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