I derive practical formulas for optimal arrangements between sophisticated stock market investors (continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e., the market portfolio). Rather than, say, the...

This paper explores the impact of low (but) positive and negative market interest rates on euro area banks' net interest margin (NIM) and its components, retail lending and retail deposit rates. Using two proprietary bank-level data sets, I find a positive impact of the level of the short-term...