To forestall what I expect to be a common line of advice, I'd like to point out that maximizing the expected return for the next day can lead to very poor results in the long (or even medium) term. Let me illustrate.
Your PDF for the stock price is the same every day and is pretty simple: it's a fair coin toss. You have 50% probability of earning 101% return and 50% probability of losing all your money (-100% return). The expected return is positive ($5 less transaction fees). This should cause you to invest into this stock every day.
The chances of being left penniless after merely 10 days are (1 - 1/2^10) or about 99.9%.
P.S. A somewhat related issue is the so-called St.Petersburg Paradox which is about three centuries old :-)
I agree, given the daily stock fluctuations, the only way to make money would be to buy and hold over a long period of time and hope the 52 day moving average is in your favor. I would keep it all in cash.
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?