Portafolio de inversión nacional

Portafolios de inversión basados en distintos criterios

Empresas

symbols <- c("GMXT.MX", "AMXL.MX", "GFNORTEO.MX", "FEMSAUBD.MX", "KOFUBL.MX",
             "AGUA.MX", "SAN.MX","GRUMAB.MX", "OMAB.MX", "ASURB.MX", "BIMBOA.MX")

Precios y retornos

prices <- quantmod::getSymbols(
  Symbols = symbols,
  src = "yahoo",
  from = "2010-12-31",
  auto.assign = TRUE,
  warnings = FALSE
) %>%
  purrr::map(.f = ~ quantmod::Ad(get(x = .x))) %>%
  purrr::reduce(.f = merge) %>%
  `colnames<-`(value = symbols)

pausing 1 second between requests for more than 5 symbols
pausing 1 second between requests for more than 5 symbols
pausing 1 second between requests for more than 5 symbols
pausing 1 second between requests for more than 5 symbols
pausing 1 second between requests for more than 5 symbols
pausing 1 second between requests for more than 5 symbols
pausing 1 second between requests for more than 5 symbols

asset_returns_xts <- xts::to.monthly(
  x = prices,
  drop.time = TRUE,
  indexAt = "lastof",
  OHLC = FALSE
) %>%
  PerformanceAnalytics::Return.calculate(method = "discrete") %>%
  stats::na.omit()

## quitas todo y solamente dejas tus retornos, diferencia entre symbols y asset returns
## opcional

rm(list = setdiff(x = ls(), y = c("symbols", "precios", "asset_returns_xts")))

Portafolio 1: Mínima varianza

# Crear un portafolio objetivo que es una lista de Portafolios
min_var_portfolio <- PortfolioAnalytics::portfolio.spec(assets = symbols)


# Agregar la restricci?n que los activos deben sumar 1
min_var_portfolio <- PortfolioAnalytics::add.constraint(
  portfolio = min_var_portfolio,
  type = "full_investment"
)



# Agreguemos una restricci?n tipo caja para asegurar que las ponderaciones est?n entre 0 y 1
min_var_portfolio <- PortfolioAnalytics::add.constraint(
  portfolio = min_var_portfolio,
  type = "box", min = 0.00, max = 1
)


# Agreguemos el objetivo para minimizar la varianza
min_var_portfolio <- PortfolioAnalytics::add.objective(
  portfolio = min_var_portfolio,
  # Minimizar riesgo
  type = "risk",
  # Correspondencia al riesgo
  name = "var"
)

# Corramos la optimizaci?n --------------------------------

global_min_portfolio <- PortfolioAnalytics::optimize.portfolio(
  R = asset_returns_xts,
  portfolio = min_var_portfolio,
  # Usar diferentes tipos de optimizaci?n, lo est?ndar es quadprog
  optimize_method = "quadprog",
  # Informaci?n adicional de los m?todos
  trace = TRUE
)

# Examinemos el resultado
global_min_portfolio

***********************************
PortfolioAnalytics Optimization
***********************************

Call:
PortfolioAnalytics::optimize.portfolio(R = asset_returns_xts, 
    portfolio = min_var_portfolio, optimize_method = "quadprog", 
    trace = TRUE)

Optimal Weights:
    GMXT.MX     AMXL.MX GFNORTEO.MX FEMSAUBD.MX   KOFUBL.MX     AGUA.MX      SAN.MX 
     0.2535      0.1149      0.0000      0.0000      0.2256      0.0406      0.0400 
  GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX 
     0.0894      0.0000      0.0000      0.2360 

Objective Measure:
 StdDev 
0.04245 

Portafolio 2: Máximos rendimientos

# Crear otro nuevo Portafolio
max_exp_return_portfolio <- PortfolioAnalytics::portfolio.spec(assets = symbols)

# Restricci?n que la suma nos de 1
max_exp_return_portfolio <- PortfolioAnalytics::add.constraint(
  portfolio = max_exp_return_portfolio,
  type = "full_investment"
)

# Restricci?n tipo box, igualemos en 0.05 y .5

max_exp_return_portfolio <- PortfolioAnalytics::add.constraint(
  portfolio = max_exp_return_portfolio,
  type = "box", min = 0.05, max = .5
)

# Busquemos maximizar retorno
max_exp_return_portfolio <- PortfolioAnalytics::add.objective(
  portfolio = max_exp_return_portfolio,
  # Maximizar retornos esperados
  type = "return",
  # Funci?n tipo media del retorno hist?rico
  name = "mean"
)

# Riesgo rendimiento, quadratic utility

max_exp_return_portfolio <- PortfolioAnalytics::add.objective(
  portfolio = max_exp_return_portfolio,
  # Maximizar retornos esperados
  type = "return",
  # Funci?n tipo media del retorno hist?rico
  name = "mean"
)



# Correr la optimizaci?n
global_max_portfolio <- PortfolioAnalytics::optimize.portfolio(
  R = asset_returns_xts,
  portfolio = max_exp_return_portfolio,
  # En este caso usa "glpk" 
  optimize_method = "glpk",
  # Regresa con informaci?n adicional
  trace = TRUE
)
# Examina el resultado
global_max_portfolio

***********************************
PortfolioAnalytics Optimization
***********************************

Call:
PortfolioAnalytics::optimize.portfolio(R = asset_returns_xts, 
    portfolio = max_exp_return_portfolio, optimize_method = "glpk", 
    trace = TRUE)

Optimal Weights:
    GMXT.MX     AMXL.MX GFNORTEO.MX FEMSAUBD.MX   KOFUBL.MX     AGUA.MX      SAN.MX 
       0.05        0.05        0.05        0.05        0.05        0.05        0.05 
  GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX 
       0.05        0.50        0.05        0.05 

Objective Measure:
   mean 
0.01741 

Portafolio 3: Rebalanceo mensual

# Computar retornos mensuales de la estrategia
portfolio_returns_xts_rebalanced_monthly <-
  PerformanceAnalytics::Return.portfolio(
    R = asset_returns_xts,
    weights = weights,
    # Rebalanceo Mensual, implica comprar/vender cada mes
    reblance_on = "months",
    geometric = FALSE
  ) %>%
  `colnames<-`("Monthly_portfolio_returns")


# grafica los rendimientos acumulados

charts.PerformanceSummary(portfolio_returns_xts_rebalanced_monthly)

Portfolio 3 vs S&P500

#asumamos que el bmk es el S&P500 (SPY)

SPY <- quantmod::getSymbols(
  Symbols = "SPY",
  src = "yahoo",
  from = "2015-12-31",
  auto.assign = TRUE,
  warnings = FALSE
) %>%
  purrr::map(.f = ~ quantmod::Ad(get(x = .x))) %>%
  purrr::reduce(.f = merge) %>%
  `colnames<-`(value = "SPY")

SPY_returns_xts <- xts::to.monthly(
  x = SPY,
  drop.time = TRUE,
  indexAt = "lastof",
  OHLC = FALSE
) %>%
  PerformanceAnalytics::Return.calculate(method = "discrete") %>%
  stats::na.omit()



compara <- cbind(portfolio_returns_xts_rebalanced_monthly, SPY_returns_xts)

# c?mo se ve

charts.PerformanceSummary(compara)

Portafolio 4: Utilidad cuadrática

quat_ut_port <- PortfolioAnalytics::portfolio.spec(assets = symbols)

quat_ut_port <- PortfolioAnalytics::add.constraint(
  portfolio = quat_ut_port,
  type = "full_investment"
)

quat_ut_port <- PortfolioAnalytics::add.constraint(
  portfolio = quat_ut_port,
  type = "box", min = 0.00, max = 0.5
)

quat_ut_port <- PortfolioAnalytics::add.objective(quat_ut_port, type="quadratic_utility",
                                                  risk_aversion=2)

max_quat_ut_port<-  PortfolioAnalytics::optimize.portfolio(
  R = asset_returns_xts,
  portfolio = quat_ut_port,
  # En este caso usa "quadprog" 
  optimize_method = "quadprog",
  # Regresa con informaci?n adicional
  trace = TRUE
)

max_quat_ut_port

***********************************
PortfolioAnalytics Optimization
***********************************

Call:
PortfolioAnalytics::optimize.portfolio(R = asset_returns_xts, 
    portfolio = quat_ut_port, optimize_method = "quadprog", trace = TRUE)

Optimal Weights:
    GMXT.MX     AMXL.MX GFNORTEO.MX FEMSAUBD.MX   KOFUBL.MX     AGUA.MX      SAN.MX 
     0.2506      0.0000      0.0000      0.0000      0.0000      0.0810      0.0000 
  GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX 
     0.0000      0.1895      0.0000      0.4789 

Objective Measure:
   mean 
0.01957 


 StdDev 
0.05001 

weights3 <- pluck(.x = max_quat_ut_port, "weights")

## Max mean and low ETL

meanETL_port <- PortfolioAnalytics::portfolio.spec(assets = symbols)

meanETL_port <- PortfolioAnalytics::add.constraint(
  portfolio = meanETL_port,
  type = "weight_sum",
  min_sum=0.99,
  max_sum=1.01
)

#meanETL_port <- PortfolioAnalytics::add.constraint(
#  portfolio = meanETL_port,
#  type = "full_investment"
#)

meanETL_port <- PortfolioAnalytics::add.constraint(
  portfolio = meanETL_port,
  type = "box", min = -0.05, max = 0.50
)
                                                
meanETL_port <- PortfolioAnalytics::add.objective(meanETL_port, type="return", name="mean")

meanETL_port <- PortfolioAnalytics::add.objective(meanETL_port, type="risk", name="ETL", arguments=list(p=0.95))

max_min_ETL_port<-  PortfolioAnalytics::optimize.portfolio(
  R = asset_returns_xts,
  portfolio = meanETL_port,
  # En este caso usa "quadprog" 
  optimize_method = "random",
  search_size = 10000,
  # Regresa con informaci?n adicional
  trace = TRUE
)

weights <- pluck(.x = max_min_ETL_port, "weights")

portfolio_returns_xts_rebalanced_monthly <-
  PerformanceAnalytics::Return.portfolio(
    R = asset_returns_xts,
    weights = weights,
    # Rebalanceo Mensual, implica comprar/vender cada mes
    reblance_on = "months",
    geometric = FALSE
  ) %>%
  `colnames<-`("Monthly_portfolio_returns")



bmk_returns <-
  PerformanceAnalytics::Return.portfolio(
    R = SPY_returns_xts,
    # Rebalanceo Mensual, implica comprar/vender cada mes
    reblance_on = "months",
    geometric = FALSE
  ) %>%
  `colnames<-`("Benchmark_Returns")

quad_returns <-
  PerformanceAnalytics::Return.portfolio(
    R = asset_returns_xts,
    weights = weights3,
    # Rebalanceo Mensual, implica comprar/vender cada mes
    reblance_on = "months",
    geometric = FALSE
  ) %>%
  `colnames<-`("Quad_Returns")

Portafolio 4 vs S&P500

compara2 <- cbind(portfolio_returns_xts_rebalanced_monthly, bmk_returns, quad_returns)

charts.PerformanceSummary(compara2)

Back test

opt_quad <- optimize.portfolio.rebalancing(asset_returns_xts,
                                           quat_ut_port,
                                           optimize_method = "ROI",
                                           rebalance_on="months",
                                           training_period = 12,
                                           rolling_window=24)

backtest_quad_ret <- Return.portfolio(asset_returns_xts, extractWeights((opt_quad)))

colnames(backtest_quad_ret) <- "Bkt_Quad"


#################3 Ejercicios sobre restricciones

quat_ut_35 <- PortfolioAnalytics::portfolio.spec(assets = symbols)

quat_ut_35 <- PortfolioAnalytics::add.constraint(
  portfolio = quat_ut_35,
  type = "full_investment"
)

# no puedes invertir m?s de 25%

quat_ut_35 <- PortfolioAnalytics::add.constraint(
  portfolio = quat_ut_35,
  type = "box", min = 0.02, max = .15
)

## Trabajar m?s a detalle

quat_ut_35 <- add.constraint(portfolio=quat_ut_35,
                             type="group",
                             groups=list(c(2, 3, 4, 5, 6, 11), c(1, 7, 8, 9, 10)), 
                             group_min=c(0.0, 0.0),
                             group_max=c(.60, 0.4),
                             group_labels=c("ESG", "NON-ESG"),
                             group_pos=c(1, 2)) #se arman grupos dependiendo de las acciones

quat_ut_35 <- PortfolioAnalytics::add.constraint(
  portfolio = quat_ut_35,
  type = "weight_sum",
  min_sum=1.00,
  max_sum=1.00
)

quat_ut_35 <- PortfolioAnalytics::add.objective(quat_ut_35, type="quadratic_utility",
                                                risk_aversion=2)

opt_quad_35 <- optimize.portfolio.rebalancing(asset_returns_xts,
                                              quat_ut_35,
                                              optimize_method = "ROI",
                                              rebalance_on="days",
                                              training_period = 12,
                                              rolling_window=24)

opt_quad_35_last<-  PortfolioAnalytics::optimize.portfolio(
  R = asset_returns_xts,
  portfolio = quat_ut_35,
  optimize_method = "quadprog",
  #momentargs=momentargs,
  # Regresa con informaci?n adicional
  trace = TRUE
)

Gráfica

library(viridisLite)
# Load the pals package
library(pals)

Attaching package: ‘pals’

The following objects are masked from ‘package:viridisLite’:

    cividis, inferno, magma, plasma, turbo, viridis

# Create 11-color palette using the tol scheme with a stepped appearance
colores <- c("#A1D4F1", "#92D051", "#E57436","#68E185", "#4DB3A7", "#3595D9", "#FACE48", "#F29070", "#80E9C7", "#7D4A1B", "#204882")



#descriptores
chart.Weights(opt_quad_35, colorset=colores, main = "Distribución óptima del portafolio")

Grupos

(extractGroups(opt_quad_35_last))

$weights
    GMXT.MX     AMXL.MX GFNORTEO.MX FEMSAUBD.MX   KOFUBL.MX     AGUA.MX      SAN.MX 
 0.15000000  0.08905094  0.04094906  0.02000000  0.15000000  0.15000000  0.02000000 
  GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX 
 0.03236557  0.15000000  0.04763443  0.15000000 

$category_weights
NULL

$group_weights
    ESG NON-ESG 
    0.6     0.4 

Backtest mensual a 3 años

(backtest_quad_35 <- Return.portfolio(asset_returns_xts, extractWeights((opt_quad_35))))

           portfolio.returns
2020-05-31       0.020012568
2020-06-30       0.068477382
2020-07-31      -0.006331255
2020-08-31       0.023177273
2020-09-30       0.025340924
2020-10-31      -0.056091161
2020-11-30       0.124659928
2020-12-31       0.082333184
2021-01-31      -0.077083338
2021-02-28       0.049877732
2021-03-31       0.074031682
2021-04-30       0.014301295
2021-05-31       0.052641720
2021-06-30      -0.004848031
2021-07-31       0.011610090
2021-08-31       0.050786407
2021-09-30      -0.015461141
2021-10-31       0.040810897
2021-11-30       0.003624098
2021-12-31       0.066938160
2022-01-31      -0.002207682
2022-02-28       0.003833863
2022-03-31       0.001335146
2022-04-30      -0.016866747
2022-05-31       0.038365322
2022-06-30      -0.066343870
2022-07-31       0.039491954
2022-08-31      -0.018044931
2022-09-30       0.013792953
2022-10-31       0.129507975
2022-11-30       0.050108013
2022-12-31      -0.035063518
2023-01-31       0.079614095
2023-02-28      -0.013884676
2023-03-31       0.006998971

benchmark <- read_excel("/Users/rogelio/Desktop/benchmark.xlsx")

benchmark$Fecha <- as.Date(benchmark$Fecha, format = "%m/%d/%Y")

#convert it to an xts object, taking the Date column as the Date and Portfolio and IPC as the values
benchmark.xts <- xts(benchmark[,c(2,3)], order.by = benchmark$Fecha)


charts.PerformanceSummary(benchmark.xts, main = "Retornos del portafolio vs IPC México")

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