typos

.Rbuildignore

@@ -8,3 +8,4 @@
 ^\.github$
 ^codecov\.yml$
 ^cran-comments\.md$
+^CRAN-SUBMISSION$

CRAN-SUBMISSION

@@ -0,0 +1,3 @@
+Version: 0.1.0
+Date: 2023-07-27 21:45:01 UTC
+SHA: bad549aabedebd983d9fc00884262e14bb5d091e

R/epo.R

@@ -1,16 +1,21 @@
 #' Enhanced Portfolio Optimization (EPO)
 #'
-#' Computes the optimal portfolio allocation using the EPO method with full-investment
-#' constraint.
+#' Computes the optimal portfolio allocation using the EPO method.
 #'
 #' @param x A data-set with asset returns. It should be a \code{tibble}, a \code{xts}
 #' or a \code{matrix}.
-#' @param signal A \code{double} with the investor's belief's (signals, forecasts).
-#' @param method A \code{character}. One of: `simple` or `anchored`.
+#' @param signal A \code{double} vector with the investor's belief's (signals, forecasts).
+#' @param lambda A \code{double} with the investor's risk-aversion preference.
+#' @param method A \code{character}. One of: `"simple"` or `"anchored"`.
 #' @param w A \code{double} between \code{0} and \code{1}. The shrinkage level
 #' increases from 0 to 1.
-#' @param anchor A \code{double} with the investor anchor (benchmark), in which
+#' @param anchor A \code{double} vector with the anchor (benchmark) in which
 #' the allocation should not deviate too much from. Only used when `method = "anchored"`.
+#' @param normalize A \code{boolean} indicating whether the allocation should be
+#' normalized to sum \code{1} (full-investment constraint). The default is `normalize = TRUE`.
+#' @param endogenous A \code{boolean} indicating whether the risk-aversion parameter
+#' should be considered endogenous (only used when `method = "anchored"`).
+#' The default is `endogenous = TRUE`.
 #'
 #' @return The optimal allocation vector.
 #' @export
@@ -24,13 +29,13 @@
 #' ##################
 #'
 #' # Traditional Mean-Variance Analysis
-#' epo(x = x, signal = s, method = "simple", w = 0)
+#' epo(x = x, signal = s, lambda = 10, method = "simple", w = 0)
 #'
 #' # 100% Shrinkage
-#' epo(x = x, signal = s, method = "simple", w = 1)
+#' epo(x = x, signal = s, lambda = 10, method = "simple", w = 1)
 #'
 #' # 50% Classical MVO and 50% Shrinkage
-#' epo(x = x, signal = s, method = "simple", w = 0.5)
+#' epo(x = x, signal = s, lambda = 10, method = "simple", w = 0.5)
 #'
 #' ####################
 #' ### Anchored EPO ###
@@ -39,57 +44,59 @@
 #' benchmark <- rep(0.25, 4) # 1/N Portfolio
 #'
 #' # Traditional Mean-Variance Analysis
-#' epo(x = x, signal = s, method = "anchored", w = 0.0, anchor = benchmark)
+#' epo(x = x, signal = s, lambda = 10, method = "anchored", w = 0.0, anchor = benchmark)
 #'
 #' # 100% on the Anchor portfolio
-#' epo(x = x, signal = s, method = "anchored", w = 1.0, anchor = benchmark)
+#' epo(x = x, signal = s, lambda = 10, method = "anchored", w = 1.0, anchor = benchmark)
 #'
 #' # Somewhere between the two worlds
-#' epo(x = x, signal = s, method = "anchored", w = 0.5, anchor = benchmark)
-epo <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL) {
+#' epo(x = x, signal = s, lambda = 10, method = "anchored", w = 0.5, anchor = benchmark)
+epo <- function(x, signal, lambda, method = c("simple", "anchored"), w, anchor = NULL, normalize = TRUE, endogenous = TRUE) {
 
   UseMethod("epo", x)
 
 }
 
 #' @rdname epo
 #' @export
-epo.default <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL) {
+epo.default <- function(x, signal, lambda, method = c("simple", "anchored"), w, anchor = NULL, normalize = TRUE, endogenous = TRUE) {
 
   rlang::abort("`x` must be a tibble, xts or a matrix.")
 
 }
 
 #' @rdname epo
 #' @export
-epo.tbl <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL) {
+epo.tbl <- function(x, signal, lambda, method = c("simple", "anchored"), w, anchor = NULL, normalize = TRUE, endogenous = TRUE) {
 
-  epo_(x = tbl_to_mtx(x), signal = signal, method = method, w = w, anchor = anchor)
+  epo_(x = tbl_to_mtx(x), signal = signal, lambda = lambda, method = method, w = w, anchor = anchor, normalize = normalize, endogenous = endogenous)
 
 }
 
 #' @rdname epo
 #' @export
-epo.xts <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL) {
+epo.xts <- function(x, signal, lambda, method = c("simple", "anchored"), w, anchor = NULL, normalize = TRUE, endogenous = TRUE) {
 
-  epo_(x = as.matrix(x), signal = signal, method = method, w = w, anchor = anchor)
+  epo_(x = as.matrix(x), signal = signal, lambda = lambda, method = method, w = w, anchor = anchor, normalize = normalize, endogenous = endogenous)
 
 }
 
 #' @rdname epo
 #' @export
-epo.matrix <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL) {
+epo.matrix <- function(x, signal, lambda, method = c("simple", "anchored"), w, anchor = NULL, normalize = TRUE, endogenous = TRUE) {
 
-  epo_(x = x, signal = signal, method = method, w = w, anchor = anchor)
+  epo_(x = x, signal = signal, lambda = lambda, method = method, w = w, anchor = anchor, normalize = normalize, endogenous = endogenous)
 
 }
 
 #' @keywords internal
-epo_ <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL) {
+epo_ <- function(x, signal, lambda, method = c("simple", "anchored"), w, anchor = NULL, normalize = TRUE, endogenous = TRUE) {
 
   # Error Handling
   assertthat::assert_that(assertthat::is.string(method))
+  assertthat::assert_that(assertthat::is.number(lambda))
   assertthat::assert_that(assertthat::is.number(w))
+  assertthat::assert_that(assertthat::is.flag(normalize))
 
   if (NCOL(signal) > 1) {
     signal <- matrix(signal)
@@ -127,15 +134,23 @@ epo_ <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL)
   # The simple EPO
   if (method == "simple") {
 
-    .epo <- inv_shrunk_cov %*% signal # equation 16
+    .epo <- (1 / lambda) * inv_shrunk_cov %*% signal # equation 16
 
   # The anchored EPO
   } else if (method == "anchored") {
 
-    # footnote 13
-    .gamma <- c((sqrt(t(a) %*% cov_tilde %*% a) / sqrt(t(s) %*% inv_shrunk_cov %*% cov_tilde %*% inv_shrunk_cov %*% s)))
-    # equation 17
-    .epo <- inv_shrunk_cov %*% (((1 - w) * .gamma * s) + ((w * I %*% V %*% a)))
+    if (endogenous) {
+
+      # footnote 13
+      .gamma <- c((sqrt(t(a) %*% cov_tilde %*% a) / sqrt(t(s) %*% inv_shrunk_cov %*% cov_tilde %*% inv_shrunk_cov %*% s)))
+      # equation 17
+      .epo <- inv_shrunk_cov %*% (((1 - w) * .gamma * s) + ((w * I %*% V %*% a)))
+
+    } else {
+
+      .epo <- inv_shrunk_cov %*% (((1 - w) * (1 / lambda) * s) + ((w * I %*% V %*% a)))
+
+    }
 
   # Error
   } else {
@@ -144,8 +159,13 @@ epo_ <- function(x, signal, method = c("simple", "anchored"), w, anchor = NULL)
 
   }
 
-  # Full-Investment constraint
-  .epo <- as.double(.epo / sum(.epo))
+  if (normalize) {
+
+    # Force full-investment constraint
+    .epo <- as.double(.epo / sum(.epo))
+
+  }
+
   .epo
 
 }

README.Rmd

@@ -18,7 +18,7 @@ knitr::opts_chunk$set(
 <!-- badges: start -->
 
 [![Lifecycle: experimental](https://img.shields.io/badge/lifecycle-experimental-orange.svg)](https://lifecycle.r-lib.org/articles/stages.html#experimental) [![R-CMD-check](https://github.com/Reckziegel/epo/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/Reckziegel/epo/actions/workflows/R-CMD-check.yaml) [![Codecov test coverage](https://codecov.io/gh/Reckziegel/epo/branch/main/graph/badge.svg)](https://app.codecov.io/gh/Reckziegel/epo?branch=main)
-
+[![CRAN status](https://www.r-pkg.org/badges/version/epo)](https://CRAN.R-project.org/package=epo)
 <!-- badges: end -->
 
 The Enhanced Portfolio Optimization (EPO) method, described in Pedersen, Babu and Levine (2021), proposes a unifying theory on portfolio optimization. Employing Principal Component Analysis (PCA), the EPO method ranks portfolios based on their variance, from the most to the least important principal components. Notably, the least important principal components emerge as "problem portfolios", primarily due to their low *estimated* risk, leading to the underestimation of their *true* risks. These portfolios offer high expected returns (*ex-ante*) and low realized Sharpe Ratios (*ex-post*), underscoring the challenges faced when using them through standard approaches.
@@ -59,13 +59,13 @@ s <- colMeans(x) # it could be any signal
 ##################
 
 # Traditional Mean-Variance Analysis
-epo(x = x, signal = s, method = "simple", w = 0)
+epo(x = x, signal = s, lambda = 10, method = "simple", w = 0)
 
 # 100% Shrinkage
-epo(x = x, signal = s, method = "simple", w = 1)
+epo(x = x, signal = s, lambda = 10, method = "simple", w = 1)
 
 # 50% Classical MVO and 50% Shrinkage
-epo(x = x, signal = s, method = "simple", w = 0.5)
+epo(x = x, signal = s, lambda = 10, method = "simple", w = 0.5)
 
 ####################
 ### The Anchored EPO 
@@ -74,13 +74,13 @@ epo(x = x, signal = s, method = "simple", w = 0.5)
 benchmark <- rep(0.25, 4) # 1/N Portfolio
 
 # Traditional Mean-Variance Analysis
-epo(x = x, signal = s, method = "anchored", w = 0.0, anchor = benchmark)
+epo(x = x, signal = s, lambda = 10, method = "anchored", w = 0.0, anchor = benchmark)
 
 # 100% on the Anchor portfolio
-epo(x = x, signal = s, method = "anchored", w = 1.0, anchor = benchmark)
+epo(x = x, signal = s, lambda = 10, method = "anchored", w = 1.0, anchor = benchmark)
 
 # 50% on Mean-Variance Analysis and 50% on the Anchor Portfolio
-epo(x = x, signal = s, method = "anchored", w = 0.5, anchor = benchmark)
+epo(x = x, signal = s, lambda = 10, method = "anchored", w = 0.5, anchor = benchmark)
 ```
 
 ## References

README.md

@@ -10,7 +10,8 @@ experimental](https://img.shields.io/badge/lifecycle-experimental-orange.svg)](h
 [![R-CMD-check](https://github.com/Reckziegel/epo/actions/workflows/R-CMD-check.yaml/badge.svg)](https://github.com/Reckziegel/epo/actions/workflows/R-CMD-check.yaml)
 [![Codecov test
 coverage](https://codecov.io/gh/Reckziegel/epo/branch/main/graph/badge.svg)](https://app.codecov.io/gh/Reckziegel/epo?branch=main)
-
+[![CRAN
+status](https://www.r-pkg.org/badges/version/epo)](https://CRAN.R-project.org/package=epo)
 <!-- badges: end -->
 
 The Enhanced Portfolio Optimization (EPO) method, described in Pedersen,
@@ -87,15 +88,15 @@ s <- colMeans(x) # it could be any signal
 ##################
 
 # Traditional Mean-Variance Analysis
-epo(x = x, signal = s, method = "simple", w = 0)
+epo(x = x, signal = s, lambda = 10, method = "simple", w = 0)
 #> [1]  0.1914569  0.9894828 -0.3681779  0.1872382
 
 # 100% Shrinkage
-epo(x = x, signal = s, method = "simple", w = 1)
+epo(x = x, signal = s, lambda = 10, method = "simple", w = 1)
 #> [1] 0.2352863 0.3659986 0.1375249 0.2611902
 
 # 50% Classical MVO and 50% Shrinkage
-epo(x = x, signal = s, method = "simple", w = 0.5)
+epo(x = x, signal = s, lambda = 10, method = "simple", w = 0.5)
 #> [1]  0.223281853  0.564005906 -0.009868083  0.222580324
 
 ####################
@@ -105,15 +106,15 @@ epo(x = x, signal = s, method = "simple", w = 0.5)
 benchmark <- rep(0.25, 4) # 1/N Portfolio
 
 # Traditional Mean-Variance Analysis
-epo(x = x, signal = s, method = "anchored", w = 0.0, anchor = benchmark)
+epo(x = x, signal = s, lambda = 10, method = "anchored", w = 0.0, anchor = benchmark)
 #> [1]  0.1914569  0.9894828 -0.3681779  0.1872382
 
 # 100% on the Anchor portfolio
-epo(x = x, signal = s, method = "anchored", w = 1.0, anchor = benchmark)
+epo(x = x, signal = s, lambda = 10, method = "anchored", w = 1.0, anchor = benchmark)
 #> [1] 0.25 0.25 0.25 0.25
 
 # 50% on Mean-Variance Analysis and 50% on the Anchor Portfolio
-epo(x = x, signal = s, method = "anchored", w = 0.5, anchor = benchmark)
+epo(x = x, signal = s, lambda = 10, method = "anchored", w = 0.5, anchor = benchmark)
 #> [1] 0.2374674 0.4557503 0.1004711 0.2063111
 ```