R Markdown
library(readxl)
## Warning: package 'readxl' was built under R version 4.3.2
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
us_sample <- read_excel("~/IMB/Magistrska naloga/Sample/Sample/US sample - končni.xlsx")
View(us_sample)
# (če si že prej bral v objektu z znakom č, ga lahko premapiraš)
# us_sample <- `US_sample_končni`
# 2) Prvi stolpec so datumi
# Poskusi pretvorbo v Date, ohrani prvotni stolpec 'Date'
if (!inherits(us_sample[[1]], "Date")) {
# Poskusi avtomatsko pretvorbo
us_sample[[1]] <- as.Date(us_sample[[1]])
}
colnames(us_sample)[1] <- "Date"
# 3) Definiraj Y in X po pozicijah:
# - Y = prvih 80 stolpcev po datumu (tj. stolpci 2:81)
# - X = zadnjih 6 stolpcev
y_cols <- colnames(us_sample)[2:81]
x_cols <- tail(colnames(us_sample), 6)
# 4) Izpisi, kar želiš:
cat("Ime stolpca z datumi:", colnames(us_sample)[1], "\n\n")
## Ime stolpca z datumi: Date
cat("Število Y spremenljivk:", length(y_cols), "\n")
## Število Y spremenljivk: 80
cat("Prva Y spremenljivka:", y_cols[1], "\n")
## Prva Y spremenljivka: DODGX
cat("Zadnja Y spremenljivka:", y_cols[length(y_cols)], "\n\n")
## Zadnja Y spremenljivka: LSVQX
cat("Število X spremenljivk:", length(x_cols), "\n")
## Število X spremenljivk: 6
cat("Imena X spremenljivk:\n")
## Imena X spremenljivk:
print(x_cols)
## [1] "Russell_1000_Growth" "Russell_1000_Value" "Russell_2000_Growth"
## [4] "Russell_2000_Value" "Bond_US" "T-Bill_US"
# (neobvezno) pripravi matrike za nadaljevanje analize
Y_mat <- as.matrix(us_sample[, y_cols])
X_mat <- as.matrix(us_sample[, x_cols])
# Hitri preverbi dimenzij
cat("\nDimenzije Y matrike:", paste(dim(Y_mat), collapse = " x "), "\n")
##
## Dimenzije Y matrike: 108 x 80
cat("Dimenzije X matrike:", paste(dim(X_mat), collapse = " x "), "\n")
## Dimenzije X matrike: 108 x 6
# Predpostavlja, da imaš objekt `us_sample` in vektor `y_cols` iz prejšnjega koraka
# y_cols = names(us_sample)[2:81]
# 1) Indeksi skupin (po 20 stolpcev)
idx_Large_Value <- 1:20
idx_Large_Growth <- 21:40
idx_Small_Growth <- 41:60
idx_Small_Value <- 61:80
# 2) Vzemi tickers po skupinah
Large_Value <- y_cols[idx_Large_Value]
Large_Growth <- y_cols[idx_Large_Growth]
Small_Growth <- y_cols[idx_Small_Growth]
Small_Value <- y_cols[idx_Small_Value]
cat("\n")
# 4) Izpis skladov v vsaki skupini
cat("Skupina Large_Value (20):\n")
## Skupina Large_Value (20):
print(Large_Value); cat("\n")
## [1] "DODGX" "AMRMX" "VWNAX" "MEIAX" "LBSAX" "OIEJX" "PEQSX" "TRPIX" "BBVLX"
## [10] "OAKMX" "NBHIX" "MUBFX" "SSHVX" "EIUTX" "PEQIX" "IEDIX" "EITVX" "CGRNX"
## [19] "PCPAX" "FLUIX"
cat("Skupina Large_Growth (20):\n")
## Skupina Large_Growth (20):
print(Large_Growth); cat("\n")
## [1] "RGAGX" "FCNKX" "SEEGX" "TBCIX" "VWUSX" "MFEIX" "FMGKX" "BBGLX" "HACAX"
## [10] "FDTRX" "NVLIX" "PLCIX" "JAGRX" "BFTIX" "TGCEX" "WPSIX" "ALVOX" "MMDEX"
## [19] "CCWRX" "CMLIX"
cat("Skupina Small_Growth (20):\n")
## Skupina Small_Growth (20):
print(Small_Growth); cat("\n")
## [1] "VSGAX" "NBGIX" "OTIIX" "FCAGX" "JSMGX" "ODIYX" "BSFIX" "FKAIX" "JVTNX"
## [10] "QUAIX" "WBSIX" "AGOZX" "BAFSX" "VLEIX" "PXQSX" "MRRGX" "OISGX" "PSGIX"
## [19] "ALFYX" "WSCGX"
cat("Skupina Small_Value (20):\n")
## Skupina Small_Value (20):
print(Small_Value); cat("\n")
## [1] "DFSVX" "UBVSX" "VSOIX" "FCVIX" "ESPNX" "ABSYX" "FVADX" "DEVIX" "NDVIX"
## [10] "ARAIX" "RTRIX" "AFDZX" "DHMYX" "CRRYX" "HNTVX" "GSITX" "HWVIX" "AVALX"
## [19] "BPSIX" "LSVQX"
# (neobvezno) Če želiš tabelo preslikave sklad -> skupina:
library(tibble)
mapping_tbl <- tibble(
fund = c(Large_Value, Large_Growth, Small_Growth, Small_Value),
group = c(rep("Large_Value", length(Large_Value)),
rep("Large_Growth", length(Large_Growth)),
rep("Small_Growth", length(Small_Growth)),
rep("Small_Value", length(Small_Value)))
)
# View(mapping_tbl) # odkomentiraj, če želiš pregled v RStudio
# 1) Izlušči samo X spremenljivke
X_data <- us_sample[, x_cols]
# 2) Izračun korelacijske matrike (Pearson)
cor_mat <- cor(X_data, use = "pairwise.complete.obs", method = "pearson")
# 3) Zaokroži na 3 decimalke
cor_mat_round <- round(cor_mat, 3)
# 4) Izpis
print(cor_mat_round)
## Russell_1000_Growth Russell_1000_Value Russell_2000_Growth
## Russell_1000_Growth 1.000 0.789 0.824
## Russell_1000_Value 0.789 1.000 0.854
## Russell_2000_Growth 0.824 0.854 1.000
## Russell_2000_Value 0.693 0.917 0.912
## Bond_US 0.444 0.327 0.359
## T-Bill_US 0.040 -0.070 -0.047
## Russell_2000_Value Bond_US T-Bill_US
## Russell_1000_Growth 0.693 0.444 0.040
## Russell_1000_Value 0.917 0.327 -0.070
## Russell_2000_Growth 0.912 0.359 -0.047
## Russell_2000_Value 1.000 0.263 -0.131
## Bond_US 0.263 1.000 0.051
## T-Bill_US -0.131 0.051 1.000
# (neobvezno) lepša vizualizacija z grafom:
# install.packages("corrplot") # če še nimaš
library(corrplot)
## Warning: package 'corrplot' was built under R version 4.3.2
## corrplot 0.92 loaded
corrplot(cor_mat, method = "color", type = "upper",
tl.col = "black", tl.srt = 45, addCoef.col = "black")
# RBSA (QP) za VSGAX, 36 mesecev: 2016-01-31 .. 2018-12-31
# Predpogoji v okolju: us_sample, x_cols
# OPOMBA: v solve.QP mora biti ENAKOSTNA omejitev PRVA kolona v Amat!
library(quadprog)
# 1) Izberi striktno vrstice 2:37 (tvoj Excel/zahteva)
sub <- us_sample[2:37, ]
# 2) Pripravi y in X (brez intercepta)
fund <- "VSGAX"
y <- as.numeric(sub[[fund]])
X <- as.matrix(sub[, x_cols, drop = FALSE])
# 3) Odstrani morebitne NA vrstice
ok <- stats::complete.cases(cbind(y, X))
y <- y[ok]
X <- X[ok, , drop = FALSE]
# 4) Kvadratno programiranje: min ||y - X w||^2 s.t. w >= 0, 1' w = 1
K <- ncol(X)
Dmat <- t(X) %*% X
dvec <- t(X) %*% y
# ENAKOST (1' w = 1) kot PRVA kolona, nato neenakosti w_i >= 0
Amat <- cbind(rep(1, K), diag(K)) # (K+1) stolpcev omejitev
bvec <- c(1, rep(0, K))
meq <- 1
# Stabilizacija (če je XtX skoraj singularen)
Dmat <- as.matrix(Dmat + diag(1e-8, K))
fit <- solve.QP(Dmat = Dmat, dvec = as.numeric(dvec),
Amat = Amat, bvec = bvec, meq = meq)
w <- as.numeric(fit$solution)
names(w) <- colnames(X)
# (varnostna normalizacija proti numeričnemu šumu)
w[w < 0] <- 0
w <- w / sum(w)
# 5) Metri ke prileganja (R^2 brez intercepta)
y_hat <- as.vector(X %*% w)
SSR <- sum((y - y_hat)^2)
SSTO <- sum((y - mean(y))^2)
R2 <- 1 - SSR / SSTO
# 6) Izpis rezultatov
cat("RBSA —", fund, "(2016-01-31 do 2018-12-31)\n")
## RBSA — VSGAX (2016-01-31 do 2018-12-31)
cat("Opazovanj:", length(y), "\n")
## Opazovanj: 36
cat("Vsota uteži:", round(sum(w), 10), " | Min utež:", round(min(w), 10), "\n")
## Vsota uteži: 1 | Min utež: 0
cat("R^2:", round(R2, 6), "\n\n")
## R^2: 0.979123
cat("Uteži po indeksih:\n")
## Uteži po indeksih:
print(round(w, 6))
## Russell_1000_Growth Russell_1000_Value Russell_2000_Growth Russell_2000_Value
## 0.229516 0.000000 0.759583 0.000000
## Bond_US T-Bill_US
## 0.010901 0.000000
library(quadprog)
library(dplyr)
library(purrr)
library(tibble)
library(openxlsx) # recommended Excel writer
## Warning: package 'openxlsx' was built under R version 4.3.3
# 1) Select the 36-month window
sub <- us_sample %>%
filter(Date >= as.Date("2016-01-31") & Date <= as.Date("2018-12-31"))
# alternatively: sub <- us_sample[2:37, ]
# 2) Function for RBSA on one fund
rbsa_one <- function(fund, data, x_cols) {
y <- as.numeric(data[[fund]])
X <- as.matrix(data[, x_cols, drop = FALSE])
ok <- complete.cases(cbind(y, X))
y <- y[ok]; X <- X[ok, , drop = FALSE]
K <- ncol(X)
Dmat <- t(X) %*% X
dvec <- t(X) %*% y
Amat <- cbind(rep(1, K), diag(K))
bvec <- c(1, rep(0, K))
meq <- 1
Dmat <- as.matrix(Dmat + diag(1e-8, K))
fit <- solve.QP(Dmat = Dmat, dvec = as.numeric(dvec),
Amat = Amat, bvec = bvec, meq = meq)
w <- as.numeric(fit$solution)
w[w < 0] <- 0
w <- w / sum(w)
names(w) <- x_cols
y_hat <- as.vector(X %*% w)
SSR <- sum((y - y_hat)^2)
SSTO <- sum((y - mean(y))^2)
R2 <- 1 - SSR/SSTO
RMSE <- sqrt(mean((y - y_hat)^2))
# round everything to 4 decimals
tibble(
Fund = fund,
Nobs = length(y),
R2 = round(R2, 4),
RMSE = round(RMSE, 4),
!!!lapply(as.list(w), function(x) round(x, 4))
)
}
# 3) Run analysis for all Small_Growth funds
results_small_growth <- map_dfr(Small_Growth, rbsa_one, data = sub, x_cols = x_cols)
# 4) Save to Excel
write.xlsx(results_small_growth, file = "RBSA_SmallGrowth_2016_2018V2.xlsx")
## Warning in file.create(to[okay]): cannot create file
## 'RBSA_SmallGrowth_2016_2018V2.xlsx', reason 'Permission denied'
# Quick preview
print(results_small_growth)
## # A tibble: 20 × 10
## Fund Nobs R2 RMSE Russell_1000_Growth Russell_1000_Value
## <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 VSGAX 36 0.984 0.0054 0.218 0
## 2 NBGIX 36 0.930 0.0102 0.102 0.294
## 3 OTIIX 36 0.973 0.0065 0.0452 0.0521
## 4 FCAGX 36 0.944 0.0105 0.282 0
## 5 JSMGX 36 0.974 0.0066 0.349 0.023
## 6 ODIYX 36 0.925 0.0123 0.331 0
## 7 BSFIX 36 0.944 0.0102 0.421 0.0155
## 8 FKAIX 36 0.856 0.0187 0.249 0
## 9 JVTNX 36 0.972 0.0072 0.268 0
## 10 QUAIX 36 0.926 0.0139 0.102 0
## 11 WBSIX 36 0.917 0.0129 0 0
## 12 AGOZX 36 0.772 0.0264 0.115 0
## 13 BAFSX 36 0.932 0.01 0.318 0
## 14 VLEIX 36 0.931 0.0095 0.138 0.232
## 15 PXQSX 36 0.855 0.0155 0.146 0.161
## 16 MRRGX 36 0.930 0.0107 0.0233 0.212
## 17 OISGX 36 0.947 0.0109 0.272 0
## 18 PSGIX 36 0.976 0.0074 0.0014 0
## 19 ALFYX 36 0.98 0.0057 0.197 0
## 20 WSCGX 36 0.966 0.0092 0.0411 0
## # ℹ 4 more variables: Russell_2000_Growth <dbl>, Russell_2000_Value <dbl>,
## # Bond_US <dbl>, `T-Bill_US` <dbl>
# ===== Batch RBSA za VSE sklade in POVPREČJA po stilih =====
# Predpogoji v okolju: us_sample, x_cols, ter vektorji:
# Large_Value, Large_Growth, Small_Value, Small_Growth
# Zahtevano okno: 2016-01-31 .. 2018-12-31
# Rezultate zaokrožimo na 4 decimale in shranimo v Excel.
library(quadprog)
library(dplyr)
library(purrr)
library(tibble)
library(openxlsx)
# --- 1) Časovno okno (36 mesecev) ---
sub <- us_sample %>%
filter(Date >= as.Date("2016-01-31") & Date <= as.Date("2018-12-31"))
# (alternativa, če želiš striktno vrstice 2:37)
# sub <- us_sample[2:37, ]
# --- 2) Preslikava sklad -> stil ---
style_map <- tibble(
Fund = c(Large_Value, Large_Growth, Small_Value, Small_Growth),
Style = c(rep("Large_Value", length(Large_Value)),
rep("Large_Growth", length(Large_Growth)),
rep("Small_Value", length(Small_Value)),
rep("Small_Growth", length(Small_Growth)))
)
all_funds <- style_map$Fund
# --- 3) Funkcija RBSA za en sklad (QP; β >= 0, sum β = 1) ---
rbsa_one <- function(fund, data, x_cols) {
y <- as.numeric(data[[fund]])
X <- as.matrix(data[, x_cols, drop = FALSE])
ok <- stats::complete.cases(cbind(y, X))
y <- y[ok]; X <- X[ok, , drop = FALSE]
K <- ncol(X)
Dmat <- t(X) %*% X
dvec <- t(X) %*% y
# ENAKOST naj bo PRVA kolona (sum β = 1), nato neenakosti (β >= 0)
Amat <- cbind(rep(1, K), diag(K))
bvec <- c(1, rep(0, K))
meq <- 1
Dmat <- as.matrix(Dmat + diag(1e-8, K)) # stabilizacija
fit <- solve.QP(Dmat = Dmat, dvec = as.numeric(dvec),
Amat = Amat, bvec = bvec, meq = meq)
w <- as.numeric(fit$solution)
w[w < 0] <- 0
w <- w / sum(w)
names(w) <- x_cols
y_hat <- as.vector(X %*% w)
SSR <- sum((y - y_hat)^2)
SSTO <- sum((y - mean(y))^2)
R2 <- 1 - SSR/SSTO
RMSE <- sqrt(mean((y - y_hat)^2))
tibble(
Fund = fund,
Nobs = length(y),
R2 = round(R2, 4),
RMSE = round(RMSE, 4),
!!!lapply(as.list(w), function(v) round(v, 4))
)
}
# --- 4) Zagon za vse sklade, pripni stile ---
fund_results <- map_dfr(all_funds, rbsa_one, data = sub, x_cols = x_cols) %>%
left_join(style_map, by = "Fund") %>%
relocate(Style, .after = Fund)
# --- 5) Povprečja po stilih (R² in uteži) ---
weight_cols <- x_cols # 6 indeksov
style_avg <- fund_results %>%
group_by(Style) %>%
summarise(
N_funds = dplyr::n(),
Avg_R2 = round(mean(R2, na.rm = TRUE), 4),
across(
all_of(weight_cols),
~ round(mean(.x, na.rm = TRUE), 4),
.names = "Avg_{.col}"
),
.groups = "drop"
)
# --- 6) Shranjevanje v Excel (več listov) ---
wb <- openxlsx::createWorkbook()
openxlsx::addWorksheet(wb, "Fund_Results")
openxlsx::addWorksheet(wb, "Style_Averages")
openxlsx::writeData(wb, "Fund_Results", fund_results)
openxlsx::writeData(wb, "Style_Averages", style_avg)
for (st in unique(fund_results$Style)) {
openxlsx::addWorksheet(wb, st)
openxlsx::writeData(wb, st, dplyr::filter(fund_results, Style == st))
}
openxlsx::saveWorkbook(wb, file = "RBSA_AllFunds_2016_2018.xlsx", overwrite = TRUE)
## Warning in file.create(to[okay]): cannot create file
## 'RBSA_AllFunds_2016_2018.xlsx', reason 'Permission denied'
# Hiter pregled
print(style_avg)
## # A tibble: 4 × 9
## Style N_funds Avg_R2 Avg_Russell_1000_Growth Avg_Russell_1000_Value
## <chr> <int> <dbl> <dbl> <dbl>
## 1 Large_Growth 20 0.909 0.912 0.0403
## 2 Large_Value 20 0.951 0.162 0.736
## 3 Small_Growth 20 0.932 0.181 0.0495
## 4 Small_Value 20 0.911 0.036 0.138
## # ℹ 4 more variables: Avg_Russell_2000_Growth <dbl>,
## # Avg_Russell_2000_Value <dbl>, Avg_Bond_US <dbl>, `Avg_T-Bill_US` <dbl>