Function for USA and Asia Portfolios
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Table 5 World Portfolio USA, Asia, Latin
America
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Figure 7 Density Function, USA-Asia-Latin
America
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Chapter VI
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Discminant Analysis

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

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Eq.1 Definition of Means
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Eq.2 Variance of Two Groups
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Eq.3Quadratic Optimization Problem Linear
Discriminant Analysis
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Eq.4 Discriminant Vector
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Eq.5 Logit Model.
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Eq.6 Likelihood Function for Logit Model
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Eq 7 Partial Derivative of Logit Model
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Eq 8 Probit Model
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Eq 9 Likelihood Function for Probit Model
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Equação 10 Partial Derivative for Probit Model

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Eq 11 Neural Network Binary Choice Model
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Eq 12 Partial Derivative for Neural Network
Model
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Figura 1 MSCI Index for Brazil
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Table 1 Performance of Moving Average
Trading Rule
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Figure 2 Latin American and US Stock Market
Indices
2000
1500
1000
500
0
12/16/91
11/15/93
10/16/95
1/15/90
ARGENTINA
MEXICO
BRASIL
USA
CHILE
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Eq 13 Dependent Variable in Buy/Sell Model
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Table 2 Performance of Trading Rules of
Alternative Models
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Table 3 Consumer Credit Model Estimates
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Table 4 Analysis of Bank Insolvency in Texas
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Figure 3 Bank Insolvency Model Partial
Derivatives Logit and Probit Models
1.5
1
0.5
Logit
0
Probit
1
5
7
11
13
15
17
19
21
-0.5
-1
-1.5
Number of Variable
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Figure 4 Bank Insolvency Model-Partial
Derivatives Neural Network Model
6E-10
4E-10
2E-10
0
1
5
7
11
13
15
17
19
21
-2E-10
-4E-10
Number of Variable