Foundation/Endowment funding operations

The more responsibility a foundation or endowment has for funding the ongoing operations of an entity the lower the risk tolerance for the foundation or endowment. Has anyone found a % of funding requirement that "flips" the tolerance from average to below average? Ie if a foundation is responsible for 50% of operating expenses it average, but if it provides 60% it should be more conservative.

I know you need to look at the entire context of the problem to decide ultimate risk tolerance but its something that has been bugging me. Thoughts?