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Wednesday 10 April 2024 by Philip Brown

The Evolution of a Bond’s Clean Price Over Time

  • Fixed income is called fixed income because the cash flows are known in advance – but the value of those cash flows can change, affecting a bond’s price.
  • Fixed rate bonds are commonly launched at 100 and mature at 100, but prices vary in between.
  • Other types of bonds have different structures though, and this piece also explains the price evolution of FRNs (Floating Rate Notes), IABs (Indexed Annuity Bonds), Linkers (Capital Indexed Bonds) and RMBS (Residential Mortgage-Backed Securities).

Understanding the likely evolution of a bond’s price is critical to successful fixed income investing. All bonds have some exposure to interest rates or other risks and the price of a bond will change over the course of the investment. However, the structural features of a bond materially affect how and by how much the bond will react to changes in market rates. This article explains the most common types of bonds and explores the likely evolution of their prices over time.

Clean Price, Coupons, Accrued Interest and Total Amount

Before we can get started, though, a quick refresher on the difference between Clean Price, Total Amount and Accrued Interest is called for.

The “Total Amount” is the simplest idea: it’s the full amount that an investor pays for a bond. The Total Amount is split into the Clean Price and Accrued Interest.

Bonds pay coupon interest periodically. In Australia, a fixed rate bond will likely pay interest every six months, which leaves most of the year being not a coupon date. If a bond is traded between coupon dates, then part of the coupon belongs to the previous owner and part to the new owner. To allow for this, bond prices include a concept of “Accrued Interest”, which reflects the portion of the next coupon payable that has already been earned by the passage of time.

The “Clean Price” is the value of the underlying bond, with the Accrued Interest removed.

The Total Amount is the sum of the Clean Price and the Accrued Interest. (The total amount is sometimes also known as the “Dirty Price”).

A Fixed Rate Bond’s Clean Price: 100 at the start and 100 at the end, but a wide array in between

Fixed Rate bonds have a fixed coupon for the life of the bond. Usually, when a new bond is created, the coupon is set so that the yield on the bond and the coupon are very similar. If the coupon and the yield are exactly the same, the bond’s clean price will be $100.

Over time, the yield on the bond will fluctuate with market conditions, but the coupon remains unchanged. As such, the bond’s price will vary – either or up down – as interest rates change in the broader market.

The longer a bond’s maturity, the more the bond’s price is affected by changes in interest rates (this is a concept called duration risk). Simply put, if you own a bond that pays a 6% coupon rate instead of a 5% market yield, you receive an extra dollar per year every year. Obviously, the larger the number of years you receive this extra dollar, the greater the benefit to you - and the more the effect on the bond price.

Unfortunately, it also applies in reverse though. If the market yield rises and you have locked in a below-market coupon rate for a long time, the price falls more. Duration means that longer bonds are more exposed to price movements, and that shorter bonds have relatively smaller exposure to interest rate risk.

In a practical sense, because the vast majority of bonds mature at the $100 par face value, this means that bonds are ‘pulled to par’ and start converging back towards $100 as time passes.

The chart below shows a conceptual likely distribution for a fixed rate bond’s Clean Price. We assume this is a standard bond that prices at $100 and then matures at $100. In between, the clean price can diverge, with the time taken for rates to move keeping the price near $100 at first, but the shorter duration and the pull to par bringing the bond back to closer to $100 well before maturity.

Fixed Rate Bond: Expected Behaviour of Clean Price

Source: FIIG Securities. Note, that these charts are conceptual and do not represent any particular bond.

For the purposes of a fixed rate bond, it doesn’t matter if the change in market rates is driven by movements in the underlying risk-free yields, or by movements in credit spreads. The result is the same either way.

A Floating Rate Note’s Clean Price: 100 at the start and 100 at the end, not far from 100 at any point

Once again, a Floating Rate Note (FRN) is almost always issued with a clean price of 100 and matures with a clean price of 100.

In contrast to a Fixed Rate bond, with its directly fixed coupon, an FRN has a coupon which is based around a floating interest rate benchmark and a fixed spread above that benchmark to represent credit risk.

The interest rate risk in an FRN is almost completely neutralised by the structural features of the note. The primary driver of the movement of Clean Price in the fixed rate space is absent from FRNs. The floating interest rate benchmark (in Australia, the bank bill swap rate) updates each quarter in line with movements in interest rates.

However, while there is almost no duration risk, there is a risk if the credit spread changes. Although credit spreads can change, they are much more stable than interest rates and – except in extreme circumstances – don’t generally move as far in either direction.

Low duration and typically stable credit risk mean that an FRN is not locked into 100 as the only price, but the price is far more constrained and stays much closer to 100.

Floating Rate Note: Clean Price much more stable than a fixed rate bond

Source: FIIG Securities. Note, that these charts are conceptual and do not represent any particular bond.

A Capital Indexed Bond: A generalised uptrend in the Capital Price

A Capital Indexed Bond, also known as a CIB or a linker, is the first bond we’ve looked at where the capital price doesn’t mature at 100 at the end of the life of the bond. Instead, the capital price of the bond trends higher over time in a manner linked to CPI.

However, although a Capital Index Bond has an inflation-linked component, it also has a fixed rate bond component. As such, the expected range for the CIB looks very much like a fixed rate bond, except with an upwards trajectory to account for the inflation link. (Remember also that CIB’s generally have a lower coupon, so the capital price is accumulating faster while the coupon payments are smaller, all else equal.)

The final payment of a Capital Indexed Bond depends on the totality of CPI during the life of the bond. In most normal circumstances, that has averaged around 2.5% or so per annum over the life of a bond. In our example, the capital price rises to around $130 over the 10-year period, thanks to compound interest.

Capital Index Bond: Like a fixed rate bond, with an upward trajectory

Source: FIIG Securities. Note, that these charts are conceptual and do not represent any particular bond.

An Indexed Annuity Bond: A slowly falling clean price, with no final payment

Although Indexed Annuity Bonds (IABs) are also inflation-linked, they have a very different structure to Capital Indexed Bonds.

IABs are annuities. A normal annuity would pay a set amount per period which slowly amortises the original investment. In a normal annuity, there is no final payment; once the periodic coupons are finished, the investment is done.

An indexed annuity is very similar, but instead of paying the exact same dollar value for each  quarterly payment, the payments are increased by CPI, so each payment has the exact same purchasing power. There is no large maturity payment, however; once the annuity has run its course, the payments cease. The return of capital happens incrementally over the course of the annuity, not in a lump sum at the end.

The value of the annuity payments is still exposed to interest rate risk. So like the fixed rate bond, the value of the annuity payments can vary up or down over the course of the annuity.

Indexed Annuity Bond: Paying down to zero over time with no final maturity payment

Source: FIIG Securities. Note, that these charts are conceptual and do not represent any particular bond.

RMBS: Paying down to zero over time, but with fits and starts

Our final type of bond is a Residential Mortgage Backed Security (RMBS). These bonds are based around mortgages, so take on some features of a mortgage. Importantly, like a mortgage (and like an IAB), the RMBS structure as a whole pays the principal and interest back at each coupon payment date. But not all parts of the RMBS participate equally in each payment.

RMBS is a broad and non-specific category. Each deal will have slightly different rules and arrangements. It is still possible to draw out some general patterns, however.

First, unlike an IAB or a single mortgage where the principal is passed through to all the investors equally every time, an RMBS differentiates between classes of notes (called tranches) and pays principal to high-ranking classes before lower-ranking classes get their turn (usually once certain conditions are met).

The higher-ranking classes normally receive a significant proportion of their principal back before lower-ranking classes receive any principal. Sometimes the higher-ranking classes are fully paid back before the lower-ranking classes receive any principal at all. (Lower-ranking classes receive higher interest rates to compensate for this extra risk.)

Second, RMBS are usually floating rate notes. So while the timing of principal payments is quite variable, there is limited interest rate risk.

Third, RMBS normally have what is called a “clean-up call”. A clean-up call is a feature where the entire RMBS structure is called and paid back once the percentage outstanding of the investment falls below a certain threshold – usually 20%. (The administrative burden of an RMBS is quite high, so it doesn’t make sense for the issuer or the investor to keep the structure in place while the final few payments are made.)

Importantly, the clean-up call applies to the percentage of the entire original transaction, not the percentage of each individual tranche. Some RMBS tranches will slowly pay back to zero, while others will receive a large payment at the end if the deal as a whole is called.

Different possibilities for RMBS principal payback depending on the rating of the tranche:

Source: FIIG Securities. Note, that these charts are conceptual and do not represent any particular bond.

Unlike our other charts, this one represents only the principal value outstanding, but as we note above when discussing FRNs, the floating rate nature of these bonds means the Clean Price sticks very close to their capital values – though some small variations are possible.

Different sorts of bonds have different sorts of exposures to interest rate risk, credit risk and mortgage risk. It is important investors understand how and when their capital will be returned.

Fixed rate bonds and FRNs return the original capital at the end of the investment. Index-linked bonds return more than the original capital because the capital is linked to CPI. Indexed annuity bonds and RMBS return capital over time rather than in a single final payment.

All the investments we’ve examined here also pay coupons over the life of the investment. However, the Clean Price of the investments will depend critically on the structure of the bond and the behaviour of interest rates.