Synthetic CDO

Hey everyone!

I need your help with understanding the mechanics of synthetic CDO. What I mean…Let’s say I have a pool of loans worth $1 bln. An average interest rate is 10%. Then it’s put into SPE and sold to investors for $1 bln. Now investors have a legal right to those cash flows from the pool of loans and expect to earn 10% (minus bank commissions). So the expected return is 10% (an average), it’s clear that it will be different for different tranches, but an average return is, let’s say, 10%.

But what is happening with synthetic CDO? LEt’s say I have the same pool of loans worth $1 bln with average int rate 10%. In the case of synthetic CDO a bank doesn’t rly transfer underlying assets but buys a CDS from another bank. He receives insurance in case of default, but in exchange, he pays an insurance premium (lets say 2% out of 10% interest rate). Now those cash inflows packed into SPE and sold to investors for which amount? For the value of subordinate tranches so the super-senior tranche isn’t funded? Does it mean that the expected return for investors is 2% (minus bank commissions)?

I can not understand how synthetic CDO generates a return on investment not less than cash CDO taking into account that actual cash inflows will be significantly lower, because insurance premiums are significantly lower than an interest rate of the underlying assets.

What I miss there?