Separating Bond Coupon Effects from Short-Term Relative Value

# Does it make sense to adjust a bond spread for price/coupon effects?


# Does it make sense to adjust a bond spread for price/coupon effects?












I have come across the practice, in the wild, of bond OAS being adjusted for the price of a bond. The idea expressed to me was something like the following. A $\$90$ corporate bond with a 10 yr maturity may have a different spread than a 10yr par bond (same issuer). Because of this empirical difference, we have to think about making a "price adjustment" to the $\$90$ bond's OAS in order to sensibly measure the relative value between the two bonds.

My understanding is that this concern is based on

- Coupon effect on yield. A bond can be considered to be the sum of an Annuity and a Zero. Bonds trading at a discount will have a yield higher than its coupon, and hence a greater proportion of its value comes from the Annuity, compared to the par bond. This will be reflected in a slightly higher spread for the discount bond, in the absence of other factors.

- Liquidity/uncertainty difference between the bonds. Par bonds are more likely to be new-issues and may command a higher/lower spread based on liquidity/uncertainty factors.

I have no insight into what formula these traders are using, but trying to eliminate coupon effects seems to me wrong-headed, since the coupon-effect is measuring a real financial difference between the cash flows of the two bonds. If you remove the effect you ignore this difference, which cannot be arbitraged away as far as I can tell.

Are coupon/price adjustments to corporate OAS/spreads wise in some situations?

If so, how is this done? How to interpret and use the output?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/51133

There is a difference between short term RV and long term RV. It is of course not useful to take a short term RV position with a relative value of 5bps if it will have a range of 4-6bps in the foreseeable future, but in the long term it is likely to be positive.

The effects you mention are valid reasons why bonds from the same issuer cannot be fully priced from a singular credit curve. There are others. Take a European government bond curve for example and the reasons why a bond may be cheaper/more expensive than the derived curve might be:

- Nominal and free float in issue, impacting liquidity.

- On the run/ off the run liquidity status.

- Transparency of the price as a CTD of a futures contract.

- Coupon effect (i.e. size of coupon) and corresponding cost per 1eur nominal.

- Monthly series (i.e is it the Mar-Sep coupon series or the Jun-Dec series) for stripping.

- Whether there is a Collective action clause (CAC), i.e. it was issued after a certain date.

- The underlying repo market for the bond and whether the bond can be included as GC in specific tenor buckets.

- Probably more...

As a trader I tried to employ certain techniques to evaluate the 'short term' RV by stripping out the 'long term' RV. I would not be adverse to adjusting the OAS/spreads although this would not necessarily be the only way of doing it.

In a completely generalist way you are building some pricing (curve) model, $T_{\theta; \phi} $, with some (fixed) hyper-parameters, $\phi$ and some variable (calibrated) parameters, $\theta$ that attempts to price your set of bonds with minimal deviation from market prices;

$$ \min_{\theta} \sum_i || T_{\theta, \phi}(b_i) - P(b_i) ||^2_2 $$

where $P(b_i)$ is the price of bond $i$ in your set.

The fact that you might vary some of the fixed hyper parameters, $\phi$, i.e. the interpolation style of the curve, or whether you permit the OAS spread flexibility or/not should not matter, it is simply a model which you can backtest for its generalist predictive power and choose to adopt it or not.

EDIT

The difference between long term RV and short term RV is a matter of holding period of your trade. Suppose you construct a credit curve and value two bonds against it: bond1 (10Y) is 5bps cheap and bond2 (10Y) is 5bps expensive. You might instinctively think it is better to buy bond1. But a historical analysis in the last year suggests bond1 was, on average, 7bps cheap and bond2 was, on average, 7bps expensive to your model. Now if you are to investto hold to maturity (long term) then bond1 is a better purchase on an RV measure. Your standardised mode of valuation has been to equate the cashflows without further considerations, and that is sound from a HTM perspective. If you are taking a trading position for the next 2 months then it may well be that bond2 is a better purchase, since it may well revert to its more expensive mean state in the short term. In this case it would have been better to attempt to strip out the nuances of each bond first before conducting the RV analysis, whatever those nuances maybe (possibly OAS).

There is no unified theory for what you are asking and it requires your own subjectivity and perspective, as well as how it will be incorporated into your risk management.

## Answer by Grognard (score 0)

https://quant.stackexchange.com/a/76564

Very interesting question as I have come across an idea a bit similar for pricing new bonds compared with the existing curve of the issuer. The idea is that the spread of bond trading at a discount, say $90, need to be adjusted to be able to price a newly issued bond at 100 (keeping all other factors similar). So typically, market participants will add 1 bps per point below par to reflect an adjusted spread to the outstanding bond. For example, the outstanding bond is trading at 90 with a spread of 40 bps so we need to adjust the spread by 10 bps which makes it 50 bps and this gives us where the issuer can print the new bond (keeping all other factors similar: maturity, covenants calls etc...). Reasons for this adjustment are:

- You need less cash to acquire the same amount of bonds when you buy the discounted bond. So, investors prefer to buy bonds that trade at a discount and thus a new bond priced at 100 will need to offer a higher spread.

- When there is a default on the bond, the CDS will pay 1-recovery rate, so as a bond holder you are better off holding the bond trading at a discount because the CDS payoff will be higher when you purchases the bond at a discount rather than par.

The main drawback I see of doing that is that a low cash price bond has much more sensitivity to interest rate risk since more of the payments come at the end of the life of the bond, at maturity. So, is it worth doing the adjustment? I am not sure. It probably makes senses when you expect a default to happen or when the maturity of a bond is far away in time. What do you think? DOes it relate to your question?