Market timing models
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.
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:
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
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")
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