Even if you put a short into the formula you will still end up with a functional droi, it will just be negative. Let me give a couple of simple examples:
Stock 1 current value of 25
Stock 1 will adjust to 50 in 10 days
Using the long formula you end up with:
[(50 / 25) ^ (1 / 10)] - 1 =
[(2) ^ (.1)] - 1 =
[1.072] - 1 =
.072
Multiply by 100 gives you 7.2% meaning your daily return on investment (DROI) will be about 7.2%
Now lets try short
Stock 1 current value of 50
Stock 1 will adjust to 25 in 10 days
Using the long formula you end up with:
[(50 / 25) ^ (1 / 10)] - 1 =
[(.5) ^ (.1)] - 1 =
[.933] - 1 =
-0.067
Multiply by 100 gives you -6.7% meaning your daily return on investment will be about 6.7%
The negative realistically means that the price is dropping that percentage daily, but for our purposes it just means short.
Now these two stocks also give a good example of how droi can be even more helpful. Since one starts at 25 and goes to 50 and the other starts at 50 and goes to 25 in the same ten days, in the end you will be making 25 for both (or a 100% total ROI). But realistically longing Stock 1 is better for you since you tie up less money over that ten days to make that 25. The values you get at the end show this since Stock 1 has a 7.2% DROI and Stock 2 has a lower 6.7% DROI. These are just a few things to keep in mind. You shouldn't base your entire play style on DROI, but it is a very useful tool to let you know if you are going in the right direction.