Fixed income, YTM, Z-spread

Regarding Fixed income, I have some troubles to make sense of different things I know.

  1. I know that (Z-spread + spot rate across different) equalize future Cash Flows and the market price.

  2. I know the YTM is the discount rate that equalize future future Cash Flows and the market price.

  3. To me it looks like 1) and 2) means that YTM = spot rate + Z-spread. Is it right?

  4. I also know that the YTM is the weithed avergae of the spot rates.

But it seems that 4) contradict with 3) since we don’t need the Z-spread but only the spot rate to compute the YTM.

Could somebody please shun light on what is a conundrum for me. I guess 3) is wrong but I don’t understand why.

YTM is the weighted average of spot rates + z-spread.

For the treasury par (or spot) curve, the z-spread is 0.

For risky corportate bonds, you build a new YTM curve using the spot rates adjusted for the Z-spread. Or build one from market prices directly if they all trade near par.