R/SignalStats.R

In JustinMShea/ExpectedReturns: Reproduction of Investment Strategies presented in Antti Ilmanen's Expected Returns and Investing Amid Low Expected Returns

#' @title Compute Trading Signals Statistics
#'
#' @description
#' Trading signals can be further analyzed with several statistics, across instruments.
#' Signal statistics currently implemented include:
#' * **Activity matrix** (`method="activity"`).
#' Represents the number of long or short positions over the periods considered.
#' It is expressed in percentage units.
#' * **Agreement matrix** (`method="agreement"`).
#' It denotes the number of periods during which signals pairs agree on the position,
#' on average across instruments. It is expressed in percentage units.
#' * **Correlation matrix** (`method="correlation"`).
#' The average correlation among signals, across instruments.
#'
#' @note
#' Some signals may result into an inactive position. Such positions are not considered
#' in the activity matrix and thus values do not sum up to unity. Whereas, they
#' are accounted for in the agreement matrix.
#'
#' @param X A list of `xts` objects storing signals series. See 'Details'.
#' @param symbols A character vector providing the names of symbols signals were computed for.
#' @param signals A character vector specifying the names of signals provided in `X`.
#' @param method A string indicating which statistics to compute among `X` signals. One of "activity", "agreement", or "correlation".
#' @param ... Any other pass through parameter.
#'
#' @return
#' Varies depending on the chosen `method`.
#'
#' @references
#' Baltas, A. N. and Kosowski, R. (2012). *Improving time-series momentum strategies: The role of trading signals and volatility estimators*.
#' [EDHEC-Risk Institute](https://risk.edhec.edu/publications/improving-time-series-momentum-strategies-role-trading-signals-and-volatility).
#'
#' @author
#' Vito Lestingi
#'
#' @seealso
#' [ExpectedReturns::MomSignal()]
#'
#' @importFrom stats complete.cases cor na.omit
#' @importFrom utils combn
#' @importFrom xts xts
#' @importFrom zoo index
#'
#' @export
#'
SignalStats <- function(X
                        , symbols
                        , signals
                        , method
                        , ...)
{
  methods.avail <- c('activity', 'agreement', 'correlation')
  method <- match.arg(method, methods.avail)
  switch (method,
    activity = {
      out <- lapply(X, function(x) {
        x.inst <- Reduce(cbind, x)
        lsp <- apply(x.inst, 2, function(j) {
          nlong <- length(which(j == 1))
          nshort <- length(which(j == (-1)))
          los <- rbind(nlong, nshort)
          y <- los / NROW(na.omit(j)) * 100
          return(y)
        })
        lsp <- t(lsp)
        rownames(lsp) <- symbols
        colnames(lsp) <- c('Long', 'Short')
        return(lsp)
      })
      names(out) <- signals
    },
    agreement = {
      sig.inst <- Reduce(function(...) Map(cbind, ...), X)
      names(sig.inst) <- symbols
      sig.combn <- combn(signals, 2)
      # Position agreement matrix by instrument
      adgmt <- lapply(sig.inst, function(x) {
        nobs <- nrow(x)
        nsc <- ncol(sig.combn)
        y <- matrix(NA, nobs, nsc)
        for (j in 1:nsc) {
          s <- sig.combn[, j]
          y[, j] <- x[, s[1]] * x[, s[2]]
        }
        colnames(y) <- apply(sig.combn, 2, paste, collapse='.')
        agr <- colSums(y > 0, na.rm=TRUE)
        dgr <- colSums(y < 0, na.rm=TRUE)
        adgmt.norm <- rbind(agr, dgr) / nobs * 100
        rownames(adgmt.norm) <- c('agree', 'disagree')
        return(adgmt.norm)
      })
      # Positions agreement across instruments
      adgmt <- Reduce(rbind, adgmt)
      agmt <- adgmt[rownames(adgmt) == 'agree', ]
      out <- colMeans(agmt)
    },
    correlation = {
      sig.avg.inst <- lapply(X, function(x) {
        x.inst <- Reduce(cbind, x)
        x.inst.avg <- xts(rowMeans(x.inst, na.rm=TRUE), index(x.inst))
        return(x.inst.avg)
      })
      sig.avg <- Reduce(cbind, sig.avg.inst)
      sig.avg <- sig.avg[complete.cases(sig.avg), ]
      colnames(sig.avg) <- signals
      out <- cor(sig.avg, ...)
    }
  )
  return(out)
}