String isn't mutable, every time you change string, you actually create a new string in string pool. That is why, it's better to save index of maximal string in array of strings. But your solution is still clever and understandable.

in opposite to Stream.API your solution is easy to understand

I like your solution : no import.

I like your use of whitespace.

Good aproach (not to long and not to short).
But i wouldn't make a for loop in an for loop. The inner for should be extracted to a method.