The word "asset", especially in the context of your question is a term from accounting. As such, it makes sense to use accounting terms for the translation.
- A house can be considered an asset. This is usually true if you buy the house so that others pay you rent.
- Bankers trade assets, that means the buy things just to sell them later, not because they need them.
The words you found are correct for the accounting terms, but I wouldn't use "Vermögen" for these examples.
"Das Vermögen" doesn't just mean wealth, in the context of accounting it is one possible word to describe the left side of a balance sheet, the side where the assets are listed traditionally. A more specific word is "Aktiva", it refers to the asset side of the balance sheet and doesn't have much other meanings. Another expression is "Aktivseite (der Bilanz)" again for the asset side of the balance sheet. Both "Vermögen" and "Aktiva" would only be used for all assets, not for some. So you wouldn't use them for the trading bankers and while not exactly wrong it would sound strange in the context of the house.
"Aktivposten" is a word for a single asset, not for all assets. The "Posten" part is related to "Position" meaning an item in the balance sheet (or more likely in the appendix).
A house as part of the assets can be called "Vermögensgegenstand".
For the bankers the word "Vermögenswerte" may be better. Most of the time the word "Wertpapiere" (Security) would be appropriate, but the meaning is narrower than assets.
The other (right) side of the balance sheet, the liabilities, are called Passiva or Passivseite.