ZURICH, Jan 29 (Reuters) - UBS and Credit Suisse lost some ground in their combined share of the Swiss funds business last year, the Asset Management Association of Switzerland said on Monday, predicting that this would fall further.

The market share of the combined bank, which became a single entity last year after UBS stepped in to rescue Credit Suisse, fell to 37.6% in 2023, down from 39.3% the previous year.

The association's head, Adrian Schatzmann, said he expected the market share of the combined bank to further drop as UBS integrated Credit Suisse and merged some of their funds.

He said some investors also wanted to avoid too large an exposure to just one financial institution.

Swisscanto, BlackRock, Pictet and Swiss Life , are among those who benefited, the association said.

Overall, the volume in the Swiss fund market rose by 3.7% to 1.37 trillion Swiss francs ($1.59 trillion) in 2023. The association attributed this growth primarily to the favourable development of the financial markets.

For the Swiss asset management market as a whole, the association estimated that assets under management grew by around 5% to 3.02 trillion in 2023.

Switzerland is now the third most important asset management location in Europe after Britain and France according to a report published by the European Fund and Asset Management Association. It is followed by Germany. ($1 = 0.8631 Swiss francs) (Reporting by Noele Illien; Editing by Alexander Smith)