I want to explain the relationship between diversification, bank risk and performance, and provide me any published quantitative papers related for this issue.
You can study this paper and see if it helps even though is is revenue diversification in credit unions: http://www.sciencedirect.com/science/article/pii/S2213297X15300021
in general, the diversification, of investment portfolio for example, associates with lower risk. for instance, if we have a portfolio and we invest in the financial securities of many different sectors and in many different countries, this will reduce the risk of loss, because if there is a problem in one sector or a country, it would not be in the other sector or country. however, since the diversification policy is more conservative, this may lead to lower returns than if we would have invested in a profitable company with higher returns.
I am no specialist in your topic but I just want to remind you of the more difficult diversification of default risk, cf. Amato/Remolona, BIS Quarterly Review, December 2003, pp. 51. As fiexd income (deposit and loan) is the main business for commercial banks and default risk is the main risk for fixed income, you should be aware of this.