R/CalculateHedgeRatio.R

In ivanliu1989/RQuantTrader: A collection of functions for pair trading

#' Hedge Ratio OLS
#'
#' Calculate Hedge Ratio by using OLS
#'
#' @param y long series
#' @param x short series
#' @param add_const keep constant (risk free profits) or not
#'
#' @details alpha < 0 too little returns based on the risks
#' @details alpha = 0 adequate returns for the risks taken
#' @details alpha > 0 excess returns to the assumed risks
#' @details beta correlated relative volatile
#'
#' @return A \code{list} of hedge ratio (beta, risk) and alpha (risk free profits)
#'
#' @examples
#' getFX("AUD/USD")
#' getFX("CAD/USD")
#' HedgeRatioOLS(AUDUSD, CADUSD)
#'
#' @export
HedgeRatioOLS <- function(y, x, add_const = TRUE){
    if(add_const){
        ols.fit <- lm(y~x+1)
    }else{
        ols.fit <- lm(y~x-1)
    }
    alpha = coef(ols.fit)["(Intercept)"][[1]]
    beta = coef(ols.fit)["x"][[1]]
    return(list(alpha = alpha,
                beta = beta))
}



kalmanInit <- function(n){
    delta = 0.0001
    Vw = delta/(1-delta)*diag(2)
    Ve = 0.001
    beta = matrix(0, nrow = 2, ncol = n)
    P = matrix(0, 2, 2)
    R = NULL
    e = rep(NA, n)
    Q = rep(NA, n)
    yhat = rep(NA, n)
    kalmanOjt = list(
        delta = delta,
        Vw = Vw,
        Ve = Ve,
        beta = beta,
        P = P,
        R = R,
        e = e,
        Q = Q,
        yhat = yhat,
        K = NULL
    )
    return(kalmanOjt)
}

kalmanFilter <- function(long, short, sdnum = 1){
    n = length(long)
    y = long
    x = cbind(short, ones = rep(1, n))
    kalman <- kalmanInit(n)
    for(t in 1:n){
        if(!is.null(kalman$R)){
            kalman$R = kalman$P + kalman$Vw
            kalman$beta[,t] = kalman$beta[,t-1]
        }else{
            kalman$R = kalman$P
        }

        kalman$yhat[t]=x[t,]%*%kalman$beta[,t] # measurement prediction. Equation 3.9

        kalman$Q[t] = x[t, ]%*%kalman$R%*%t(x[t,])+kalman$Ve # measurement variance prediction. Equation 3.10

        kalman$e[t]=y[t]-kalman$yhat[t] # measurement prediction error

        kalman$K=kalman$R%*%t(x[t,])/kalman$Q[t] # Kalman gain

        kalman$beta[,t] = kalman$beta[,t]+as.vector(kalman$K)*kalman$e[t] # State update. Equation 3.11
        kalman$P=kalman$R-kalman$K%*%(x[t,]%*%kalman$R) # State covariance update. Euqation 3.12
    }

    longsEntry=kalman$e < -sqrt(kalman$Q)*sdnum # a long position means we should buy long
    longsExit=kalman$e > -sqrt(kalman$Q)*sdnum
    shortsEntry=kalman$e > sqrt(kalman$Q)*sdnum
    shortsExit=kalman$e < sqrt(kalman$Q)*sdnum

    numUnitesLong = rep(NA, length(long))
    numUnitesShort = rep(NA, length(long))
    numUnitesLong[1] = 0
    numUnitesLong[longsEntry] = 1
    numUnitesLong[longsExit] = 0
    numUnitesLong <- fillMissingData(numUnitesLong)

    numUnitesShort[1] = 0
    numUnitesShort[shortsEntry] = -1
    numUnitesShort[shortsExit] = 0
    numUnitesShort <- fillMissingData(numUnitesShort)

    numUnits = numUnitesLong + numUnitesShort

    positions = merge(numUnits*long, numUnits*-kalman$beta[1,]*short)
    colnames(positions) = c("long", "short")

    res <- list(
        kalman = kalman,
        long = long,
        short = short,
        hedgeRatio = kalman$beta[1,],
        longsEntry = longsEntry,
        longsExit = longsExit,
        shortsEntry = shortsEntry,
        shortsExit = shortsExit,
        numUnits = numUnits,
        positions = positions
    )
    return(res)
}