“Practica 1- Analisis de gestion del riesgo”

instalando archivos ## R Markdown

## [[1]]
## [1] "pdfetch"   "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [7] "methods"   "base"     
## 
## [[2]]
## [1] "tseries"   "pdfetch"   "stats"     "graphics"  "grDevices" "utils"    
## [7] "datasets"  "methods"   "base"     
## 
## [[3]]
##  [1] "forcats"   "stringr"   "dplyr"     "purrr"     "readr"     "tidyr"    
##  [7] "tibble"    "ggplot2"   "tidyverse" "tseries"   "pdfetch"   "stats"    
## [13] "graphics"  "grDevices" "utils"     "datasets"  "methods"   "base"     
## 
## [[4]]
##  [1] "forecast"  "forcats"   "stringr"   "dplyr"     "purrr"     "readr"    
##  [7] "tidyr"     "tibble"    "ggplot2"   "tidyverse" "tseries"   "pdfetch"  
## [13] "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
## [19] "base"

pregunta1: importando datos

DJIdata <- pdfetch_YAHOO("^GSPC",from = as.Date("2019-01-01"),to = as.Date("2020-01-01"), interval = '1d')  #DATOS DE DJI

• creando la serie de tiempo

tsDJI <- ts(DJIdata$`^GSPC.close`,start = c(2019,1),frequency=356.25)

pregunta2: calculando los retornos

• 1. Discretos

d_DJI <- diff(tsDJI)/tsDJI[-length(tsDJI)]
mu <- mean(d_DJI)
s2 <- var(d_DJI)
s <- sd(d_DJI)

• 2. Continuos

d_DJI <- diff(tsDJI)/tsDJI[-length(tsDJI)]
mu <- mean(d_DJI)
s2 <- var(d_DJI)
s <- sd(d_DJI)

pregunta3: analisis descriptivo

l_DJI<-diff(tsDJI)/tsDJI[-length(tsDJI)]
mu<-mean(l_DJI)
s2<-var(l_DJI)
s<-sd(l_DJI)

pregunta4: grafico de la distribucion de los retorno (continuos)

x<-seq(-0.1,0.1,by=0.01)
hist(
     l_DJI,prob=TRUE,ylim=c(0,80),xlim = c(-0.1,0.1),breaks = 50,col = "grey94",
     main = c("Histograma de los retornos"),
     xlab = expression(r==ln(P[t]/P[t-1])),
     ylab=c("Densidad"),
    )
lines(density(l_DJI),lwd=1.5,lty=2)
curve(dnorm(x,mean=mu,sd=s),lwd=2,lty=2,col="red",add = T)

pregunta5:tres test de normalidad

• 1. jaquer-Bera
• 2. kolmogorov
• 3. shapiro-wilk

jarque.bera.test(l_DJI)

## 
##  Jarque Bera Test
## 
## data:  l_DJI
## X-squared = 119.73, df = 2, p-value < 0.00000000000000022

ks.test(l_DJI, "pnorm", mean=mu, sd=s)

## 
##  One-sample Kolmogorov-Smirnov test
## 
## data:  l_DJI
## D = 0.087899, p-value = 0.04136
## alternative hypothesis: two-sided

shapiro.test(l_DJI)

## 
##  Shapiro-Wilk normality test
## 
## data:  l_DJI
## W = 0.94521, p-value = 0.00000004361

pregunta6: Calcule el valor at Risk

• 1. value at risk de con datos historicos para α

W<-100000

alpha <- 0.01
q1 <- quantile(x=l_DJI, alpha)
mean(exp(q1)-1)

## [1] -0.02503288

VAR1 <- W*(exp(q1)-1)

W<-100000

alpha <- 0.05
q1 <- quantile(x=l_DJI, alpha)
mean(exp(q1)-1)

## [1] -0.01201352

VAR1 <- W*(exp(q1)-1)

W<-100000

alpha <- 0.1
q1 <- quantile(x=l_DJI, alpha)
mean(exp(q1)-1)

## [1] -0.007256285

VAR1 <- W*(exp(q1)-1)

2. Value at Risk asumiendo una que los datos se distribuyen como una normal con media µ y varianza σ2, para un nivel de confianza de α.

set.seed(1000)
VARp<-qnorm(0.01,mean = mu,sd = s,lower.tail = T);VARp

## [1] -0.01727668

#En términos discretos
exp(VARp)-1

## [1] -0.0171283

• 3. Value at Risk - Montecarlo Para cada α realice las siguiente simulacion:

set.seed(1000)
simulacion <- rnorm(10000,mean = mu,sd = s)
VARsim<-quantile(simulacion,0.01);VARsim

##          1% 
## -0.01717708

exp(VARsim)-1

##         1% 
## -0.0170304

Var: Monte Carlo

VAR.mc <- numeric()
for (i in 1:1000) {
  changes <- rnorm(length(l_DJI),mean=1+mu,sd=s)
  sim.ts <- cumprod(c(as.numeric(tsDJI[1]),changes))
  sim.R <- diff(log(sim.ts))
  sim.q <- quantile(sim.R,0.01,na.rm = T)
  sim.VAR <- exp(sim.q)-1
  VAR.mc[i] <- sim.VAR
}
mean(VAR.mc)

## [1] -0.01657148

sd(VAR.mc)

## [1] 0.001658639

plot(density(VAR.mc))

quantile(VAR.mc,0.225)

##       22.5% 
## -0.01769907

quantile(VAR.mc,0.975)

##       97.5% 
## -0.01359873