  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.
