Tuesday, June 10, 2008

How are bonds quoted?

By popular demand, welcome to yet another installment of Accrued Interest's How To series. This is on the subject of how bonds and various bond instruments are quoted. We'll go from the simple to the complicated, and even include a few derivative products. I know we get some readers who are primarily equity people, but lately have been trying to pay more attention to the bond market.

The Very Basics
Bonds pay interest based on a par amount. For example, if the coupon is 5%, it pays that 5% based on the par amount of the bond. The par amount is also the amount that the bond will pay at maturity. You could think of it as the principal of the bond.

When a bond is quoted in a dollar price, that price is a percentage of par. So a bond price of $104.312 is really 104.312% of the par amount.

Treasury Bonds
Unlike every where else in the world, the U.S. Treasury market still trades in fractions. It is assumed you know this when the bond is quoted, so you'll see it written as something like this...


That means that the bond's price is 98 and 4/32's, or 98.125% of par. Sometimes there is also a + added to the end. The + is worth 1/64. So if the price is 98-4+, that's 98 and 4.5/32. If you watch Bloomberg you may see yet more fractions thrown in there too. If you saw 98-4 1/8, that would be 98 and 4.125/32. In bond parlance, 1/32 is a "tick."

Treasury bills are quoted on a discount basis. I'm not going to get into this in deep detail, suffice to say that it isn't the same as a yield, but its usually in the ball park of the yield.

For the most part, TIPS and Agency MBS are also quoted in this manner.

Other bonds, when quoted in dollar price, are in fractions, but other than municipals and high-yield bonds, most other bonds are quoted in spread.

Bond Spreads
Plain vanilla agency and investment-grade corporate bonds typically are quoted on spread. Most commonly they are quoted based on the yield differential between the bond in question and the nearest benchmark Treasury in basis points. A "Benchmark" Treasury is the most recently auctioned Treasury of a certain maturity. Currently there are 2, 5, 10, and 30-year "benchmarks."

It is usually assumed you know what the benchmark is for a bond, but its not always obvious. For example, the HSBC 5.25 of 4/15 (That's an HSBC bond with a 5.25% coupon, maturing in April 2015), is generally quoted off the 10-year Treasury, not off the 5-year. Why? Who knows? The street tends to like to make bonds look tighter, and since the 10-year currently yields more than the 5-year, they tend to like to keep stuff against the 10-year as it ages.

Floating rate bonds trade on what's called a "discount margin" or the spread to the bond's floating index. If the index is 3-month LIBOR, the bond will be quoted on a spread to 3-month LIBOR. When calculating the dollar price, it is assumed that LIBOR resets at its current rate at next reset and then remains there for life.

Some fixed-rate bonds trade on a spread to "swaps." This can be indicated as N+(number) or S+(number) depending on what it is. CMBS usually trade this way. The "swap" rate is the rate on the fixed-leg of a plain-vanilla interest rate swap. Bloomberg calculates an interpolated swaps curve and this is what's usually used for pricing bonds. Bloomberg pretty much rules the bond world, in case you haven't noticed.

By the way, swap "spreads" are the difference between the swap rate and the corresponding Treasury rate. Since interest rate swaps almost always have some highly-rated financial institution as the counter-party, the swap spread rate is a good gauge of perceived credit risk of very highly-rated banks.

Municipals are usually just quoted in dollar price or yield. If you do see a spread, its probably versus the Municipal Market Data curve, or MMD. This curve only updates at the end of every day. Muni guys aren't the quickest of people...

Agency mortgage-backed bonds sometimes trade on a "To Be Announced" basis or TBA. Remember that MBS are backed by actual loans made to actual home owners. So its common that a lender would like to lock in the rate they can offer borrowers by pre-selling their loans to investors. Hence the TBA market.

Since most fixed-rate MBS are eligible for TBA delivery, bids and offers on specific pools trade on a spread versus TBA. For example a "seasoned" pool (or one that is older) might be more valued by the market than generic pools, and therefore more expensive. The spread is expressed not in yield but in dollar price difference, usually in ticks. So a seasoned pool might be +8 to TBA, or 8/32 more in dollar price than the generics.

Hybrid-ARM MBS trade on a Z-spread basis. This is a spread to the interpolated spot curve as calculated by Bloomberg. When calculating this it is assumed the bond will pay 15 CPR until the reset date, no matter what the coupon or structure. Its kind of stupid but that's what's done.

Callable Bonds
Bonds with call features, most common with munis and agencies, are often just quoted with a yield instead of a spread. The yield quoted is the lower of the yield to maturity or yield to call, called yield to worst.

Sometimes agencies are quoted on an OAS or AOAS basis. OAS stands for "option-adjusted spread." On most callable bonds, the OAS is calculated against the LIBOR curve, but it could be calculated against anything. Common buyers of callable agencies include many yield-sensitive buyers, i.e., people who don't care about spreads, only about straight yield. Banks and credit unions are great examples. Hence callable agencies are more often just quoted on yield than other bonds.

Agencies which are callable on a single day only are quoted on an AOAS basis. Suffice to say this is an OAS curve based on Bloomberg's calculation of the agency curve itself.

Credit Default Swaps
CDS are quoted one of two ways: either as a spread or as "points up front." I won't go into the nitty gritty of CDS here. (I wrote more extensively about how CDS work here). Suffice to say that the buyer of a CDS is buying insurance against default. That buyer typically pays a percentage of the notional amount protected, which is the spread quoted. So if Lehman Brothers is quoted as 260, that means to buy protection on $1 million, you must pay $26,000 to the seller of protection each year. The payments are actually transmitted quarterly.

High yield bonds often trade as points up front. To buy protection on Ambac, for example, you have to pay 30 percentage points up front and 500bps per year. The quote would only reference the points up front, the 500bps is a given. The points paid up front is akin to the discount a cash bond would be trading at given a 5% coupon.

Unless otherwise stated, CDS quotes are for a 5-year term.

Hope that helps. If anyone has any other types of bonds that I haven't thought of, please post a comment or e-mail me accruedint at gmail.com.


PNL4LYFE said...

One thing I've noticed is that many longer dated corporates are quoted against the one-old long bond instead of the OTR. Is this done to avoid some technical factor in the long bond? Thanks in advance.

Accrued Interest said...

Yeah. There was a time when there was a large difference in yield between old 30's and OTR 30's. Now not really. But old habits die hard.

Anonymous said...

Thank you, by the way. These are very helpful.

Iggy said...

"Hybrid-ARM MBS trade on a Z-spread basis. This is a spread to the interpolated spot curve as calculated by Bloomberg. When calculating this it is assumed the bond will pay 15 CPR until the reset date, no matter what the coupon or structure. Its kind of stupid but that's what's done."

Is it stupid because there's an embedded option, and Z-spread doesn't account for that? As well as the flat prepayment assumptions? (Does this also mean that there are much greater miss-pricing opportunities?)

Accrued Interest said...

Its the flat prepayment method. I've never been a fan of trading MBS on spread anyway, because prepayments make such a difference, and that's always an estimate. But it makes even less sense to assume all bonds will prepay at the same speed!

Anonymous said...

Is there a quick way to calculate implied yield from treasury FUTURE prices?

Accrued Interest said...

I don't personally trade futures, so my knowledge of them is purely academic. You have to be careful in that futures operate on a cheapest-to-deliver basis. The CTD is almost never the bond named in the future. For example, TYA (10-year future) will almost never have the actual 10-year as the CTD.

Anonymous said...

Maybe you can help me with my problem. I can't find 9% FHR or FNR ttibs with a 6 strike on the street at par right now but I still have my clearing firm pricing them at 94. What gives?

Accrued Interest said...

Sometimes mark to model works against you! I have that problem all the time. As a overwhelmingly high-grade buyer, I rarely have the problem of a bond that's become a problem yet the pricing service doesn't know it. Its more often that I own something that's been improving and the service doesn't know that. You just have to live with it.

Anonymous said...


pepper said...

hi, could you guide me where on bloomberg should i look under if for example someone quoted me CT5+380? or MS+70?

Accrued Interest said...


BTMM is a good base page. CT5 is the 5-year. The on USSW shows swaps. If you have a 3-year bond, find the 3-year swap and add 70bps.

Anonymous said...

The Bloomberg is one of the weakest possible sources for any market. Try Asset Backed Alert. Anyone following this, take it with a grain of salt. I work in the industry, and trusting the Bloomberg is my last possible resort for literally any news or information whatsoever on the market.