Position Sizing Puzzle

I have a question about risk management that keeps bugging me. I have yet to reach a satisfactory conclusion in my mind about it so I thought I'd get a feel for what others thought.

Example:
Say you have two trades you are considering in EURUSD. You aren't trying to decide between them because you plan to trade them both but your concern is how much to risk on each one. Assume for the sake of argument that they are uncorrelated trades occuring at different times and have the same probability of success.

One trade is a short-term trade that you expect will last a day at most. Your stop is 40 pips away and your target is 80 pips way for a 2:1 reward:risk ratio.

The next trade is a longer-term trade on a daily chart that you expect might last for weeks given how far away the target is. Your stop is 200 pips and your target is 400 pips, again for a 2:1 reward:risk ratio.

Before you arrived at this dilemma, you had a plan to never risk more than 0.25% of your equity on any one trade. If you have $100,000 then you would risk $250. So this would mean trading 62,500 units for the short-term trade and 12,500 units for the long-term trade.

This is where the head-scratching comes in. Sure, this is what is necessary to follow your rule but does it really make sense? Does the simple fact that one trade is at a higher timeframe (inevitably leading to bigger stops) mean that you should trade less size? If you don't follow your rule, then you risk losing 5 times as much or 1.25% on the long-term trade. But maybe that's reasonable, you think to yourself, because doesn't the fact that you might hold the trade longer mean that you really are following your rule in a way? After all, if you were willing to lose 0.25% in one day in a short-term trade, wouldn't it be reasonable to lose 1.25% in a trade that might drag out over 5 days? But then again, you have no real way of knowing ahead of time how long a trade will last. Arg!

To look at it another way, how would you deal with both trades winning? Would you be able to swallow that you made $500 on both trades by following your rule when the long-term trade captured a much bigger move in the market and took longer to pan out. The fact that more time passed to realize the same gain means you really made less on an annualized basis.

So there you have it. What would you do? Treat all trades the same because of your risk rule or be flexible based on some rule related to timeframe. If the latter, what is that rule and why?

if the probability is the same on the long and short term trade, of course you would risk the same amount as you pointed out. the only GOOD reason to change your per trade risk is if the probability is better on one trade over another. but then you have to battle with the question...why take the inferior trade at all? for this reason, i either take a trade with my standard risk, or i dont take it...there is no in between for me. this is an easy concept to understand but very hard to accept. its all about understanding the math of probabilities (love the new smiles btw)

Another question... how does this effect mid-trade adjustments to risk? For instance 3 days after your long term trade opens you see a chance to move your SL to break-even and remove the risk.

If you're going for a risk per day approach, as opposed to a risk per trade approach... would you increase your trade size then in order to keep that constant risk level? If not, how do you justify the change in risk?

Once I reach of point of funding a stop, either through moving the stop to break even or removing a portion of the trade so that if it goes back to the original stop I would break even, I consider the risk at 0.

I will rarely add to a position. Once a stop is funded, I move on to another pair when a trade sets up.