In its early days, the word portfolio was sometimes spelled port-folio or portefolio, but when it was first attested in a 1713 collection of stories, it was Porto Folio. This hints at the noun's origin in Italian portafoglio, which meant "case for carrying papers" much like one of the definitions today. That's composed of the verb portare, or "to carry", and the word foglio, "sheet" - the connection should be obvious. Portare, through Latin, ultimately derives from the Proto-Indo-European root per, meaning "traverse", and foglio traces to the Latin word for "leaf", folium (this is the etymon of foliage, frond, foil, and other such words). That in turn is from Proto-Indo-European bleh, which could be defined as "blossom" or "flower". So, if you go really far back, a portfolio is a "blossom traverse" - as if "carry sheet" wasn't cool enough already.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.