PerformanceAnalytics (version 2.0.8)

MarketTiming: Market timing models

Description

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: $$R_{p}-R_{f}=\alpha+\beta (R_{b} - R_{f})+\gamma (R_{b}-R_{f})^2+ \varepsilon_{p}$$ \(\gamma\) 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.

Usage

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

Arguments

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

Author

Andrii Babii, Peter Carl

Details

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: $$R_{p}-R_{f}=\alpha+\beta (R_{b}-R_{f})+\gamma D+\varepsilon_{p}$$ where all variables are familiar from the CAPM model, except for the up-market return \(D=max(0,R_{f}-R_{b})\) and market timing abilities \(\gamma\)

References

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

See Also

CAPM.beta

Examples

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")