The Mathematics of Market Timing

TL;DR

This paper uses mathematical modeling and historical data to analyze market timing strategies, revealing that successful timing is as likely as not and often results in below-median returns, challenging their effectiveness.

Contribution

It provides a simple mathematical framework to evaluate the feasibility and likely outcomes of market timing, showing that optimal timing paths are indistinguishable from random sequences.

Findings

Market timing returns are asymmetrically distributed with a high chance of below-median outcomes.

Historical optimal timing paths resemble random sequences, indicating limited predictive power.

Median market timing return closely matches a static 60:40 portfolio return.

Abstract

Market timing is an investment technique that tries to continuously switch investment into assets forecast to have better returns. What is the likelihood of having a successful market timing strategy? With an emphasis on modeling simplicity, I calculate the feasible set of market timing portfolios using index mutual fund data for perfectly timed (by hindsight) all or nothing quarterly switching between two asset classes, US stocks and bonds over the time period 1993--2017. The historical optimal timing path of switches is shown to be indistinguishable from a random sequence. The key result is that the probability distribution function of market timing returns is asymetric, that the highest probability outcome for market timing is a below median return. Put another way, simple math says market timing is more likely to lose than to win---even before accounting for costs. The median of the market timing return probability distribution can be directly calculated as a weighted average of the returns of the model assets with the weights given by the fraction of time each asset has a higher return than the other. For the time period of the data the median return was close to, but not identical with, the return of a static 60:40 stock:bond portfolio. These results are illustrated through Monte Carlo sampling of timing paths within the feasible set and by the observed return paths of several market timing mutual funds.