This definition is close to the one that I am using but includes mutual funds.
The definition used by Adrian and Shin (2010) is also close to the one that I am using but includes public financial institutions (specifically, GSEs and agency and GSE-backed  BIS central bankers’ speeches  1  In the first quarter of this year, U.S. financial firms held credit market debt equal to $ trillion, or 2.2 times the gross domestic product (GDP) of the United States.