Asset Swaps and Z-spreads -- Chapter 1 - YouTube

This Chapter 1 reviews important notions of bond yields and credit spreads, which are

critical to your subsequent understanding of the materials covered in this module.

More detail on all these notions is found in our 2-part module entitled Bond Fundamentals.

For bonds of equal maturities and payment frequencies trading at par, we can compare

coupons directly to determine which bond pays the highest return and which the lowest return.

So if I am comparing a 5-year US treasury note with a 6% coupon to a 5-year note issued

by JP Morgan with a 6.5% coupon, and finally to a 5-year note issued by Alcatel with a

7% coupon, then assuming all are trading at par, I would be certain that the one with

the lowest coupon, i.e. the UST note, offers the lowest return, followed by the JP Morgan

note, followed by the one from Alcatel.

It is also customary to describe the JP Morgan note as yielding 50 bps more than the UST

note, or more simply T + 50, and the Alcatel note as yielding 100 bps more than the UST

note, or T + 100, since the UST note is generally regarded as the risk-free instrument for that

maturity.

Note importantly that this comparison is exact only if the 3 instruments have the same day

count convention, in addition to having the same payment frequency; otherwise, an accurate

comparison would need to reflect this additional consideration, as explained in detail in the

modules mentioned above on Bond Fundamentals.

We would be tempted to conclude, from the differences in the returns of the 3 bonds

above, that the UST note is the one that carries the least credit risk, and that Alcatel’s

is the riskiest; but while this is generally a reasonable starting assumption, we would

be well-advised to consider also factors of a more technical nature, such as the relative

liquidity of each bond, differences in tax treatment, and the like, which can skew coupons

and yields up and down quite separate from their credit fundamentals.

A thorough examination of these technical factors is provided in our module on Pricing

Credit Default Swaps.

If we have to reason to believe that these technical factors do not play a significant

role in the determination of the coupon on each note, then our earlier statement about

the relative credit risk of each note becomes even more reasonable.

When two bonds are not trading at par, a comparison of their coupons alone no longer suffices

for purposes of comparing their returns.

In our modules on Bond Fundamentals, we discussed in detail the notion of yield to maturity,

which attempts to expand the comparison and make it more comprehensive, by taking account

not only of each bond’s coupon, but also any price discount or premium at which they

trade relative to par.

In short, you may recall that YTM is defined as that single value for y that makes the

following equation hold:

which states in summary that a bond’s price equals the sum of its aggregate CFs, appropriately

discounted.

To illustrate a typical application of YTM, assume you are asked to evaluate the risk/reward

tradeoff of the following four 5-year notes with semi-annual coupons, and which, conveniently,

also have identical day count conventions:

Worksheet YTM should serve as a useful reminder of how we use excel function RATE to derive

each bond’s yield-to-maturity.

For example in Cell __, you see how we input each of the bond’s principal characteristics

in each relevant empty space, but then also remember to multiply by 2 to obtain the annualized

YTM, all as taught in the earlier modules Bond Fundamentals.

The problem that YTM attempts to tackle is that a comparison only of the coupons gives

a very misleading impression of each bond’s total return if it is held to maturity and

pays in full.

Only the UST and the JP Morgan notes can be compared for purposes of total return on the

sole basis of their coupons.

The Alcatel bond, despite its lower coupon than the UST note, yields 145 bps more if

held to maturity given the 8% discount from par at which it can be purchased; and the

Brazil bond, although priced closer to par than the one from Alcatel, turns out in reality

to yield 79 bps extra when its far higher coupon is taken into account.

Note finally in the bottom row, for the three non-UST notes, the conventional expression

of their YTM as a spread over the YTM of the UST note given their equal maturities and

payment frequencies.

We remind you finally of a few characteristics of YTM measures that were covered in detail

in the Bond Fundamentals module, before proceeding with the construction of an very simple asset

swap: 1.

YTM is always higher than the coupon for a bond trading below par, and lower than the

coupon for a bond trading above par; 2.

A weakness of YTM, that is obvious from the above formula, is that it is based on the

discounting of all CFs over the bond’s life at a unique annualized discount rate, that

is held constant across all maturities, even if the RF yield curve is very steep or severely

inverted rather than flat.

A better measure would presumably attempt to recognize the shape of the RF curve, but

also possibly the so-called “term structure of credit spreads” – which refers to the

tendency of credit spreads to become larger the further out into the future a cash flow

occurs.

Nonetheless, YTM is used extensively by practitioners, because it can be derived quickly, requires

limited data and mathematical skill, and allows a decently accurate comparison of the potential

returns of two bond instruments of comparable maturity, even when their trading prices and

coupons vary significantly.

This completes this brief summary of bond yields and credit spreads and allows us to

move to the description of a simply asset swap in Chapter 2.