To be fair though, that's only because of the strict limitations of the OP's thought experiment. If you could bet say 1% of your cash on a stock with your specifications, then assuming the transaction fees aren't a problem you should do so every day.
Well, of course the given setting limits the solutions. For example, if you can invest only a part of your wealth, the Kelly Rule comes into play.
Let's suppose you start with $1000 to invest, and the only thing you can invest it in is stock ABC. You are only permitted to occupy two states:
* All assets in cash
* All assets in stock ABC
You incur a $2 transaction fee every time you buy or sell.
Kind of annoying limitations to operate under. But you have a powerful advantage as well. You have a perfect crystal ball that each day gives you the [probability density function](http://en.wikipedia.org/wiki/Probability_density_function) of ABC's closing price for the following day (but no further ahead in time).
What would be an optimal decision rule for when to buy and sell?