Low-for-long nominal interest rates have resulted in strong growth in mort- gage lending and real house prices in Switzerland. Domestically-oriented, small banks have mostly contributed to this expansion in mortgage lending while the two big, global systemic banks (UBS and Credit Suisse) have lost market share. We develop a model with two types of banks and monopolistic competition in the deposit and mortgage market, which we calibrate to the Swiss banking sec- tor. In this model, a contemporaneous expansion in the housing market and change in market shares as in the data emerges only if the monetary policy rate is reduced and capital requirements on the big banks are tightened. Any of the two policies in isolation fails to match the empirical evidence.