Seminário — Econometria

class: center, middle, inverse, title-slide

.title[
# <b><strong> Seminário — Econometria<br><br><br><br><br><br>
]
.subtitle[
## <b>Modelos GARCH para séries de retorno
]
.author[
### Márcio Roger Piagio – RA:67384<br><br>
]
.date[
###                                                                                                                                  28 de abril de 2023
]

---

<center><h1 class="animate__animated  animate__rubberBand">💸Banco do Brasil 💰.A. (BBAS3.💰.A).💸</h1></center>

.panelset[
.panel[.panel-name[Apresentação]

- Frequência diária.

- Tempo da série: 4 de janeiro de 2010 até 27 de abril de 2023.

- Quatidade de observações: 3336.

- Fonte: <https://finance.yahoo.com/>
]

.panel[.panel-name[Gráfico da Série]

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.panel[.panel-name[Sobre os retornos]

1) Possuem media condicional igual a zero: E<sub>t-1</sub> [ y<sub>t</sub> ] = 0.

2) Entao: Var<sub>t-1</sub> [ y<sub>t</sub> ] = E<sub>t-1</sub> [ y<sup>2</sup><sub>t</sub> ].

3) A presença de autocorrelacao em y<sup>2</sup> sugere que a variancia condicional nao constante.

4) Tem curtose > 3 (distribuicao leptocurtica), ou seja, a distribuicao dos retornos apresenta caudas mais pesadas que a distribuicao normal.

5) Movimentos de baixa no mercado financeiro costumam ser mais rapidos que os movimentos de alta, isto reflete nos retornos, tornando-os assimetricos a esquerda (Coeficiente de assimetria < 0).

]

---

<center><h1 class="animate__animated animate__swing">Verificação dos retornos para modelo GARCH</h1></center>

.panelset[
.panel[.panel-name[Autocorrelações]

]

.panel[.panel-name[Variância autocorrelacionada]

<div>
]

.panel[.panel-name[Testes Gráficos]

</div>
]

.panel[.panel-name[Estatísticas dos testes]

]

---

<center><h1 class="animate__animated animate__wobble">GARCH(1,1) com erros normais</h1></center>

.panelset[
.panel[.panel-name[Estimativas]

]

.panel[.panel-name[Gráficos dos resíduos]
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.panel[.panel-name[Estatísticas dos testes]
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    <th class="tg-c26g">Teste</th>
    <th class="tg-c26g">Residuals</th>
    <th class="tg-c26g">Estatística</th>
    <th class="tg-c26g">Valor p</th>
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</thead>
<tbody>
  <tr>
    <td class="tg-qlrq">ARCH Engle</td>
    <td class="tg-qlrq">R</td>
    <td class="tg-qlrq">3.518</td>
    <td class="tg-qlrq">0.9906465</td>
  </tr>
  <tr>
    <td class="tg-6alp">Ljung-Box Q(10)</td>
    <td class="tg-buwd">R</td>
    <td class="tg-buwd">9.205</td>
    <td class="tg-buwd">0.513</td>
  </tr>
  <tr>
    <td class="tg-0cf8">Ljung-Box Q(15)</td>
    <td class="tg-qlrq">R</td>
    <td class="tg-qlrq">17.01</td>
    <td class="tg-qlrq">0.318</td>
  </tr>
  <tr>
    <td class="tg-buwd">Ljung-Box Q(20)</td>
    <td class="tg-buwd">R</td>
    <td class="tg-6alp">18.547</td>
    <td class="tg-6alp">0.551</td>
  </tr>
  <tr>
    <td class="tg-qlrq">Ljung-Box Q(10)</td>
    <td class="tg-qlrq">R<sup>2</sup></td>
    <td class="tg-qlrq">2.423</td>
    <td class="tg-qlrq">0.993</td>
  </tr>
  <tr>
    <td class="tg-buwd">Ljung-Box Q(15)</td>
    <td class="tg-buwd">R<sup>2</sup></td>
    <td class="tg-buwd">4.304</td>
    <td class="tg-buwd">0.997</td>
  </tr>
  <tr>
    <td class="tg-qlrq">Ljung-Box Q(20)</td>
    <td class="tg-0cf8">R<sup>2</sup></td>
    <td class="tg-qlrq">5.714</td>
    <td class="tg-qlrq">0.991</td>
  </tr>
  <tr>
    <td class="tg-buwd">Normalidade (Jarque Bera)</td>
    <td class="tg-buwd">R</td>
    <td class="tg-buwd">2084.992</td>
    <td class="tg-buwd">&lt;0.001</td>
  </tr>
  <tr>
    <td class="tg-qlrq">Normalidade (Shapiro-Wilk)</td>
    <td class="tg-qlrq">R</td>
    <td class="tg-qlrq">0.976</td>
    <td class="tg-qlrq">&lt;0.001</td>
  </tr>
</tbody>
</table>
]

.panel[.panel-name[Retornos e Volatilidade]

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<center><h1 class="animate__animated animate__wobble">Com erros t-student assimetrica padronizada (sstd)</h1></center>

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]

---

<center><h1 class="animate__animated animate__wobble">Comparando os Modelos </h1></center>

.panelset[
.panel[.panel-name[Previsão da volatilidade]

]

.panel[.panel-name[Taxa de cobertura]

* 0.04267 de taxa de cobertura para o modelo GARCH(1,1) com a componente de erro Normal

* 0.04843 de taxa de cobertura para o modelo GARCH(1,1) com a componente de erro SSTD

]

.panel[.panel-name[VaR - Value at Risk]

* A ideia básica do VaR é responder a seguinte pergunta: Em condições normais do mercado, qual a perda máxima esperada dentro de um horizonte de tempo e de uma probabilidade?

<center><h3 class="animate__animated animate__wobble">VaR(95%) para 1 semana e 1 mês  via modelo GARCH(1,1) com erros N(0,1).</h3></center>

* Com 95% de probabilidade, a perda máxima esperada para um semana é de 6,92% do capital investido

* Com 95% de probabilidade, a perda máxima esperada para um mês é de 15,7% do capital investido

<center><h3 class="animate__animated animate__wobble">VaR(95%) para 1 semana e 1 mês  via modelo GARCH(1,1) com erros (SSTD).</h3></center>

* Com 95% de probabilidade, a perda máxima esperada para um semana é de 6,76% do capital investido

* Com 95% de probabilidade, a perda máxima esperada para um mês é de 15,3% do capital investido
]
.panel[.panel-name[.]

```r
## perda máxima esperada para um mês de R$ 1.000.000,00 N(0,1)
(Vn <- 100000*0.1569757)
## [1] 15697.57

## perda máxima esperada para um mês de R$ 1.000.000,00 (SSTD)
(Vt <- 100000*0.1533397)
## [1] 15333.97

##  Diferencia
Vn - Vt
## [1] 363.6
```

]