Estimating Spread Changes for Deeply Discounted Bonds

# Does the spread of discounted bonds behave differently than the spread of par bonds?


# Does the spread of discounted bonds behave differently than the spread of par bonds?












Say that you look up the spread of a particular bond segment, like Norwegian fixed-coupon corporates, on Bloomberg, and it tells you that discount margins increased by 50bps compared to yesterday.

You have yourself a bond in this segment, but unlike most bonds that trade near par, yours is particularly discounted and was trading yesterday at, say, 40 % of par.

Unforunately there is no "spread time series for Norwegian corporates that trade at 40 % of par" on Bloomberg, and you also do not have access to liquid price data for this bond, so you must estimate it by taking the spread increase and multiplying it with the spread duration.

Can you do this using the 50bps increase from the "par bonds", or should an adjustment of some kind be made here? Is there any meaningful relationship between these two segments vis-a-vis the increase in the discount margin?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/85253

A bond trading at 40 cents on a dollar is most likely, but not necessarily, credit-distressed, or even already defaulted. It's also possible, although less likely, that it's a zero-coupon bond maturing in some years and trading since inception at a discount from face value; or that it pays some fixed coupon, and was trading at close to face value at inception; but since then, the interest rates rose a lot, and recently issued fixed-coupon bonds have to pay much more coupon to trade at face value.

The Bloomberg statement that some credit spread (Z-spread would be more common for fixed-coupon bonds that discount margin) of some population of bonds widened 50 bps could mean that each bond widened 50 bps in parallel, or maybe that 1 bond widened 1000 bps, while 19 other bonds tightened 50 bps, resulting in the average change being 50 bps wider, or something else. For the purpose of your question, assume that you checked that indeed all of them did widen 50 bps.

You can't tell much from this bond's price directly. If you know the cash flows that the bond promises to pay, then you can find its credit spread, and compare to the credit spreads of the population that Bloomberg reported. If the credit spreads in the same ballpark, then yours is one of those rare non-distressed deeply discounted bonds, and it's a good guess that whatever common fear caused those other bonds to widen, would have comparable effect on your bond's credit spread. You can calculate your bond's new price from a bumped spread.

However if your bond's credit spread is much wider - if it is a bona fide distressed bond, which is most likely - then the major drivers of its price are the market's perception of this issuer's probability of default (PD) and loss given default (LGD) - what the defaulted bond would be worth after a default, what the bondholders might get eventually from bankruptcy. Nobody knows how this issuer will react to whatever caused the other bonds to widen. However if you know that the credit spread of same distressed issuer's other bonds have moved by some amount, then it's a good guess that your bond's credit spread will move similarly.

Instead of treating credit-risky bonds as interest rate instruments with some inscrutable credit spread, you might gain better insight with the approaches in papers by Tomasz Bielecki and by Duffie and Singleton - try to figure out the PD and the LGD from the price.