Learn Turkish: Borsaya gireli aldıklarımı zararına sattım. - Since I entered the stock market, I sold what I bought at a loss.

This is the headless use of the -dık participle from your current lesson. It is built from al- (buy) + -dık (participle) + -lar (plural) + -ım (my) + -ı (accusative). Because the noun is obvious from context, Turkish simply drops it and attaches the plural, possessive, and case endings directly to the participle. It acts as a noun meaning "the things I bought".

What is the grammatical function of the final -ı on aldıklarımı?

It is the accusative case marker. The core word is aldıklarım (the things I bought). You add the specific direct object marker -ı to the end because these things are receiving the action of the verb sattım (I sold).

I don't see a standalone word for "since". How does gireli mean "since I entered"?

The suffix -(y)AlI means "since doing" the action of the verb. Attached to gir- (enter), gireli means "since entering". Notice that it does not take a personal ending like "I"; the person performing the action is understood from the main verb sattım.

Why does zararına use the dative case to mean "at a loss"?