Optimal Probabilistic Market Timing Using Bull Bear Cycle Statistics

Abstract

Under the historical market view of binary bull and bear cycles, what is an ex ante optimal trading strategy? Similar to an original optimal stopping time model (Dai, et al 2010, 2011) to maximize long term investment returns, we introduce a market timing strategy based on the probability that the market is currently in a bull or bear regime. In doing so, we adjust the Wonham filter (1965) for the regime conditional probability calculation to allow time-varying volatilities and utilize expected bull/bear regime risk-adjusted average returns as statistically estimated parameter inputs. Further, we derive explicit formula to approximate the optimal probabilistic buying or selling thresholds and extend the analytical formulation to allow both long only and long/flat/short positions for a hysteresis trading implementation.

Considering the fractal characteristics of stock market indexes and other asset class index data at different frequencies, we devise a systematic procedure to separate historical bull bear regimes and obtain detailed market cycle statistics. This allows using different index gain, loss and duration thresholds to define historical bull/bear cycles in the same manner as an earlier study (Wagner, 1992). We back test the methodology on two broad stock indexes: S&P 500 Index (SPX 1928-2014) and Shanghai Stock Exchange Composite Index (SSEC 1995-2014). The results, including that of an out-of-sample test case on the SPX since 1940 using 10-cycle look-back rolling statistics, indicate out-performance over the buy-and-hold approach and a popular trend following technical trading strategy, the Golden Cross.

Keywords: bull/bear market cycle, probabilistic market timing, optimal trend following, Wonham Filter, hysteresis trading rule, Golden Cross, Back Test, in sample, out-of-sample

JEL Classification: C44, C61, D81