Foreign investment in the banking sector may be subject to a reciprocity requirement if foreigners hold more than half of the votes or otherwise control a Swiss-incorporated bank.
"Art. 1
1 This law governs banks, private bankers (individual reasons, general partnerships and limited partnerships) and savings banks. All of these companies are hereinafter referred to as banks.
2 Natural or legal persons who are not subject to this law may not accept deposits from the public on a professional basis. The Federal Council may provide for exceptions if the protection of depositors is guaranteed. The issuance of loans is not considered to be accepting deposits from the public on a professional basis.
3 This law does not apply in particular:
a. to stockbrokers and brokerage houses which limit themselves to trading in securities and carrying out related transactions directly, without carrying out banking activities;
b. asset managers, notaries and business agents who limit themselves to administering their clients' funds without carrying out banking activities.
4 Only institutions that have received authorization from the Federal Financial Market Supervisory Authority (FINMA) as banks may include the term “bank” or “banker” in their corporate name or in the designation of their social purpose or use it for advertising purposes. Art. 2, al. 3, is reserved. 
5 The Swiss National Bank and the mortgage bond issuers are only subject to this law in so far as it expressly provides.
[...]
Art. 3
1 The bank can only start its activity after obtaining authorization from FINMA; it cannot register in the commercial register before having received this authorization.
[...]
Art. 3bis 
1 FINMA may also make the granting of the authorization to establish in Switzerland subject to the fulfillment of the following conditions, in the case of a bank organized under Swiss law but which is in foreign hands , a branch or the permanent representative of a foreign bank:
a. reciprocity is guaranteed by the states where foreigners holding qualifying holdings have their civil domicile or registered office; the differing provisions of international commitments are reserved;
b. the corporate name of the bank must not lead to the conclusion that the establishment is Swiss or suggest such a character;
c. ...
1bis When a bank is part of a financial group or a financial conglomerate, FINMA may make the granting of its authorization subject to the approval of the competent foreign authorities.
2 The bank is required to inform the National Bank about the business it deals with as well as about its relations with foreign countries.
3 The provisions of para. 1 apply to a bank organized under Swiss law and in which the qualified foreign direct or indirect participations amount to more than half of the votes or which is otherwise dominated by foreigners. The following are considered foreign:
a. natural persons who do not have Swiss nationality and do not have a business permit;
b. legal persons and partnerships which have their registered office abroad or which, if they have their registered office in Switzerland, are in the hands of foreign persons within the meaning defined under let. a.[...]" (Federal Banking Act (RO 51 121, 8 November 1934), last amended on 1 January 2020, Articles 1, 3 and 3bis [google translation])
Federal Banking Act (RO 51 121, 8 November 1934), last amended on 1 January 2020, Articles 1, 3 and 3bis 
[<a href="">https//www.fedlex.admin.ch/eli/cc/51/117_121_129/fr</a>]