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Every company is, of course, different so let me make some general observations. In the offices of major carriers an Associates Degree is not much of a door opener. With that said lets consider what skills are of most value and how to acquire them.
I always wished that I had spent a couple of years more moving up the Underwriting ranks because "product knowledge" is one of the most valuable traits that one can bring to the table in almost any role in your industry.
Clearly, a CPCU designation will help you both in terms of product and industry knowledge while raising your profile with your employer. If you have proven your worth as a people person and can build your reputation as a knowledge repository other doors will open to you and you will see what additional degrees, designations or experience will be needed to take those steps.
One of my last acts before retirement was to convince a Business Analyst that they had the systems, product and people skills to take a step up to a Marketing position in another state. The individual was hesitant but, in the years since has done very well in that Marketing position.