MarketTiming: Market timing models
In PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

Description Usage Arguments Details Author(s) References See Also Examples

Allows to estimate Treynor-Mazuy or Merton-Henriksson market timing model. The Treynor-Mazuy model is essentially a quadratic extension of the basic CAPM. It is estimated using a multiple regression. The second term in the regression is the value of excess return squared. If the gamma coefficient in the regression is positive, then the estimated equation describes a convex upward-sloping regression "line". The quadratic regression is:

Rp - Rf = alpha + beta(Rb -Rf) + gamma(Rb - Rf)^2 + epsilonp

gamma is a measure of the curvature of the regression line. If gamma is positive, this would indicate that the manager's investment strategy demonstrates market timing ability.

1	MarketTiming(Ra, Rb, Rf = 0, method = c("TM", "HM"), ...)

`Ra`	an xts, vector, matrix, data frame, timeSeries or zoo object of the asset returns
`Rb`	an xts, vector, matrix, data frame, timeSeries or zoo object of the benchmark asset return
`Rf`	risk free rate, in same period as your returns
`method`	used to select between Treynor-Mazuy and Henriksson-Merton models. May be any of: TM - Treynor-Mazuy model, HM - Henriksson-Merton model By default Treynor-Mazuy is selected
`...`	any other passthrough parameters

The basic idea of the Merton-Henriksson test is to perform a multiple regression in which the dependent variable (portfolio excess return and a second variable that mimics the payoff to an option). This second variable is zero when the market excess return is at or below zero and is 1 when it is above zero:

Rp - Rf = alpha + beta * (Rb - Rf) + gamma * D + epsilonp

where all variables are familiar from the CAPM model, except for the up-market return D = max(0, Rf - Rb) and market timing abilities gamma

Andrii Babii, Peter Carl

J. Christopherson, D. Carino, W. Ferson. Portfolio Performance Measurement and Benchmarking. 2009. McGraw-Hill, p. 127-133.
J. L. Treynor and K. Mazuy, "Can Mutual Funds Outguess the Market?" Harvard Business Review, vol44, 1966, pp. 131-136
Roy D. Henriksson and Robert C. Merton, "On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecast Skills," Journal of Business, vol.54, October 1981, pp.513-533

CAPM.beta

data(managers)
MarketTiming(managers[,1], managers[,8], Rf=.035/12, method = "HM")
MarketTiming(managers[80:120,1:6], managers[80:120,7], managers[80:120,10])
MarketTiming(managers[80:120,1:6], managers[80:120,8:7], managers[80:120,10], method = "TM")