6. You have implemented a butterfly spread whereby the strategy will make money if the stock ends up between $44 and $56 (8 months from now). The stock currently trades at $48, its historical arithmetic average return is 12%, and its standard deviation is 30%. Compute the probability that you face of making a profit. The natural logarithm of the stock In(S+) is normally distributed with: mean = variance = sigma = The probability that In(S) is less than In(56) is thus: The probability that In(S) is less than In(44) is thus: The probability that In(S) is between In(44) and In(56) is therefore: The probability that S is between 44 and 56 is therefore: