what's the best strategy for such play?

If you observe that S&P500 roses in certain period 15 out 20 times in the past, historically.

What's the best strategy for such play?

 

Depends on the size of and the time required for the move.

 

Time is 1 month;

but the size of the move is unknown...

of course you can collect stats of the sizes of the past 20 movements... 15 of them were positive, 5 of them were negative. And then you have a very crude distribution.

 

1) Wilmott.
2) What has been the average magnitude of the upmove AND downmove?
3) ?......a debit-spread constructed so that the long-leg is struck at-the money OR slightly in-the-money and the short-leg is struck slightly beyond the magnitude of the expected move of the time-frame you are looking at.
4) The other "rocket scientists" here can enhance that.

 

With the limited amount of information you have, an option position is not best for the circumstances.

Your best bet is long ES (the S&P mini-futures).

You are making a directional bet without regard to the greeks. Futures are best for that. If you have an IV prediction too, then there might be a more appropriate option strat.

 

Size of the move is essential to determine ideal strategy. Programs like Optionvue (last I saw it) will scan the chains and determine maximum performance. If moves are small, options may not be the best vehicle. If large, outright calls. If medium and risk averse, perhaps spreads.