library(tidyverse)
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library(tidyquant)
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## method from
## as.zoo.data.frame zoo
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library(lubridate)
tickers <- c("AAPL","MSFT","NVDA","TSLA","NESN.SW","SIEGY","BBAJIOO.MX","FEMSAUBD.MX")
start <- as.Date("2022-01-01")
end <- Sys.Date()
prices <- tq_get(tickers, from = start, to = end, get = "stock.prices") %>%
select(symbol, date, adjusted) %>%
arrange(symbol, date)
rets <- prices %>%
group_by(symbol) %>%
mutate(ret_log = log(adjusted/lag(adjusted))) %>%
ungroup() %>%
filter(!is.na(ret_log))
Tabla <- rets %>%
group_by(symbol) %>%
summarise(
media = mean(ret_log, na.rm = TRUE),
sd = sd(ret_log, na.rm = TRUE),
var = var(ret_log, na.rm = TRUE),
.groups = "drop"
) %>%
as.data.frame()
rownames(Tabla) <- Tabla$symbol
Tabla <- Tabla[, c("media","sd","var")]
wide <- rets %>%
select(date, symbol, ret_log) %>%
pivot_wider(names_from = symbol, values_from = ret_log) %>%
arrange(date)
mat_cov <- cov(wide[, tickers], use = "pairwise.complete.obs")
activos <- c("NESN.SW","MSFT","NVDA")
EY <- as.numeric(Tabla[activos, 1])
S <- as.matrix(mat_cov[activos, activos])
one <- rep(1, 3)
w_gmv_unc <- solve(S, one) / as.numeric(t(one) %*% solve(S, one))
names(w_gmv_unc) <- activos
ER_gmv_unc <- sum(w_gmv_unc * EY)
VR_gmv_unc <- as.numeric(t(w_gmv_unc) %*% S %*% w_gmv_unc)
SD_gmv_unc <- sqrt(VR_gmv_unc)
paso <- 0.01
grid <- expand.grid(a = seq(0,1,by=paso), b = seq(0,1,by=paso))
grid$c <- 1 - grid$a - grid$b
grid <- grid[grid$c >= 0, ]
W <- as.matrix(grid[, c("a","b","c")])
ER <- as.numeric(W %*% EY)
VR <- rowSums((W %*% S) * W)
SD <- sqrt(VR)
grid$ER <- ER; grid$VR <- VR; grid$SD <- SD
idx_gmv_lo <- which.min(grid$VR)
w_gmv_lo <- as.numeric(W[idx_gmv_lo, ])
names(w_gmv_lo) <- activos
ER_gmv_lo <- grid$ER[idx_gmv_lo]
SD_gmv_lo <- grid$SD[idx_gmv_lo]
riesgo_obj_mult <- 1.25
SD_obj <- SD_gmv_lo * riesgo_obj_mult
cand <- grid[grid$SD <= SD_obj + 1e-12, ]
idx_maxER <- which.max(cand$ER)
w_risky <- as.numeric(W[as.integer(rownames(cand))[idx_maxER], ])
names(w_risky) <- activos
ER_risky <- cand$ER[idx_maxER]
SD_risky <- cand$SD[idx_maxER]
pr <- function(w) sprintf("%s: %.2f%%", names(w), 100*w)
cat("\nGMV (sin restricción no-neg):\n", paste(pr(w_gmv_unc), collapse=" | "),
"\nE[R]=", round(ER_gmv_unc,6), " SD=", round(SD_gmv_unc,6), "\n", sep="")
##
## GMV (sin restricción no-neg):
## NESN.SW: 71.61% | MSFT: 28.88% | NVDA: -0.49%
## E[R]=-0.000209 SD=0.009306
cat("\nGMV long-only:\n", paste(pr(w_gmv_lo), collapse=" | "),
"\nE[R]=", round(ER_gmv_lo,6), " SD=", round(SD_gmv_lo,6), "\n", sep="")
##
## GMV long-only:
## NESN.SW: 72.00% | MSFT: 28.00% | NVDA: 0.00%
## E[R]=-0.000206 SD=0.009307
cat("\nCartera rendidora (SD <=", round(SD_obj,6), "):\n", paste(pr(w_risky), collapse=" | "),
"\nE[R]=", round(ER_risky,6), " SD=", round(SD_risky,6), "\n", sep="")
##
## Cartera rendidora (SD <=0.011634):
## NESN.SW: 31.00% | MSFT: 37.00% | NVDA: 32.00%
## E[R]=0.000233 SD=0.011633
ord <- order(SD)
sd_s <- SD[ord]
er_s <- ER[ord]
keep <- logical(length(er_s))
m <- -Inf
for (i in seq_along(er_s)) {
if (er_s[i] > m) {
keep[i] <- TRUE
m <- er_s[i]
}
}
ef_idx <- ord[keep]
ef_ord <- order(SD[ef_idx])
library(plotly)
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## Attaching package: 'plotly'
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## layout
SD_e <- SD[ef_idx][ef_ord]
ER_e <- ER[ef_idx][ef_ord]
W_e <- W[ef_idx, ][ef_ord, ]
fig <- plot_ly(
x = SD_e,
y = ER_e,
z = W_e[,1],
type = "scatter3d",
mode = "lines+markers",
line = list(color = "red", width = 4),
marker = list(size = 3, color = ER_e, colorscale = "Rainbow")
) %>%
layout(
scene = list(
xaxis = list(title = "Riesgo"),
yaxis = list(title = "Rendimiento"),
zaxis = list(title = "Peso")
),
title = "Frontera eficiente en 3D"
)
fig