Each bank is different and there is no mathematical equation (unfortunately), but I wondered if there was a general rule of thumb so to speak.

Mathematically, it actually doesn't matter whether the syndicator takes part of the money and put it back in as an investment (as the OP is assuming) or go blow it all in Vegas.  

You seem comparatively young, which gives you a mathematically higher threshold for risk (although your personal threshold/appetite should also be considered).

Those reasons all appear to be mathematically sound.

@Brian Volland- the statement about ROI on paying down any debt early was just a general statement of mathematical fact. 

I am a student at Boston University studying Mathematical Finance.

If we find assets again in a range that makes sense mathematically, we'll go back in.

Mathematically, I could be entirely wrong.

If the Fed pushed overnight rates to zero and nominal 10 year rates went negative it would mean the deflationary environment is accelerating - which mathematically would mean "real" rates are rising and the risk premium on loans would spike.

The mathematical equilibrium.