Yes...bet sizing is something I worry about a lot, but it isn't clear to me how to apply the kelly criterion to a game where the risk/reward is mostly unknown and only based on a hunch.
You could make a table where row is guessed probability(input to Kelly criterion) and column it's actual probability and cells contain expected value and expected log value. And pick something which looks reasonable.
One better-than-nothing way is to look at historical data:
Looking at the closing price for each trading day, count how many times the stock ended higher and how many times it ended lower than the previous day.