As predicted back in October, dollar LIBOR is now being priced (roughly) off certificate of deposit (CD) rates. Imagine being a bank's treasurer responsible for submitting LIBOR quotes to the BBA. If you can't justify how you obtained your rate and someone accuses you of LIBOR manipulation, it could cost you your job and more. The sources of LIBOR rates were supposed to be quotes on interbank loans. But unsecured interbank lending volumes have been suppressed since the financial crisis. In fact current levels are similar to what they were in the 80s (see chart below). And most of the activity is in the overnight markets with very little transacted at maturities of one month or greater. (Note: some confuse the sources of LIBOR rates, such as interbank lending, with products that price using LIBOR rates, such as interest rate swaps. Here we are discussing the sources.)
With little to go by in the way of actual quotes, setting these rates becomes a real headache for banks. By pricing LIBOR off something that's highly transparent, like CD rates, makes the quotes easier to justify. After all, a CD rate is where a bank is willing to borrow money for a fixed term - which is what LIBOR is supposed to be. That's why LIBOR has been fixed at a fairly constant average spread to CD rates. The 3-month LIBOR is now roughly 7 basis points above the 3-month CD rate (note that the CD average here includes retail quotes - larger term deposits yield more and the spread of those large CDs to LIBOR is even tighter).

Ironically CD volumes are declining as well. But as long as banks continue to openly quote the full CD term structure (across different maturities), banks will use the CD curve as a guide to set LIBOR rates.

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Ironically CD volumes are declining as well. But as long as banks continue to openly quote the full CD term structure (across different maturities), banks will use the CD curve as a guide to set LIBOR rates.
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