# 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.

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

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.

• Thanks for the answer, @Attack68. I'm not sure how this relates to the question of whether an "OAS" adjustment makes sense. I understand your answer to be saying something like "maybe it does, here's a hint about how you might backtest such an idea". Maybe your concept of "short term RV" vs "long term RV" is the source of my confusion. Can you connect those to the OAS adjustment? I would really like to understand what you're getting at. Feb 13 '20 at 12:35
• An Option Adjusted Spread is the valuation adjustment placed on a bond with an embedded option, say to be called. That option depends vol, expiry, and strike, and it may well differ to another bond. Therefore in order to equate the fairest sense of credit discounted cashflows (in the absense of the optionality) then extracting the OAS standardises the bonds, just as in my answer you are essentially trying to build a model that 'standardises' bonds across many cross-sections. The answer to your questions is: Yes! With some model!
– Attack68
Feb 13 '20 at 12:46
• But what I am asking applies also to the spread, where there is no option-adjustment. Even without the option spread can be somewhat affected by price/coupon effects. Feb 13 '20 at 14:46
• My main question is: in what sense is an adjustment for this necessary? I thought you were trying to get at that with long-term vs short-term RV, but the point was not clear to me. Feb 13 '20 at 14:46
• This is a great answer. I'd like to make explicit something @Attack68 left implicit in his final formula: those coupons can be treated as little bonds themselves. Feb 13 '20 at 14:59