Is it okay to open this bank account? If not, Why?

My boss, who I've been working for a year wants me to take the managers position at his small business. He wants me to open a business bank account at bank of America for him, under my name, so that I can manage some of the businesses money ( he trusts me enough to manage about 10000 in inventory money). However, he wants the pword to the account. Is there any ID theft problems or etc. that should deter me from doing so?