#**Nombres:**
## Tatiana Parra
## Karol Ferreira
## Katherine Arenas
library(data.table)
## Warning: package 'data.table' was built under R version 3.5.3
library(backports)
## Warning: package 'backports' was built under R version 3.5.3
library(fBasics)
## Warning: package 'fBasics' was built under R version 3.5.3
## Loading required package: timeDate
## Warning: package 'timeDate' was built under R version 3.5.2
## Loading required package: timeSeries
## Warning: package 'timeSeries' was built under R version 3.5.3
library(highcharter)
## Warning: package 'highcharter' was built under R version 3.5.3
## Highcharts (www.highcharts.com) is a Highsoft software product which is
## not free for commercial and Governmental use
library(anytime)
## Warning: package 'anytime' was built under R version 3.5.3
library(readxl)
## Warning: package 'readxl' was built under R version 3.5.3
Bancolombia <- read_excel("C:/Users/ERICK/Downloads/Copia de Final Finanzas Comp.xlsx",
sheet = "Bancolombia")
## New names:
## * `26620` -> `26620...2`
## * `26700` -> `26700...3`
## * `26700` -> `26700...4`
## * `26620` -> `26620...5`
colnames(Bancolombia)<-c("Date","Close","Open","High","Low","Vol", "Change%")
View(Bancolombia)
library(readxl)
Davivienda <- read_excel("C:/Users/ERICK/Downloads/Copia de Final Finanzas Comp.xlsx",
sheet = "Davivienda")
## New names:
## * `27820` -> `27820...3`
## * `27820` -> `27820...5`
colnames(Davivienda)<-c("Date","Close","Open","High","Low","Vol", "Change%")
View(Davivienda)
library(readxl)
GEB <- read_excel("C:/Users/ERICK/Downloads/Copia de Final Finanzas Comp.xlsx",
sheet = "Grupo energÃÂa de Bogotá")
## New names:
## * `1605` -> `1605...2`
## * `1605` -> `1605...5`
colnames(GEB)<-c("Date","Close","Open","High","Low","Vol", "Change%")
View(GEB)
Acciones<-data.frame(Bancolombia,GEB)
pcierre<-data.frame(Bancolombia$Date,Bancolombia$Close,GEB$Close)
colnames(pcierre)<-c("Date", "Bancolombia","GEB" )
View(pcierre)
#INTRODUCCION
### A partir de la información tomada de la página de Investing la cual es una página
### web que proporciona información financiera acerca de los mercados alrededor del
### mundo y especÃÂficamente de Estados Unidos._
### Se extrajo la información de cinco acciones, las cuales entendidas desde lo financiero
### son "las partes en las que se divide el capital social de una empresa" y estas
### generalmente son negociadas en mercados autorizados para realizarlo.
### Estas negociaciones en la mayorÃÂa de acciones se realiza de manera diaria exceptuando
### algunos dÃÂas festivos y de acuerdo a las negociaciones realizadas históricamente se pueden
### hacer análisis que permitan determinar la factibilidad y los rendimientos de las acciones.
### Con lo anterior en mente y con el fin de poder realizar diversas pruebas que permitan obtener información, se ha consolidado en un archivo excel la información de cinco acciones del mercado Colombiano el cual contiene las siguientes variables.
# 1. Fecha: Esta corresponde al dÃÂa en el cual la acción fue negociada (La fecha más antigua data de Mayo del 2014)
# 2. Precio de cierre: Esta corresponde al precio definitivo en el cual quedó la acción, es decir es el último nivel de cotización en un dÃÂa determinado.
# 3. Precio máximo: Este corresponde al precio más alto en el cual se negoció la acción.
# 4. Precio mÃÂnimo: Este corresponde al precio más bajo en el cual se negoció la acción.
# 5. % Variación: Este corresponde a la variación porcentual entre el precio del dÃÂa anterior y el precio actual, entendiendo variación porcentual como el cambio que tuvo el valor de la acción respecto al total del valor de la acción del dÃÂa anterior.
# Después de consolidado el archivo excel se tomaron dos esas acciones (Bancolombia y Grupo EnergÃÂa de Bogotá) y se les realizaron las siguientes pruebas:
#PRUEBAS DE NORMALIDAD
# La prueba de normalidad detecta si existe normalidad en una serie con el fin de analizar cómo influye la existencia o la ausencia de esta. En caso de que no se presentará la normalidad en un modelo econométrico influirá en que, los estimadores no serÃÂan
# de mÃÂnima varianza y tanto los contrastes de significación como las pruebas de hipótesis para los parámetros no serán exactos.
## Jarque-Bera
# El Test de Jarque-Bera determina si una distribución de probabilidad se asemeja a una normal y lo hace por medio del estudio de la asimetrÃÂa y la curtosis, normalmente se utiliza para comprobar el supuesto de normalidad en los errores del modelo, además
# se aconseja realizar un histograma o gráficas para comprobar visualmente su comportamiento.
# Prueba Jarque-Bera para los cierres de las acciones de Bancolombia y Davivienda en los últimos 5 años:
library(fBasics)
jbcierre<-as.timeSeries(pcierre)
jarqueberaTest(jbcierre)
##
## Title:
## Jarque - Bera Normalality Test
##
## Test Results:
## STATISTIC:
## X-squared: 326.0558
## P VALUE:
## Asymptotic p Value: < 2.2e-16
##
## Description:
## Tue May 28 23:43:23 2019 by user: ERICK
basicStats(jbcierre, ci= 0.95)
## Bancolombia GEB
## nobs 1.215000e+03 1.215000e+03
## NAs 0.000000e+00 0.000000e+00
## Minimum 1.906000e+04 1.515000e+03
## Maximum 4.142000e+04 2.230000e+03
## 1. Quartile 2.528000e+04 1.700000e+03
## 3. Quartile 3.160000e+04 1.995000e+03
## Mean 2.835768e+04 1.838938e+03
## Median 2.726000e+04 1.830000e+03
## Sum 3.445458e+07 2.234310e+06
## SE Mean 1.211950e+02 4.620035e+00
## LCL Mean 2.811990e+04 1.829874e+03
## UCL Mean 2.859545e+04 1.848002e+03
## Variance 1.784621e+07 2.593384e+04
## Stdev 4.224477e+03 1.610399e+02
## Skewness 5.947580e-01 6.142800e-02
## Kurtosis 5.076300e-02 -1.095487e+00
# Para considerar que la distribución de los precios de cierre de las acciones se distribuye siguiendo una distribución normal el p-value deberÃÂa ser mayor a 0,05. En este caso el p-value o p-valor es menor al nivel de significancia de 0,05 por lo que los
# precios de cierre no se distribuyen de manera normal.
# Este resultado se debe a que los retornos están compuestos por una alta volatilidad en el periodo lo que causa que no exista una distribución normal entre los datos
## Shapiro Test
# Esta prueba se usa para muestras de tamaño máximo de 50, para efectuar se calcula la media y la varianza muestral ordenando las observaciones de menor a mayor,
# luego de esto se calculan las diferencias entre el primero y el último, el segundo y el penúltimo, el tercero y el antepenúltimo y asàsucesivamente y se corrigen
# con unos coeficientes calculados por ellos.
# Se rechaza su hipótesis nula de normalidad si el estadÃÂstico W es menor que el valor crÃÂtico proporcionado por la tabla o un p-value mayor a 0,5 a un nivel de significancia de 0,05.
# Aunque esta es una muestra con más de 50 observaciones se decidió calcular esta prueba con el fin de conocer y aprender el concepto de la prueba y su aplicación.
# Prueba Shapiro-Wilk para los cierres de las acciones de Bancolombia y Davivienda en los últimos 5 años:
shapiroTest(as.vector(jbcierre))
##
## Title:
## Shapiro - Wilk Normality Test
##
## Test Results:
## STATISTIC:
## W: 0.7639
## P VALUE:
## < 2.2e-16
##
## Description:
## Tue May 28 23:43:24 2019 by user: ERICK
#RETORNOS
library(fBasics)
jbcierre<-as.timeSeries(pcierre)
jarqueberaTest(jbcierre)
##
## Title:
## Jarque - Bera Normalality Test
##
## Test Results:
## STATISTIC:
## X-squared: 326.0558
## P VALUE:
## Asymptotic p Value: < 2.2e-16
##
## Description:
## Tue May 28 23:43:24 2019 by user: ERICK
C<-subset(pcierre,select = c(Bancolombia,GEB))
diff(as.matrix(log(C)),1,1)
## Bancolombia GEB
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## 11 -0.0070505580 0.000000000
## 12 -0.0071006215 0.006430890
## 13 -0.0007920792 -0.006430890
## 14 0.0039541372 -0.009724550
## 15 0.0102081766 -0.013114942
## 16 0.0231670593 0.019608471
## 17 -0.0107445393 -0.013029500
## 18 0.0030816665 0.019481136
## 19 0.0061349886 0.000000000
## 20 0.0068571697 0.012779727
## 21 0.0135748691 -0.003179653
## 22 -0.0037523496 0.000000000
## 23 0.0000000000 0.000000000
## 24 -0.0015048912 0.003179653
## 25 0.0156895262 0.000000000
## 26 0.0007410152 0.012618464
## 27 -0.0022246950 0.000000000
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## 44 0.0244910200 0.003200003
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## 46 0.0000000000 0.015949301
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library(knitr)
## Warning: package 'knitr' was built under R version 3.5.3
kable(basicStats(jbcierre, ci=0.95))
| nobs |
1.215000e+03 |
1.215000e+03 |
| NAs |
0.000000e+00 |
0.000000e+00 |
| Minimum |
1.906000e+04 |
1.515000e+03 |
| Maximum |
4.142000e+04 |
2.230000e+03 |
| 1. Quartile |
2.528000e+04 |
1.700000e+03 |
| 3. Quartile |
3.160000e+04 |
1.995000e+03 |
| Mean |
2.835768e+04 |
1.838938e+03 |
| Median |
2.726000e+04 |
1.830000e+03 |
| Sum |
3.445458e+07 |
2.234310e+06 |
| SE Mean |
1.211950e+02 |
4.620035e+00 |
| LCL Mean |
2.811990e+04 |
1.829874e+03 |
| UCL Mean |
2.859545e+04 |
1.848002e+03 |
| Variance |
1.784621e+07 |
2.593384e+04 |
| Stdev |
4.224477e+03 |
1.610399e+02 |
| Skewness |
5.947580e-01 |
6.142800e-02 |
| Kurtosis |
5.076300e-02 |
-1.095487e+00 |
boxPlot(jbcierre)
### Es también conocido como el gráfico de caja y bigotes y sirve para mostrar la distribución de los datos.
### Para entender lo que nos dice esta caja de datos, esta nos indica, cual es la media de los datos y dónde se encuentran la mayor parte de la información, esto lo logra dividiendo la caja en cuartiles o en otras palabras en cuatro partes, en donde la primera división realizada es en dos partes y a su vez esas dos partes son divididas en dos más, para completar los cuartiles.
### El cuartil 1, es el que se encuentra entre la lÃÂnea de la izquierda y la primera lÃÂnea divisoria, el cuartil 2, es el que se encuentra entre la primera lÃÂnea divisoria y la lÃÂnea del medio, el cuartil 3 es el que se encuentra entre la lÃÂnea del medio y la tercera lÃÂnea y el cuartil 4 es el que se encuentra entre la tercera lÃÂnea y la lÃÂnea final.
### El punto más bajo de los datos es la lÃÂnea final de la izquierda y el dato máximo es la lÃÂnea final de la derecha; La lÃÂnea ubicada en el medio es la mediana de todos los datos, es decir, todos los datos se encuentren ubicadas a la izquierda de la mediana tienen valores inferiores a la mediana y los que estén ubicados a la derecha de la mediana son aquellos valores que están ubicados a la derecha de la mediana.
### En el caso de Bancolombia, la mediana se encuentra entre 25.000 y 30.000 mientras que en GEB no se logra identificar por la diferencia entre los valores de Bancolombia y la GEb
### El valor mÃÂnimo de Bancolombia es de 20.000, el cual corresponde al primer cuartil, mientras que el valor máximo se encuentra en 40.000 el cual corresponde al cuarto cuartil.
sampleMED(jbcierre)
## MED
## 10645
sampleIQR(jbcierre)
## IQR
## 25415
sampleSKEW(jbcierre)
## SKEW
## 0.3063152
sampleSKEW(jbcierre)
## SKEW
## 0.3063152
sampleKURT(jbcierre)
## KURT
## 0.2602794
qqnormPlot(jbcierre)
### La distribución teórica es una aproximación de la distribución empÃÂrica, los cuantiles de los datos deben ser próximos a los de la distribución teórica, en el gráfico se evidencia que las acciones de Bancolombia y GEB no presentan una distribución normal, debido a la volatilidad que se generan en los retornos.
# GRAFICAS
library(xts)
## Warning: package 'xts' was built under R version 3.5.3
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.5.3
##
## Attaching package: 'zoo'
## The following object is masked from 'package:timeSeries':
##
## time<-
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Attaching package: 'xts'
## The following objects are masked from 'package:data.table':
##
## first, last
library(quantmod)
## Warning: package 'quantmod' was built under R version 3.5.3
## Loading required package: TTR
## Warning: package 'TTR' was built under R version 3.5.3
##
## Attaching package: 'TTR'
## The following object is masked from 'package:fBasics':
##
## volatility
## Version 0.4-0 included new data defaults. See ?getSymbols.
library(TTR)
plot.ts(C)
# Por medio de las lÃÂneas de tendencia podemos observar el movimiento de los precios de las acciones de Bancolombia vienen con tendencia bajista hasta el punto en el que los
# precios se rompen desde el 14 de enero de 2018 dirigiéndose a una tendencia alcista, con un punto mÃÂnimo el 29 de marzo de 2019 cambiando hacia una tendencia bajista, para
# las acciones de Grupo EnergÃÂa de Bogotá se evidencia que las acciones vienen con una estabilidad sobre el precio de las acciones hasta el 14 de septiembre de 2018 cuando los
# precios atraviesan una tendencia bajista, pero para el 22 de noviembre de 2018, se observa la ruptura de una lÃÂnea de tendencia bajista que termina con un cambio de dirección
# del movimiento de los precios hacia el alza, por lo tanto podemos concluir que las acciones del GEB tienen mayor estabilidad en sus precio y se encuentran al alza.
#BANCOLOMBIA
suppressPackageStartupMessages(library(quantmod))
bancolombia1<- subset(Bancolombia, select = c(Date, Close, Open, High, Low))
bancolombia3 <- as.matrix(bancolombia1 [2:5])
head(bancolombia3)
## Close Open High Low
## [1,] 26660 26600 26700 26400
## [2,] 26400 26460 26660 26340
## [3,] 26160 26220 26220 26000
## [4,] 25400 25800 25800 25400
## [5,] 25700 25320 25700 25160
## [6,] 25400 25460 25640 25240
rownames(bancolombia3) <- as.character(bancolombia1$Date)
bancolombia3 <- as.xts (bancolombia3)
is.OHLC(bancolombia3)
## [1] TRUE
has.Cl(bancolombia3)
## [1] TRUE
has.Vo(bancolombia3)
## [1] FALSE
head(Cl(bancolombia3))
## Close
## 2014-05-12 26660
## 2014-05-13 26400
## 2014-05-14 26160
## 2014-05-15 25400
## 2014-05-16 25700
## 2014-05-19 25400
chartSeries(bancolombia3, theme = "white")
addBBands()
addMACD()
dr <- dailyReturn(bancolombia3)
hist(dr,col="blue",main="Retornos diarios")
wr <- weeklyReturn(bancolombia3)
mr <- monthlyReturn(bancolombia3)
#GEB
suppressPackageStartupMessages(library(quantmod))
GEB1<- subset(GEB, select = c(Date, Close, Open, High, Low))
GEB3 <- as.matrix(GEB1 [2:5])
head(GEB3)
## Close Open High Low
## [1,] 1600 1610 1615 1600
## [2,] 1620 1605 1620 1605
## [3,] 1615 1615 1620 1605
## [4,] 1615 1600 1615 1600
## [5,] 1615 1600 1615 1600
## [6,] 1625 1615 1625 1600
rownames(GEB3) <- as.character(GEB1$Date)
GEB3 <- as.xts (GEB3)
is.OHLC(GEB3)
## [1] TRUE
has.Cl(GEB3)
## [1] TRUE
has.Vo(GEB3)
## [1] FALSE
head(Cl(GEB3))
## Close
## 2014-05-12 1600
## 2014-05-13 1620
## 2014-05-14 1615
## 2014-05-15 1615
## 2014-05-16 1615
## 2014-05-19 1625
chartSeries(GEB3, theme = "white")
addBBands()
addMACD()
dr <- dailyReturn(GEB3)
hist(dr,col="blue",main="Retornos diarios")
wr <- weeklyReturn(GEB3)
mr <- monthlyReturn(GEB3)
#COMPARACION
### La comparación que realizaremos se tendran en cuenta las acciones de Bancolombia y las del Grupo Energia de Bogota (GEB)
### En primer lugar debemos mencionar que los precios de las acciones tienen valores demasiado diferentes pues la accion bancolombia toma precios
### que varian y estan superiores a los 30000 mientras que los de GEB son precios que se mueven por debajo oscilando al rededor de 1500 pesos
## DIAGRAMA DE VELAS JAPONESAS
### son una forma de representación gráfica de la información esencial de la cotización de un activo financiero en un determinado periodo de tiempo.
### nos informan, en general, de cuatro parámetros. Nos informan del precio de apertura, de cierre, el máximo y el mÃÂnimo. Además, para distinguir
### entre periodos alcistas y bajistas, se suelen rellenar los cuerpos de cada vela con distintos colores. A continuación se muestra un ejemplo de un gráfico en forma de velas japonesas
### Podemos diferenciar entre velas japonesas alcistas y bajistas. Dicho sea de paso, y para abreviar, en ocasiones haremos referencia al término «velas» como sinónimo de velas japonesas.
### Las velas alcistas se colorean de blanco o de verde, mientras que las bajistas se colorean de negro o de rojo.
### Lo que representa cada parte de la vela se explica a continuación:
### Apertura: Es el primer precio al que cotiza el activo financiero en el periodo de referencia.
### Cierre: Es el último precio al que cotiza el activo financiero en el periodo de referencia.
### Cuerpo: Conjunto de precios que se encuentran entre la apertura y el cierre en el periodo.
### Máximo: Es el precio más alto al que ha cotizado el activo en el periodo de referencia.
### MÃÂnimo: Es el precio más bajo al que ha cotizado el activo en el periodo de referencia.
### Sombra: Nos informa de precios a los que ha cotizado el activo, pero que no son ni el precio de cierre, ni el de apertura, ni mÃÂnimos, ni máximos.
## Dado lo anterior se puede definir segun los diagramas de velas japonesas mostrados anteriormente que el comportamiento del GEB tiene una tendencia mayor a
## crecer a diferencia de Bancolombia aunque los precios de Bancolombia sean mucho mas atos y su tendencia tambien sea alcista su inclinacion o proporcion es inferior a la del GEB.
## Por lo tanto, tambien podemos observar que la duracion de cada periodo de cambio entre un comportamiento y el otro es mas larga en el GEB ya que esta depende del largo que tiene cada vela,
## y este comportamiento esta mas visible en el grafico del GEB que en el de Bancolombia.
#MACD
### En la gráfica podemos evidenciar la tendencia que proporciona las señales de compra y venta por esta razón analizaremos las acciones de GEB, por medio de la lÃÂnea punteada y la lÃÂnea continua
### podemos determinar que para el mes de noviembre hay una señal de venta de estas acciones ya que la lÃÂnea continua se cruza con la lÃÂnea punteada de forma descendente, para las acciones de Bancolombia
### determinamos que en el mes de abril se presentaron exceso de compra debido a que la lÃÂnea continua, se cruza de forma ascendente con la lÃÂnea punteada, en el mes de noviembre de 2017 se evidencia un exceso
### de venta, ya que el cruce de las lÃÂneas se genera de forma descendente.
# BANDAS DE BOLLINGER
#HISTOGRAMAS
### El histograma, como se puede evidenciar, es una representación gráfica de los datos de la acción, este busca, permitir que la información pueda ser analizada de forma visualmente organizadas y que de este gráfico pueda comprenderse los datos numéricos en conjunto, los cuales, en algunas ocasiones, por ser cantidades grandes no pueden analizarse de manera individual.
library(xts)
library(quantmod)
library(TTR)
hist((C$Bancolombia))
hist((C$GEB))
# SERIES TEMPORALES
library(dygraphs)
## Warning: package 'dygraphs' was built under R version 3.5.3
dygraph(jbcierre) %>%
dyRangeSelector()
### Entendiendo que una serie de tiempo es una "secuencia de observaciones sobre intervalos de tiempo separados de manera regular" lo cual, dicho en otras palabras es una lista de fechas, cada una de las cuales se asocia a un valor numérico.
### Estas series de tiempo al igual que los histogramas permiten visualizar la evolución de los valores en el tiempo, éstas a menudo son usadas para realizar pronósticos futuros usando la información histórica disponible.
### Las series de tiempo comprenden algunos componentes los cuales son: Tendencia, estacionalidad, ciclos, movimiento irregular.
library(highcharter)
suppressPackageStartupMessages(library(highcharter))
highchart(type = "stock") %>%
hc_add_series(dr, type = "line",color="green")
#SEGUNDO PUNTO
suppressPackageStartupMessages(library(quantmod))
Davivienda1<- subset(Davivienda, select = c(Date, Close, Open, High, Low))
Davivienda3 <- as.matrix(Davivienda1 [2:5])
head(Davivienda3)
## Close Open High Low
## [1,] 28300 28200 28300 27900
## [2,] 28220 28200 28300 28200
## [3,] 28720 28300 28720 28240
## [4,] 27980 28240 28240 27800
## [5,] 27980 27660 27980 27660
## [6,] 28000 27600 28000 27600
rownames(Davivienda3) <- as.character(Davivienda1$Date)
Davivienda3 <- as.xts (Davivienda3)
is.OHLC(Davivienda3)
## [1] TRUE
has.Cl(Davivienda3)
## [1] TRUE
has.Vo(Davivienda3)
## [1] FALSE
head(Cl(Davivienda3))
## Close
## 2014-05-12 28300
## 2014-05-13 28220
## 2014-05-14 28720
## 2014-05-15 27980
## 2014-05-16 27980
## 2014-05-19 28000
chartSeries(Davivienda3, theme = "white")
addBBands()
addMACD()
dr <- dailyReturn(Davivienda3)
hist(dr,col="blue",main="Retornos diarios")
wr <- weeklyReturn(Davivienda3)
mr <- monthlyReturn(Davivienda3)