1% Generated by roxygen2: do not edit by hand 2% Please edit documentation in R/MarketTiming.R 3\name{MarketTiming} 4\alias{MarketTiming} 5\title{Market timing models} 6\usage{ 7MarketTiming(Ra, Rb, Rf = 0, method = c("TM", "HM"), ...) 8} 9\arguments{ 10\item{Ra}{an xts, vector, matrix, data frame, timeSeries or zoo object of 11the asset returns} 12 13\item{Rb}{an xts, vector, matrix, data frame, timeSeries or zoo object of 14the benchmark asset return} 15 16\item{Rf}{risk free rate, in same period as your returns} 17 18\item{method}{used to select between Treynor-Mazuy and Henriksson-Merton 19models. May be any of: \itemize{ \item TM - Treynor-Mazuy model, 20\item HM - Henriksson-Merton model} By default Treynor-Mazuy is selected} 21 22\item{\dots}{any other passthrough parameters} 23} 24\description{ 25Allows to estimate Treynor-Mazuy or Merton-Henriksson market timing model. 26The Treynor-Mazuy model is essentially a quadratic extension of the basic 27CAPM. It is estimated using a multiple regression. The second term in the 28regression is the value of excess return squared. If the gamma coefficient 29in the regression is positive, then the estimated equation describes a 30convex upward-sloping regression "line". The quadratic regression is: 31\deqn{R_{p}-R_{f}=\alpha+\beta (R_{b} - R_{f})+\gamma (R_{b}-R_{f})^2+ 32\varepsilon_{p}}{Rp - Rf = alpha + beta(Rb -Rf) + gamma(Rb - Rf)^2 + 33epsilonp} 34\eqn{\gamma}{gamma} is a measure of the curvature of the regression line. 35If \eqn{\gamma}{gamma} is positive, this would indicate that the manager's 36investment strategy demonstrates market timing ability. 37} 38\details{ 39The basic idea of the Merton-Henriksson test is to perform a multiple 40regression in which the dependent variable (portfolio excess return and a 41second variable that mimics the payoff to an option). This second variable 42is zero when the market excess return is at or below zero and is 1 when it 43is above zero: 44\deqn{R_{p}-R_{f}=\alpha+\beta (R_{b}-R_{f})+\gamma D+\varepsilon_{p}}{Rp - 45Rf = alpha + beta * (Rb - Rf) + gamma * D + epsilonp} 46where all variables are familiar from the CAPM model, except for the 47up-market return \eqn{D=max(0,R_{f}-R_{b})}{D = max(0, Rf - Rb)} and market 48timing abilities \eqn{\gamma}{gamma} 49} 50\examples{ 51 52data(managers) 53MarketTiming(managers[,1], managers[,8], Rf=.035/12, method = "HM") 54MarketTiming(managers[80:120,1:6], managers[80:120,7], managers[80:120,10]) 55MarketTiming(managers[80:120,1:6], managers[80:120,8:7], managers[80:120,10], method = "TM") 56 57} 58\references{ 59J. Christopherson, D. Carino, W. Ferson. \emph{Portfolio 60Performance Measurement and Benchmarking}. 2009. McGraw-Hill, p. 127-133. 61\cr J. L. Treynor and K. Mazuy, "Can Mutual Funds Outguess the Market?" 62\emph{Harvard Business Review}, vol44, 1966, pp. 131-136 63\cr Roy D. Henriksson and Robert C. Merton, "On Market Timing and Investment 64Performance. II. Statistical Procedures for Evaluating Forecast Skills," 65\emph{Journal of Business}, vol.54, October 1981, pp.513-533 \cr 66} 67\seealso{ 68\code{\link{CAPM.beta}} 69} 70\author{ 71Andrii Babii, Peter Carl 72} 73