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", "CMOCTEZ.MX")

t <- tibble(symbols)

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 
     0.1238      0.0549      0.0000      0.0000      0.0456      0.0194 
     SAN.MX   GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX  CMOCTEZ.MX 
     0.0289      0.1079      0.0000      0.0000      0.0929      0.5266 

Objective Measure:
 StdDev 
0.02984 

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 
       0.05        0.05        0.05        0.05        0.05        0.05 
     SAN.MX   GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX  CMOCTEZ.MX 
       0.05        0.05        0.45        0.05        0.05        0.05 

Objective Measure:
   mean 
0.01639 

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")

Warning: index does not have a ‘tclass’ attributeWarning: number of assets in beginning_weights is less than number of columns in returns, so subsetting returns.Warning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attributeWarning: index does not have a ‘tclass’ attribute

# 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=5)

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 
     0.3131      0.0070      0.0000      0.0000      0.0000      0.0608 
     SAN.MX   GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX  CMOCTEZ.MX 
     0.0000      0.0000      0.0336      0.0266      0.3553      0.2036 

Objective Measure:
   mean 
0.01616 


 StdDev 
0.03897 

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 = 0.05, max = .17
)

## Trabajar m?s a detalle

quat_ut_35 <- add.constraint(portfolio=quat_ut_35,
                             type="group",
                             groups=list(c(2, 3, 4, 5, 6, 7, 8, 11), c(1, 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="months",
                                              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

#descriptores
chart.Weights(opt_quad_35, colorset=brewer.pal(11, "Paired"))

Grupos

(extractGroups(opt_quad_35_last))

$weights
    GMXT.MX     AMXL.MX GFNORTEO.MX FEMSAUBD.MX   KOFUBL.MX     AGUA.MX 
       0.17        0.05        0.05        0.05        0.05        0.13 
     SAN.MX   GRUMAB.MX     OMAB.MX    ASURB.MX   BIMBOA.MX 
       0.05        0.05        0.17        0.06        0.17 

$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      0.0295510038
2020-06-30      0.0755937911
2020-07-31     -0.0264516199
2020-08-31      0.0332697816
2020-09-30      0.0005103903
2020-10-31     -0.0501127872
2020-11-30      0.1503769424
2020-12-31      0.1036271160
2021-01-31     -0.0701811189
2021-02-28      0.0612357988
2021-03-31      0.0558464459
2021-04-30      0.0209400657
2021-05-31      0.0304515441
2021-06-30      0.0047933374
2021-07-31     -0.0030034452
2021-08-31      0.0195284299
2021-09-30     -0.0075355692
2021-10-31      0.0484338686
2021-11-30     -0.0183897471
2021-12-31      0.0660781313
2022-01-31      0.0128704653
2022-02-28      0.0125992889
2022-03-31     -0.0087178671
2022-04-30     -0.0019757165
2022-05-31      0.0182226734
2022-06-30     -0.0747057758
2022-07-31      0.0358193358
2022-08-31     -0.0283194459
2022-09-30      0.0023575899
2022-10-31      0.1382212346
2022-11-30      0.0459817287
2022-12-31     -0.0304830893
2023-01-31      0.0976427856
2023-02-28     -0.0027840794
2023-03-31      0.0131105226

# Rendimiento vs S&P500
comp <- cbind(backtest_quad_35, SPY_returns_xts)

charts.PerformanceSummary(comp)