# Credit Spreads and Relative Value : floating vs fixed bond

I would like to study if, in these weeks during the italian credit crisis, floating govy bonds were more resilient than fixed govy bonds. For each floating issue (CCTS) I chose the fixed issue with the closest maturity.

What should I compare to analyse relative values? I tried two ways:

• Yield-to-maturity (for fixed bonds) vs Fixed-equivalent-yield (for floating bonds). Historical fixed equivalent yields are estimated using forward rates for cash flows.

• Asset swap spread for both (fix and float).

The problem is that I have different results for the two options. In the first case CCTs seemed to have higher yields, in the other case CCTs seemed to have lower spreads.

It could be related to the estimations I did, in fact I couldn't download historical ASW spreads and fixed equivalent yields for floatings and I had to calc them.

I read reports where the relative value analysis was made using discount margin for floating bonds and asset swap spread for fixed bonds, but I don't understand how.

Theoretically speaking, which approach should be used? Thank you

## 1 Answer

My understanding is that you may have the following scenario:

• A nominal Italian bond paying a coupon, $c\%$, is equivalent to,
• A CCT-eu paying a floating coupon of Euribor 6M combined with receiving fixed on a cleared EUR IRS,

These structures inherently contain the same delta risk but suppose you could buy a 10Y fixed rate Italian GB and sell a 10Y CCT-eu and pay fixed on a EUR-IRS, then (if the rates/coupons hypothetically align) you have no cashflows forecast initially and have the same ItGB credit exposure, since you theoretically have zero exposure to ItGBs overall.

But after a market movement the credit exposure is different. If IRS rates fall while nominal Italian GB rates rise (reflecting Italian debt worse credit outlook) then the IRS will have a negative mark-to-market NPV (say -10), while the floating bond will have a substantially higher MTM-NPV (say +15), compared to just the fixed Italian bond (say -5). Note the total NPV is zero but the exposure to IGBs is now +10, whilst to IRS is -10.

Arguably, you are in a worse position if the credit outlook is worse since you have acquired an Italian GB asset as a result of this strategy. This is effectively a second order risk - a credit risk cross-gamma.

For anyone that recognises this effect upfront you might attempt to price this effect accounting for stochastic movements and placing a value on the credit exposure changes. Undoubtedly this 'premium' would factor volatility. But, once priced, if other factors remained the same the difference in price between floating and fixed ItGBs should not necessarily move simply because the market trends up or down.

For the record a similar dynamic exists between IRS and Zero-Coupon-Swaps whose prices should theoretically be the same but due to cross-gamma risks (akin to the credit exposure cross-gamma) have premiums.

The observable might be though that the market, whilst unaware of the credit cross-gamma is reactive and so upon observance of their changed credit exposure hedge by selling their ItGB asset, i.e. fixed rate ItGBs weaken, relatively, (although this will also affect delta away from zero most probably)

I recognise this doesn't necessarily answer the question. I was just following a train of thought and have genuinely never studied or used this, so do take this answer with a pinch of salt and happily question or critique it...