[python] Caesar Cipher Function in Python

I'm trying to create a simple Caesar Cipher function in Python that shifts letters based on input from the user and creates a final, new string at the end. The only problem is that the final cipher text shows only the last shifted character, not an entire string with all the shifted characters.

Here's my code:

plainText = raw_input("What is your plaintext? ")
shift = int(raw_input("What is your shift? "))

def caesar(plainText, shift): 

    for ch in plainText:
        if ch.isalpha():
            stayInAlphabet = ord(ch) + shift 
            if stayInAlphabet > ord('z'):
                stayInAlphabet -= 26
            finalLetter = chr(stayInAlphabet)
        cipherText = ""
        cipherText += finalLetter

    print "Your ciphertext is: ", cipherText

    return cipherText

caesar(plainText, shift)

I realize that this answer doesn't really answer your question, but I think it's helpful anyway. Here's an alternative way to implementing the caesar cipher with string methods:

def caesar(plaintext, shift):
    alphabet = string.ascii_lowercase
    shifted_alphabet = alphabet[shift:] + alphabet[:shift]
    table = string.maketrans(alphabet, shifted_alphabet)
    return plaintext.translate(table)

In fact, since string methods are implemented in C, we will see an increase in performance with this version. This is what I would consider the 'pythonic' way of doing this.