Assume that the forward curve is downward sloping.
If you short a forward contract, you lose on mark to market as the forward price converges to spot. If you borrow cash, you must pay interest.
Is there some other way to get short delta exposure?
Downward sloping forward curve may not be the most accurate statement to get to the heart of your problem (for instance, USDJPY may be downward sloping for different reasons than GBPUSD). It would be more accurate to say the currency you think will depreciate has a higher interest rate than the other. The U.K. has a higher interest rate than the U.S., so that may provide a good example. You think the pound will depreciate against the dollar, so you would want to borrow pounds, sell them, and invest them in short-term dollar deposits. I’m not really sure how you would get around the carry here. That’s sort of the essence of what you’re trying to do and I would guess that any derivative transactions have this effect built-in, as you note with the forward contracts (I believe the Garman–Kohlhagen would reflect the difference between the rates in the value of options).
Well, if you are stuck between a particular pair of currencies, I’d say you’re stuck. That’s one of the things implied when you say “assume the forward curve is downward sloping.” My instinctive response is “if you are shorting because you have a negative view on a currency or currency zone, then you need to short it against another currency that you like with a similar or higher short term interest rate.” The other question is why you want to short in the first place. If you are speculating, then the carry is just the hurdle rate for your speculation. So you can’t short something unless you think it is going to depreciate by more than the cost of carry. If you are hedging, then the cost of carry is simply the price of risk reduction. Would this still be a good investment at x basis points less return (x being the cost of carry), but no currency risk? If so, do it. Otherwise, don’t.
good answer bchad…i’m was dumbfounded by his question…