How do I subtract the previous row from the current row in a pandas dataframe and apply it to every row; without using a loop?

you can use pct_change() or/and diff() methods

Demo:

In [138]: df.Close.pct_change() * 100
Out[138]:
0         NaN
1    0.469484
2    0.467290
3   -0.930233
4    0.469484
5    0.467290
6    0.000000
7   -3.255814
8   -3.365385
9   -0.497512
Name: Close, dtype: float64

In [139]: df.Close.diff()
Out[139]:
0      NaN
1    0.125
2    0.125
3   -0.250
4    0.125
5    0.125
6    0.000
7   -0.875
8   -0.875
9   -0.125
Name: Close, dtype: float64

MaxU solutions suits in your case. If you want to perform more complex computations based on your previous rows you should use shift