1. Carga de Paquetes
library(quantmod)
library(tseries)
library(PerformanceAnalytics)
library(fitdistrplus)
library(ggplot2)
library(readxl)
library(fGarch)
2. Carga y Preparación de Datos
# Seleccionar archivo interactivamente
datos <- read_excel(file.choose())
# Procesamiento inicial
datos$Fecha <- as.Date(datos$Fecha)
datos <- datos[order(datos$Fecha),]
precios <- xts(datos$`EMBONOR-B`, order.by = datos$Fecha)
rendimientos <- na.omit(diff(log(precios)))
3. Análisis Exploratorio
Evolución de Precios
ggplot(fortify(precios), aes(x = Index, y = precios)) +
geom_line(color = "steelblue") +
labs(title = "Serie Temporal de Precios EMBONOR-B",
x = "Fecha", y = "Precio (CLP)") +
theme_minimal() +
theme(plot.background = element_rect(fill = "white"))
Distribución de Rendimientos
ggplot(data.frame(Rendimientos = coredata(rendimientos)), aes(x = Rendimientos)) +
geom_histogram(aes(y = ..density..), bins = 30, fill = "skyblue", alpha = 0.7) +
stat_function(fun = dnorm,
args = list(mean = mean(rendimientos), sd = sd(rendimientos)),
color = "red", linetype = "dashed") +
geom_density(color = "darkblue", linewidth = 1) +
labs(title = "Distribución de Rendimientos Diarios",
x = "Rendimiento Logarítmico", y = "Densidad") +
theme_minimal()
Q-Q Plot
ggplot(data.frame(Rendimientos = coredata(rendimientos)), aes(sample = Rendimientos)) +
stat_qq(color = "blue", alpha = 0.6) +
stat_qq_line(color = "red", linetype = "dashed") +
labs(title = "Q-Q Plot vs Distribución Normal",
x = "Cuantiles Teóricos", y = "Cuantiles Muestrales") +
theme_minimal()
4. Pruebas de Normalidad
cat("### Resultados de Pruebas de Normalidad:\n")
## ### Resultados de Pruebas de Normalidad:
if(length(rendimientos) < 5000) print(shapiro.test(coredata(rendimientos)))
##
## Shapiro-Wilk normality test
##
## data: coredata(rendimientos)
## W = 0.94717, p-value = 8.927e-08
print(jarque.bera.test(coredata(rendimientos)))
##
## Jarque Bera Test
##
## data: coredata(rendimientos)
## X-squared = 24.424, df = 2, p-value = 4.971e-06
5. Modelamiento con Distribución t-Student
# Definición de funciones de distribución
dstd_robust <- function(x, mu, sigma, nu) fGarch::dstd(x, mean = mu, sd = sigma, nu = nu)
pstd_robust <- function(q, mu, sigma, nu) fGarch::pstd(q, mean = mu, sd = sigma, nu = nu)
qstd_robust <- function(p, mu, sigma, nu) fGarch::qstd(p, mean = mu, sd = sigma, nu = nu)
# Ajuste de parámetros
fit_t <- fitdist(
data = as.numeric(coredata(rendimientos)),
distr = "std_robust",
start = list(mu = 0, sigma = sd(rendimientos), nu = 5),
lower = c(mu = -0.1, sigma = 0.001, nu = 2.1),
upper = c(mu = 0.1, sigma = 0.5, nu = 30),
control = list(trace = 1)
)
## Nelder-Mead direct search function minimizer
## function value for initial parameters = -2.698600
## Scaled convergence tolerance is 4.02123e-08
## Stepsize computed as 0.500000
## BUILD 4 99999999999999996864064668260046802.000000 -2.698600
## SHRINK 9 99999999999999996864064668260046802.000000 -2.698600
## SHRINK 14 99999999999999996864064668260046802.000000 -2.698600
## HI-REDUCTION 16 -0.668315 -2.698600
## LO-REDUCTION 18 -1.231120 -2.698600
## HI-REDUCTION 20 -1.678294 -2.698600
## HI-REDUCTION 22 -1.706665 -2.698600
## HI-REDUCTION 24 -1.989677 -2.698600
## HI-REDUCTION 26 -2.059652 -2.698600
## HI-REDUCTION 28 -2.238226 -2.698600
## HI-REDUCTION 30 -2.312195 -2.698600
## HI-REDUCTION 32 -2.422011 -2.698600
## LO-REDUCTION 34 -2.480441 -2.698600
## HI-REDUCTION 36 -2.619452 -2.698600
## HI-REDUCTION 38 -2.673745 -2.698600
## HI-REDUCTION 40 -2.691475 -2.698600
## HI-REDUCTION 42 -2.693892 -2.698600
## HI-REDUCTION 44 -2.696654 -2.698600
## REFLECTION 46 -2.697895 -2.698656
## LO-REDUCTION 48 -2.698103 -2.698834
## REFLECTION 50 -2.698600 -2.699093
## HI-REDUCTION 52 -2.698656 -2.699107
## REFLECTION 54 -2.698834 -2.699296
## HI-REDUCTION 56 -2.699093 -2.699296
## HI-REDUCTION 58 -2.699107 -2.699296
## EXTENSION 60 -2.699250 -2.699779
## LO-REDUCTION 62 -2.699265 -2.699779
## LO-REDUCTION 64 -2.699296 -2.699779
## EXTENSION 66 -2.699722 -2.700652
## LO-REDUCTION 68 -2.699764 -2.700652
## LO-REDUCTION 70 -2.699779 -2.700652
## EXTENSION 72 -2.700373 -2.701824
## LO-REDUCTION 74 -2.700383 -2.701824
## EXTENSION 76 -2.700652 -2.702957
## LO-REDUCTION 78 -2.701203 -2.702957
## EXTENSION 80 -2.701824 -2.704472
## LO-REDUCTION 82 -2.702835 -2.704472
## EXTENSION 84 -2.702957 -2.705736
## HI-REDUCTION 86 -2.703954 -2.705736
## EXTENSION 88 -2.704216 -2.706605
## LO-REDUCTION 90 -2.704472 -2.706605
## REFLECTION 92 -2.705736 -2.707162
## EXTENSION 94 -2.705819 -2.707794
## EXTENSION 96 -2.706605 -2.709523
## HI-REDUCTION 98 -2.707162 -2.709523
## LO-REDUCTION 100 -2.707695 -2.709523
## EXTENSION 102 -2.707794 -2.709552
## EXTENSION 104 -2.708545 -2.710788
## REFLECTION 106 -2.709523 -2.711164
## HI-REDUCTION 108 -2.709552 -2.711164
## LO-REDUCTION 110 -2.710530 -2.711317
## REFLECTION 112 -2.710788 -2.712583
## HI-REDUCTION 114 -2.711164 -2.712583
## HI-REDUCTION 116 -2.711317 -2.712583
## LO-REDUCTION 118 -2.711679 -2.712583
## HI-REDUCTION 120 -2.712090 -2.712583
## EXTENSION 122 -2.712171 -2.712785
## HI-REDUCTION 124 -2.712277 -2.712785
## LO-REDUCTION 126 -2.712470 -2.712785
## LO-REDUCTION 128 -2.712583 -2.712789
## REFLECTION 130 -2.712742 -2.712826
## HI-REDUCTION 132 -2.712785 -2.712826
## HI-REDUCTION 134 -2.712789 -2.712826
## LO-REDUCTION 136 -2.712813 -2.712839
## LO-REDUCTION 138 -2.712823 -2.712847
## HI-REDUCTION 140 -2.712826 -2.712847
## LO-REDUCTION 142 -2.712839 -2.712850
## HI-REDUCTION 144 -2.712845 -2.712850
## REFLECTION 146 -2.712847 -2.712852
## HI-REDUCTION 148 -2.712848 -2.712852
## EXTENSION 150 -2.712850 -2.712858
## HI-REDUCTION 152 -2.712851 -2.712858
## EXTENSION 154 -2.712852 -2.712865
## LO-REDUCTION 156 -2.712854 -2.712865
## EXTENSION 158 -2.712858 -2.712873
## EXTENSION 160 -2.712861 -2.712884
## EXTENSION 162 -2.712865 -2.712904
## LO-REDUCTION 164 -2.712873 -2.712904
## EXTENSION 166 -2.712884 -2.712936
## EXTENSION 168 -2.712903 -2.712966
## EXTENSION 170 -2.712904 -2.712990
## EXTENSION 172 -2.712936 -2.713035
## REFLECTION 174 -2.712966 -2.713056
## LO-REDUCTION 176 -2.712990 -2.713056
## LO-REDUCTION 178 -2.713035 -2.713056
## REFLECTION 180 -2.713046 -2.713073
## HI-REDUCTION 182 -2.713049 -2.713073
## LO-REDUCTION 184 -2.713056 -2.713073
## REFLECTION 186 -2.713060 -2.713076
## REFLECTION 188 -2.713069 -2.713083
## LO-REDUCTION 190 -2.713073 -2.713083
## EXTENSION 192 -2.713076 -2.713095
## LO-REDUCTION 194 -2.713082 -2.713095
## EXTENSION 196 -2.713083 -2.713111
## EXTENSION 198 -2.713094 -2.713129
## LO-REDUCTION 200 -2.713095 -2.713129
## EXTENSION 202 -2.713111 -2.713149
## LO-REDUCTION 204 -2.713117 -2.713149
## EXTENSION 206 -2.713129 -2.713177
## LO-REDUCTION 208 -2.713143 -2.713177
## HI-REDUCTION 210 -2.713149 -2.713177
## EXTENSION 212 -2.713163 -2.713197
## HI-REDUCTION 214 -2.713170 -2.713197
## LO-REDUCTION 216 -2.713177 -2.713197
## EXTENSION 218 -2.713178 -2.713212
## HI-REDUCTION 220 -2.713196 -2.713212
## HI-REDUCTION 222 -2.713197 -2.713212
## LO-REDUCTION 224 -2.713197 -2.713212
## LO-REDUCTION 226 -2.713202 -2.713212
## REFLECTION 228 -2.713211 -2.713214
## LO-REDUCTION 230 -2.713212 -2.713214
## HI-REDUCTION 232 -2.713212 -2.713214
## REFLECTION 234 -2.713214 -2.713215
## HI-REDUCTION 236 -2.713214 -2.713215
## LO-REDUCTION 238 -2.713214 -2.713215
## REFLECTION 240 -2.713215 -2.713216
## LO-REDUCTION 242 -2.713215 -2.713216
## LO-REDUCTION 244 -2.713215 -2.713216
## REFLECTION 246 -2.713216 -2.713216
## LO-REDUCTION 248 -2.713216 -2.713216
## EXTENSION 250 -2.713216 -2.713216
## LO-REDUCTION 252 -2.713216 -2.713216
## LO-REDUCTION 254 -2.713216 -2.713216
## REFLECTION 256 -2.713216 -2.713217
## HI-REDUCTION 258 -2.713216 -2.713217
## LO-REDUCTION 260 -2.713216 -2.713217
## LO-REDUCTION 262 -2.713216 -2.713217
## REFLECTION 264 -2.713216 -2.713217
## EXTENSION 266 -2.713216 -2.713217
## LO-REDUCTION 268 -2.713217 -2.713217
## EXTENSION 270 -2.713217 -2.713217
## LO-REDUCTION 272 -2.713217 -2.713217
## EXTENSION 274 -2.713217 -2.713217
## LO-REDUCTION 276 -2.713217 -2.713217
## LO-REDUCTION 278 -2.713217 -2.713217
## REFLECTION 280 -2.713217 -2.713217
## REFLECTION 282 -2.713217 -2.713217
## LO-REDUCTION 284 -2.713217 -2.713217
## Exiting from Nelder Mead minimizer
## 286 function evaluations used
## Nelder-Mead direct search function minimizer
## function value for initial parameters = -2.714718
## Scaled convergence tolerance is 4.04525e-08
## Stepsize computed as 0.222295
## BUILD 4 99999999999999996864064668260046802.000000 -2.714718
## SHRINK 9 99999999999999996864064668260046802.000000 -2.714718
## HI-REDUCTION 11 -0.291081 -2.714718
## LO-REDUCTION 13 -1.840761 -2.714718
## LO-REDUCTION 15 -1.986662 -2.714718
## HI-REDUCTION 17 -2.287098 -2.714718
## HI-REDUCTION 19 -2.332881 -2.714718
## HI-REDUCTION 21 -2.468087 -2.714718
## HI-REDUCTION 23 -2.518418 -2.714718
## LO-REDUCTION 25 -2.577670 -2.714718
## HI-REDUCTION 27 -2.661349 -2.714718
## HI-REDUCTION 29 -2.692866 -2.714718
## LO-REDUCTION 31 -2.695972 -2.714718
## LO-REDUCTION 33 -2.705094 -2.714718
## HI-REDUCTION 35 -2.709425 -2.714718
## HI-REDUCTION 37 -2.711291 -2.714718
## LO-REDUCTION 39 -2.713017 -2.714718
## HI-REDUCTION 41 -2.713320 -2.714718
## HI-REDUCTION 43 -2.714253 -2.714718
## HI-REDUCTION 45 -2.714321 -2.714718
## HI-REDUCTION 47 -2.714548 -2.714718
## LO-REDUCTION 49 -2.714580 -2.714718
## HI-REDUCTION 51 -2.714635 -2.714718
## LO-REDUCTION 53 -2.714667 -2.714718
## LO-REDUCTION 55 -2.714673 -2.714718
## EXTENSION 57 -2.714689 -2.714743
## REFLECTION 59 -2.714713 -2.714747
## HI-REDUCTION 61 -2.714718 -2.714747
## REFLECTION 63 -2.714741 -2.714779
## REFLECTION 65 -2.714743 -2.714783
## HI-REDUCTION 67 -2.714747 -2.714783
## EXTENSION 69 -2.714769 -2.714827
## LO-REDUCTION 71 -2.714779 -2.714827
## LO-REDUCTION 73 -2.714783 -2.714827
## LO-REDUCTION 75 -2.714802 -2.714827
## REFLECTION 77 -2.714820 -2.714841
## LO-REDUCTION 79 -2.714823 -2.714841
## LO-REDUCTION 81 -2.714827 -2.714841
## REFLECTION 83 -2.714835 -2.714850
## LO-REDUCTION 85 -2.714840 -2.714850
## HI-REDUCTION 87 -2.714841 -2.714850
## REFLECTION 89 -2.714846 -2.714853
## LO-REDUCTION 91 -2.714848 -2.714853
## EXTENSION 93 -2.714850 -2.714860
## LO-REDUCTION 95 -2.714852 -2.714860
## LO-REDUCTION 97 -2.714853 -2.714860
## EXTENSION 99 -2.714857 -2.714868
## LO-REDUCTION 101 -2.714857 -2.714868
## LO-REDUCTION 103 -2.714860 -2.714868
## REFLECTION 105 -2.714865 -2.714871
## EXTENSION 107 -2.714867 -2.714873
## EXTENSION 109 -2.714868 -2.714879
## HI-REDUCTION 111 -2.714871 -2.714879
## EXTENSION 113 -2.714873 -2.714883
## LO-REDUCTION 115 -2.714874 -2.714883
## REFLECTION 117 -2.714878 -2.714884
## LO-REDUCTION 119 -2.714879 -2.714884
## EXTENSION 121 -2.714883 -2.714890
## HI-REDUCTION 123 -2.714884 -2.714890
## LO-REDUCTION 125 -2.714884 -2.714890
## REFLECTION 127 -2.714886 -2.714890
## LO-REDUCTION 129 -2.714889 -2.714891
## LO-REDUCTION 131 -2.714890 -2.714891
## LO-REDUCTION 133 -2.714890 -2.714891
## HI-REDUCTION 135 -2.714891 -2.714891
## LO-REDUCTION 137 -2.714891 -2.714891
## HI-REDUCTION 139 -2.714891 -2.714891
## HI-REDUCTION 141 -2.714891 -2.714891
## REFLECTION 143 -2.714891 -2.714891
## LO-REDUCTION 145 -2.714891 -2.714891
## Exiting from Nelder Mead minimizer
## 147 function evaluations used
## Nelder-Mead direct search function minimizer
## function value for initial parameters = -2.714977
## Scaled convergence tolerance is 4.04563e-08
## Stepsize computed as 0.211081
## BUILD 4 99999999999999996864064668260046802.000000 -2.714977
## SHRINK 9 99999999999999996864064668260046802.000000 -2.714977
## HI-REDUCTION 11 -0.299531 -2.714977
## LO-REDUCTION 13 -1.858118 -2.714977
## HI-REDUCTION 15 -2.206114 -2.714977
## HI-REDUCTION 17 -2.300837 -2.714977
## LO-REDUCTION 19 -2.392366 -2.714977
## HI-REDUCTION 21 -2.551474 -2.714977
## HI-REDUCTION 23 -2.614225 -2.714977
## LO-REDUCTION 25 -2.629375 -2.714977
## LO-REDUCTION 27 -2.676589 -2.714977
## LO-REDUCTION 29 -2.684417 -2.714977
## HI-REDUCTION 31 -2.704297 -2.714977
## LO-REDUCTION 33 -2.706097 -2.714977
## LO-REDUCTION 35 -2.713061 -2.714977
## HI-REDUCTION 37 -2.713118 -2.714977
## HI-REDUCTION 39 -2.713796 -2.714977
## HI-REDUCTION 41 -2.714519 -2.714977
## HI-REDUCTION 43 -2.714551 -2.714977
## LO-REDUCTION 45 -2.714806 -2.714977
## HI-REDUCTION 47 -2.714826 -2.714977
## LO-REDUCTION 49 -2.714853 -2.714977
## HI-REDUCTION 51 -2.714921 -2.714977
## LO-REDUCTION 53 -2.714925 -2.714977
## LO-REDUCTION 55 -2.714933 -2.714977
## LO-REDUCTION 57 -2.714956 -2.714977
## LO-REDUCTION 59 -2.714957 -2.714977
## HI-REDUCTION 61 -2.714967 -2.714977
## LO-REDUCTION 63 -2.714970 -2.714977
## LO-REDUCTION 65 -2.714974 -2.714977
## EXTENSION 67 -2.714976 -2.714981
## LO-REDUCTION 69 -2.714977 -2.714981
## EXTENSION 71 -2.714977 -2.714983
## LO-REDUCTION 73 -2.714979 -2.714983
## REFLECTION 75 -2.714981 -2.714983
## REFLECTION 77 -2.714983 -2.714984
## HI-REDUCTION 79 -2.714983 -2.714984
## HI-REDUCTION 81 -2.714983 -2.714984
## HI-REDUCTION 83 -2.714984 -2.714985
## HI-REDUCTION 85 -2.714984 -2.714985
## REFLECTION 87 -2.714984 -2.714985
## HI-REDUCTION 89 -2.714985 -2.714985
## HI-REDUCTION 91 -2.714985 -2.714985
## HI-REDUCTION 93 -2.714985 -2.714985
## LO-REDUCTION 95 -2.714985 -2.714985
## LO-REDUCTION 97 -2.714985 -2.714985
## LO-REDUCTION 99 -2.714985 -2.714985
## EXTENSION 101 -2.714985 -2.714985
## HI-REDUCTION 103 -2.714985 -2.714985
## REFLECTION 105 -2.714985 -2.714985
## LO-REDUCTION 107 -2.714985 -2.714985
## Exiting from Nelder Mead minimizer
## 109 function evaluations used
## Nelder-Mead direct search function minimizer
## function value for initial parameters = -2.714995
## Scaled convergence tolerance is 4.04566e-08
## Stepsize computed as 0.210107
## BUILD 4 99999999999999996864064668260046802.000000 -2.714995
## SHRINK 9 99999999999999996864064668260046802.000000 -2.714995
## HI-REDUCTION 11 -0.300616 -2.714995
## LO-REDUCTION 13 -1.859281 -2.714995
## HI-REDUCTION 15 -2.231098 -2.714995
## HI-REDUCTION 17 -2.305065 -2.714995
## LO-REDUCTION 19 -2.404367 -2.714995
## HI-REDUCTION 21 -2.555663 -2.714995
## HI-REDUCTION 23 -2.613963 -2.714995
## LO-REDUCTION 25 -2.629830 -2.714995
## LO-REDUCTION 27 -2.674978 -2.714995
## LO-REDUCTION 29 -2.679875 -2.714995
## HI-REDUCTION 31 -2.701821 -2.714995
## LO-REDUCTION 33 -2.706042 -2.714995
## HI-REDUCTION 35 -2.712333 -2.714995
## LO-REDUCTION 37 -2.713017 -2.714995
## HI-REDUCTION 39 -2.713562 -2.714995
## HI-REDUCTION 41 -2.714415 -2.714995
## HI-REDUCTION 43 -2.714547 -2.714995
## HI-REDUCTION 45 -2.714768 -2.714995
## HI-REDUCTION 47 -2.714849 -2.714995
## HI-REDUCTION 49 -2.714865 -2.714995
## LO-REDUCTION 51 -2.714912 -2.714995
## HI-REDUCTION 53 -2.714958 -2.714995
## LO-REDUCTION 55 -2.714958 -2.714995
## LO-REDUCTION 57 -2.714969 -2.714995
## HI-REDUCTION 59 -2.714978 -2.714995
## LO-REDUCTION 61 -2.714980 -2.714995
## HI-REDUCTION 63 -2.714986 -2.714995
## LO-REDUCTION 65 -2.714987 -2.714995
## HI-REDUCTION 67 -2.714988 -2.714995
## HI-REDUCTION 69 -2.714990 -2.714995
## HI-REDUCTION 71 -2.714991 -2.714995
## REFLECTION 73 -2.714992 -2.714995
## HI-REDUCTION 75 -2.714993 -2.714995
## LO-REDUCTION 77 -2.714994 -2.714995
## HI-REDUCTION 79 -2.714994 -2.714995
## REFLECTION 81 -2.714995 -2.714995
## HI-REDUCTION 83 -2.714995 -2.714995
## HI-REDUCTION 85 -2.714995 -2.714995
## HI-REDUCTION 87 -2.714995 -2.714995
## LO-REDUCTION 89 -2.714995 -2.714995
## HI-REDUCTION 91 -2.714995 -2.714995
## HI-REDUCTION 93 -2.714995 -2.714995
## LO-REDUCTION 95 -2.714995 -2.714995
## HI-REDUCTION 97 -2.714995 -2.714995
## Exiting from Nelder Mead minimizer
## 99 function evaluations used
6. Cálculo de Medidas de Riesgo
nivel_confianza <- 0.95
# Método paramétrico
var_t <- qstd_robust(1 - nivel_confianza,
mu = fit_t$estimate["mu"],
sigma = fit_t$estimate["sigma"],
nu = fit_t$estimate["nu"])
cvar_t <- integrate(function(x) x * dstd_robust(x,
mu = fit_t$estimate["mu"],
sigma = fit_t$estimate["sigma"],
nu = fit_t$estimate["nu"]),
-Inf, var_t)$value / (1 - nivel_confianza)
# Método empírico
var_emp <- quantile(rendimientos, 1 - nivel_confianza)
cvar_emp <- mean(rendimientos[rendimientos <= var_emp])
7. Visualización Comparativa
df_comp <- data.frame(
Metodo = rep(c("Paramétrico", "Empírico"), each = 2),
Medida = rep(c("VaR", "CVaR"), 2),
Valor = c(var_t, cvar_t, var_emp, cvar_emp)
)
ggplot(df_comp, aes(x = Medida, y = Valor, fill = Metodo)) +
geom_col(position = position_dodge(), width = 0.7) +
scale_fill_manual(values = c("Paramétrico" = "tomato", "Empírico" = "steelblue")) +
geom_text(aes(label = round(Valor, 4)),
position = position_dodge(width = 0.7),
vjust = -0.5, size = 4) +
labs(title = "Comparación de Medidas de Riesgo al 95% de Confianza",
x = "Medida de Riesgo", y = "Valor (%)") +
theme_bw()
8. Interpretación de Resultados
Resultados Finales
cat("**VaR t-Student:**", round(var_t, 5), "\n")
## **VaR t-Student:** -0.02761
cat("**CVaR t-Student:**", round(cvar_t, 5), "\n")
## **CVaR t-Student:** -0.0555
cat("**VaR Empírico:**", round(var_emp, 5), "\n")
## **VaR Empírico:** -0.02454
cat("**CVaR Empírico:**", round(cvar_emp, 5))
## **CVaR Empírico:** -0.03715
Análisis Clave
- No Normalidad de los Datos
- Valores p < 0.05 en ambas pruebas confirman desviación de la
normalidad
- Los rendimientos muestran colas más pesadas que la distribución
normal
- Justifica el uso de distribuciones con colas pesadas como la
t-Student
- Parámetros Estimados t-Student
- σ ≈ 0.0441: Volatilidad diaria del 4.41%
- ν ≈ 2.1: Grados de libertad indican colas 3x más
pesadas que la normal
- μ ≈ -3.7^{-4}: Tendencia central neutra en el
periodo analizado
- Diferencias entre Métodos
- VaR paramétrico más conservador (-2.76% vs -2.45%):
- La t-Student captura mejor el riesgo de cola
- Método empírico subestima riesgo en colas no observadas
históricamente
- Brecha en CVaR (-5.55% vs -3.72%):
- Indica presencia de eventos extremos no modelados
- Sugiere necesidad de análisis de estrés complementario