Abstract: It has been widely believed that the overall systemic risk instead of the individual risk should be paid more attention in the modern financial system. Meanwhile, the investment portfolios diversification theory which benefits the individual bank in traditional economics is no longer desirable as a result of the systemic risk. Therefore, the relationship between investment portfolios diversification of banks and the systemic risk still needs a further study. In a simplified financial market, the balance sheet is used to describe the connection between banks and assets, then a mathematical model is set up to depict the bankruptcy boundary of banks. The difference and relationship among individual risk, systematic risk, systemic risk with interbank loans, systemic risk with both fire sale and interbank loans are respectively studied based on the mathematical model. Finally, the mathematical model is numerical tested according to actual parameter values in the financial market and the results show that, investment portfolios of different banks will become similar with each other because of diversification which incurs the systemic risk more easily. The existence of fire sale and interbank loans will also increase the systemic risk. Therefore, the systemic risk can be controlled to a certain extent by reducing investment portfolio diversification and interbank loans ratio and this result provides a high reference value for the supervision of systemic risk.

Key words: systemic risk, investment portfolios, diversification, interbank loans, fire sale