The Journal used this risk-premium information to construct an alternative “borrowing rate” for each of the 16 banks. There were two steps to the process: First, the Journal estimated what Libor would be if there was no risk that any of the banks would default. Then, it added each bank’s risk premium to that number, yielding 16 different “borrowing rates.”
If there was no risk that any of the banks would default, “Libor” would be the same as the OIS fixed leg with the same tenor. CDS premium are above Libor by arbitrage and it is not correct to use Libor-CDS spread to get a “risk-free Libor”, we already know what it is [OIS fixed leg].
To back the default risk out of Libor, the Journal made one important assumption: The cost of default insurance on the most credit-worthy bank provides a reasonable estimate for the default-risk compensation contained in Libor. That’s because all 16 banks have been reporting nearly the same Libor rates — as if they were all equally credit-worthy.
On April 16, for example, the lowest rate reported by the 16 banks to the Libor panel was 2.72%. The cheapest default insurance was for Bank of Tokyo-Mitsubishi: 0.25 percentage points. So the Journal’s estimate of what Libor would be if there were no risk of defaults came to 2.72 minus 0.25, or 2.47%.
Pre-credit crunch, pre-august 9th 2007, when OIS-Libor spread was below 10 bp, the Journal calculation would have resulted in a “risk-free Libor” below the OIS fixed, a proxy for a risk-free rate.