Certificates of Deposit : credit spread?

In a previous post, I mentioned that one possible explanation for why two identically termed CDs available from two companies might have different yields.  I'm not so sure any more.  In the US anyway, there is the FDIC system, which covers short dated CDs up to a quarter of a million dollars per person per bank.  It ought in principle to be possible for one person to pay an intermediary to spread around any arbitrary sum across N banks such that no one bank gets more than a quarter of a million dollars of his money.  In other words, it ought to be possible to put much larger sums in CDs, if you so desire, and receive the US government's full backing.  Maybe the net effect of this possibility is to drop off the credit risk associated with you having lent an institution some of your cash.  If your CD was with Lehman Brothers in 2009 versus Wells Fargo, then if it wasn't for deposit insurance then you'd expect to get a higher yield for leaving your cash with Lehman.  This yield differential $y_{L}$ versus $y_{WF}$ is a kind of credit spread.  The credit spread is the little bit extra you expect to get for leaving your cash with an institution which could go bust.  But perhaps FDIC pushes both of these rates down towards a common $y$, since the deposit insurance takes virtually all of the (domestic currency valued) risk out of the saving.  This therefore must be a constraint from above on CDs.  You can offer no more than $y_h$ since any higher is effectively ignoring the FDIC factor.  

And the constraint from below must be bounded by inflation: since if the CD supplier offers a nominal rate which is lower than expected inflation $y_{l}$, then capital is being constantly eroded.  It does not make sense for an economic agent to lend his money and get back less in real terms than he lent.  This window $y_l \leq y \leq y_h$ is probably quite narrow, meaning the product is more or less going to keep your cash safe from inflation, probably.    The 'probably' comes from many factors, not least of which is the fact that no-one can predict future inflation, even over a short time period, with any certainty, so there'll be a prediction error in the offered near-inflation rate.

CD providers like to throw in extra terms and conditions on the purchase of a CD, all if which can affect the valuation.  This makes it harder for customers to do side-by-side comparisons.  This is a familiar trick.  The CD I have been describing in the last couple of postings has been as simplistic a schematic CD as you could imagine.

All of this is a bit too vague.  I'd like to continue thinking about the rate implied in CDs, but before diving into some detail on CD rates, I'd like to pull back and ask a general question: what goes into a rate in the first place?  What factors make up a rate?  What risk are you taking in lending your cash to someone else for a while?