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Outline how bonds are traded and account for how bond yields behave.

FRM® Part I · Financial Markets and Products · Corporate Bonds · FRM1.FM.17.a

The idea

Corporate bonds trade mainly over the counter. Dealers quote a bid, where they buy, and an ask, where they sell. They hold inventory and negotiate with investors, so liquidity is thinner and transaction costs wider than in listed equities, especially for smaller or older issues. Quotes are clean prices. The buyer also pays accrued interest, which for US corporates uses a 30/360 day count, to give the dirty (invoice) price. A corporate bond's yield moves when Treasury yields move or when the spread moves with credit and liquidity conditions. In its simplest form, the yield is built up from a benchmark and a spread as Yield = benchmark Treasury yield + spread. Price and yield move inversely, and a bond's price is pulled toward par as maturity approaches. The usual error is to forget that the spread, not only the Treasury yield, drives corporate yields.

Formulas

Accrued interest

accrued interest = coupon × (t ÷ T)

coupon
the full coupon for the period
t
days from the last coupon date to settlement
T
days in the coupon period

US corporate bonds use 30/360, so a semiannual coupon period counts 180 days whatever the calendar says.

Dirty (invoice) price of a corporate bond

dirty price = clean price + accrued interest

clean price
the quoted price, without accrued interest
accrued interest
the coupon earned since the last coupon date

The dirty price is what the buyer pays; quotes are clean.

Yield on a corporate bond

corporate yield = Treasury yield + spread

Treasury yield
the yield on the benchmark Treasury
spread
the credit and liquidity spread over that benchmark

The two parts can move in opposite directions and net out; forgetting the spread is the usual error.

A practice question

From the question bank, with the reason each wrong option is wrong.

How are most corporate bonds traded in the secondary market?

  1. Over the counter, with dealers quoting bid and ask prices and trading from their own inventory. - correct
  2. On a centralised exchange order book that matches buyers and sellers anonymously at a single price.Why not: Describes the exchange model used for listed equities; corporate bonds trade mainly in dealer markets.
  3. Through a clearing house that sets a daily settlement price and margins every bond position.Why not: Confuses bond trading with futures markets, where a clearing house fixes daily settlement prices.
  4. Directly between the issuer and each investor at par, since the bonds cannot be resold.Why not: Confuses primary issuance with secondary trading; corporate bonds can be resold through dealers.

Corporate bonds are traded mainly OTC in dealer markets. Dealers quote a bid (where they buy) and an ask (where they sell), which is why liquidity is thinner and trading costs higher than for listed equities.

A harder one

A US corporate bond pays a 6% semi-annual coupon (face 100) using a 30/360 day count. It is quoted at a clean price of 98.50 and settles 70 days after the last coupon date. What invoice (dirty) price does the buyer pay?

  1. 100.83Why not: Computes accrued interest from the annual 6 instead of the semi-annual 3 coupon, doubling the accrued amount.
  2. 99.67 - correct
  3. 97.33Why not: Subtracts accrued interest from the clean price; the buyer pays it to the seller on top of the clean price.
  4. 98.50Why not: Treats the quoted clean price as the amount paid; the buyer also pays accrued interest.

Accrued interest = 3 x 70/180 = 1.1667. Dirty price = clean price + accrued = 98.50 + 1.1667 = 99.67.

The hardest tier

A dealer quotes a corporate bond at 98.20 bid and 98.90 ask. Its modified duration is 5.0. Using the mid-price (98.55) as the base, what is the approximate size of the bid-ask spread in yield terms, and which price has the higher yield?

  1. About 14 bp, with the higher yield at the ask price.Why not: Right size, wrong direction: the lower price (bid) carries the higher yield.
  2. About 71 bp, with the higher yield at the bid price.Why not: Divides the price gap by price only and ignores duration, which converts price points to yield points.
  3. About 14 bp, with the higher yield at the bid price. - correct
  4. About 7 bp, with the higher yield at the bid price.Why not: Takes half the quoted spread (distance from mid to one side) rather than the full bid-ask gap in yield terms.

Price gap 0.70 / (98.55 x 5.0) = 0.00142, about 14 bp. Price and yield are inversely related, so the lower bid price implies the higher yield.

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