We know that, taken every discount curve, it's possible to calculate its forward rates according to our tenor preferences.
We know also that it's actually possible to extract an implied term structure from every discount curve simply using the appropriate forward rates.
This is indeed true for risk free discount curves, because the arbitrage-free assumption which returns the forward rates is fair.
Now let a risky discount curve, that is, every discount curve obtained from liquid issues' yields possibly interpolated and bootstrapped... and so on.
- does it make sense to extract an implied term structure from it like we're used to do with a risk free zero rate curve?
- Is the implied term structure obtained in such a way an arbitrage-free forecast of the future yield curve shape?
- If not so, is the assumption that allows to calculate the forward rates valid for risk-free curves only?
- Does it make sense to obtain an implied term structure from, say, a CDS spread curve? Why?
- If the answer to 5. was affirmative, would that implied term structure be an arbitrage-free forecast of the issuer's default risk?