In an upward-sloping yield curve, the Z-DM will be below the DM. Why is this?

Last week I sent an erratum to CFA Institute on this one; I’ve done a few examples in Excel and for an upward-sloping yield curve the Z-DM always comes out higher than the DM.

If I hear anything from them, I’ll post it here.

Thanks a lot sir…

so did you hear anything from the institute ? still not able to understand

Nothing.

The discount margin is the fixed add-on to the current MRR rate that is required to reprice the bond considering a change in the perceived credit quality of the issuer.

The forward rate curve used to (re) discount the bond is flat. It does not take into account the term structure of interest rate.

The Zero Discount Margin (Z-DM) is the parallel shift to the forward MRR curve that is required to reprice the FRN.

This time, the term structure of interest rate is not flat.

And we also consider the same assumption considering the change in perceived change in the issuer’s credit quality.

In short, If we consider an upward yield curve, the Z DM is the DM + the yield add-on considering the upward yield curve.

It means that the discount rate used to reprice the FRN is higher, hence his theoretical price will be RELATIVELY LOWER than the price of the bond repriced at a then HIGHER discount rate. So the Z DM will NEED to be lower considering an upward sloping yield curve.

It’s a bit simplistic because if the MRR goes up the coupon also goes up so we could assume that even if the yield is upward sloping than the HIGHER discount rate in the denominator will be offset by a HIGHER coupon in the numerator (remember that the FRN pays the MRR plus a constant spread which rarely changes).

My intuition is that in the denominator there is a geometric progression and in the numerator an arithmetic progression hence the denominator will eventually be HIGHER than the numerator.

Hence the bond price will be LOWER repriced in this new environment (HIGHER discount rate) and the add-on required (Z-DM) NEEDED to reprice the bond will be LOWER ( LOWER discount rate) in an upward sloping yield curve then the DM.

What can happen is that if the maturity is too short and the accrued interests are not precisely taken into account the result can be misleading.

Hope this helps.