On Turning to Market Timing: A Binomial Approximation

Abstract

Utilizing simple binomial modeling techniques, I consider the potential impact of technical analysis on expected returns, expected volatility, and higher moment risk. While limited as a practical evaluation tool, this approach allows for relatively intuitive observations relevant to the ongoing discourse regarding the efficacy of market timing. I demonstrate the impact that timeframe reference can have on the perception of risk, showing that market timing can resemble an option strategy in the short-run while it is more accurately described as an allocation shift away from the risky asset. Absent the presence of serial autocorrelation and over any time horizon, this allocation shift is highly inefficient as it can magnify volatility (measured as variance or standard deviation) relative to a return equivalent buy-and-hold allocation to the risky asset and provides inferior downside protection as well. However, market-timing's shortcomings as a down-side-protection strategy are likely to be masked over shorter observations periods, particularly if the analysis omits an apples-to-apple comparison to a return equivalent buy-and-hold strategy. Serial autocorrelation improves the outlook for market timing in terms of return, volatility and down-side risk, but the level required to reach a risk-adjusted break-even is likely to be higher than has been present in the empirical record. I utilize techniques which are admittedly elementary in order to develop and document the key observations in way that is hopefully more accessible to a specific target audience - students in early statistics / pre-calculus courses with an interest in continued studies in finance and investing and investors with less exposure to more formal conventions of notation. Advanced students/practitioners will find this treatment a bit unorthodox, but hopefully interesting nonetheless.