I believe this is testing a false premise. The premise is, that when investors think the market is going to go up in the next month, they move money into mutual funds, and that when investors think the market is going to go down in the next month, they move money out.

I'm sure some proportion of investors move money in and out of mutual funds based on their market expectations, but I do not believe they do so with a single months time horizon, nor do I believe they are the majority.

I submit that a potentially quite large proportion of investors-- especially in mutual funds-- are not doing this, but are instead moving money into those mutual funds each month as a percentage of their paycheck goes into their 401k or into their savings plan. Further, some large proportion is likely investors moving from one mutual fund to another, while others are cashing out because they retire, etc. I bet a check on your flow dates to see if its correlated with an annual peak in employment change dates (e.g.: what month are people most likely to retire, or change jobs?) might find some correlation.

Worse, if I'm reading it correctly, this plot shows the return of the asset class over the course of a single month.

This means that you're assuming that these mutual fund investors are trying to time the market on the scale of the expected return within a month. This seems implausible to me given that mutual funds are managed and thus not well suited for timing (a lot easier to time the earnings announcement of Google, for instance, than guess what moves a mutual fund manager is going to make in a particular month.)

I suspect that most investors who choose mutual funds have at least a years time horizon, if not 5 years or more.