Fund Manager Duty To Invest?

Hi, are fund managers generally obligated to invest as much of the fund as possible? I understand there might be different methodologies, policies, rules and guidelines, but generally speaking, are they supposed to leave as little as possible in cash position?

I have a small robo-investor account and I DCA weekly into it, and I notice they haven't used my cash at all last week. I'm not bothered by it, just wondering because my fund usually got used up on the same day of my DCA.

And on a similar note, as a thought experiment, if you are given $10,000 to invest and will only end up with two outcomes, which one would you prefer?

1. You keep buying dips until all $10,000 is exhausted, and the market is still dipping.
2. You keep buying dips slowly, by the time the market has recovered, you still have $5K left in cash.