Zero Coupon Bond

This reading covers how bonds repay principal and pay coupons, the embedded options that can change those cash flows, and the legal, regulatory and tax factors that shape where and how bonds are issued. A candidate must be able to compute amortizing and balloon payments, floating-rate and inflation-linked coupons and conversion values, and say which party an embedded option benefits.

LOS 52.a — Cash flow structures and contingency provisions

Principal repayment structures

Calculator (END mode, P/Y = C/Y = 1): N = 4; I/Y = 6; PV = −10,000; FV = 0; CPT PMT = 2,885.91. The amortization schedule is then built one year at a time:

1. Interest for the year = opening balance × 6%.
2. Principal repaid = payment − interest.
3. Closing balance = opening balance − principal repaid. It becomes the next year's opening balance.

The payment stays level while the balance falls, so the interest part shrinks and a larger part of each payment retires principal. The last payment is 2 cents higher because of rounding.

A partially amortizing version of the same loan that leaves a $2,000 balloon keeps the same inputs except FV = 2,000: N = 4; I/Y = 6; PV = −10,000; FV = 2,000; CPT PMT = 2,428.73. The final payment is $2,428.73+2,000=\$4,428.73$. The three structures compare as follows:

Compared with a fully amortizing loan, a partially amortizing one has lower regular payments and a higher final payment. It repays less principal along the way, so more principal stays outstanding, and its interest in every year after the first is higher (year-1 interest is the same, because no principal has been repaid yet).

A sinking fund provision obliges the issuer to pay off part of the issue according to a set schedule over the bond's life. Typically the bond trustee redeems a fixed amount of principal each year from holders chosen at random. For bondholders, a sinking fund has two effects:

• It lowers credit risk, because less principal is left to be repaid at maturity.
• It adds reinvestment risk, the risk of receiving cash early and having to reinvest it at lower yields. If rates have fallen, the bonds trade above par, yet holders whose bonds are drawn receive only par. Holders of premium bonds therefore prefer that their bonds are not drawn.

Amortizing structures carry the same trade-off, since a sinking fund is one form of amortization. The more principal a structure repays before maturity (bullet, then partially amortizing, then fully amortizing), the lower its credit risk and the higher its reinvestment risk.

A sinking fund is an obligation of the issuer and is not an embedded option. Waterfall structures, another form of amortization schedule, are used for ABS and MBS. They pay principal to senior tranches first. Junior tranches receive principal only after senior tranches are repaid, although all tranches still receive interest.

Coupon structures

• Floating-rate notes (FRNs) pay the market reference rate (MRR) plus a fixed margin (the credit spread) stated in basis points. Most reset and pay quarterly: the MRR observed at the start of a quarter sets the coupon paid at the end of that quarter. The per-period coupon is $(\text{MRR}+\text{margin})/\text{payments per year}$. Example. With an MRR of 3.10%, a margin of 60 bps and quarterly payments, the coupon is $(3.10\%+0.60\%)/4=0.925\%$ of par.
• Step-up coupon bonds: the coupon rises on a predetermined schedule, which gives investors some protection against rising interest rates.
• Credit-linked coupon bonds and credit-linked notes: the coupon rises if the issuer's credit rating falls and falls if it improves. Leveraged loans may step up if debt/EBITDA rises. Some green bonds pay more if environmental targets are missed.
• Payment-in-kind (PIK) bonds: the issuer can pay interest by increasing the principal (paying with more bonds). They are used by highly leveraged issuers, so yields are higher.
• Index-linked bonds tie coupons or principal to a published index. Inflation-linked bonds (linkers) are the most common.
  • Interest-indexed bonds: the coupon rate is adjusted for inflation, and the principal is unchanged (not protected).
  • Capital-indexed bonds (the most common type, e.g., US Treasury Inflation-Protected Securities (TIPS)): the coupon rate stays fixed, and the principal is adjusted up for inflation (down for deflation). The fixed coupon rate is effectively a real rate. Because the coupons and the principal repaid both rise with the index, the investor's purchasing power is fully protected over the bond's life. Adjusted principal can fall below par during the bond's life, but at maturity TIPS repay the greater of the inflation-adjusted principal and par.
  • Example. A bond has €5,000 par and a 2% annual coupon paid semiannually. Inflation over the first six months is 1.5%, so the principal becomes $5,000\times 1.015=€5,075$ and the coupon is $5,075\times 0.02/2=€50.75$.
• Zero-coupon bonds make one payment of par at maturity, so they must trade below par to give investors a positive return. They appeal to investors who want to minimize reinvestment risk. A zero-coupon bond is the extreme case of a deferred coupon bond.
• Deferred coupon bonds pay no coupons for an initial period after issuance and then pay regular coupons to maturity. In some issues the skipped coupons accrue and are paid as one lump sum when the deferral period ends; otherwise the bond is simply sold at a deeper discount. Like zero-coupon bonds, they often trade below par. The structure suits low-rated issuers or projects that generate cash only later.

Periodic coupons also have to be reinvested, so reinvestment risk rises with the coupon rate, and a call feature adds to it. Holding a coupon bond to maturity does not remove it; only a zero-coupon bond held to maturity has none.

Contingency provisions (embedded options)

A contingency provision allows an action to be taken if a specified event occurs. In a bond indenture such provisions are embedded options: they are part of the bond contract and are not separate securities. An embedded option benefits whoever holds the right to exercise it. Bonds without them are straight bonds (option-free bonds).

• Callable bonds: the period before the first call date is call protection. The call price often steps down over time (e.g., 103, then 101.5, then par). Holders face call risk, and during the call period the call price caps the bond's market value. Example. A 5.5% bond with $1,000 par reaches its first call date, callable at 101, just as its market yield falls to 3.5%. The issuer pays $1,010 per bond and borrows that amount at 3.5%, which cuts annual interest from $55 to $1,010\times 0.035=\$35.35$ per bond. The holder receives $1,010 early and can reinvest it only at the lower yield.
• Convertible bonds: the conversion price is the par amount per share received, the conversion ratio is par divided by the conversion price, and the conversion value is the conversion ratio times the current share price. Example. A $1,000 par bond with a conversion price of $25 converts into 40 shares. At a share price of $28, the conversion value is $40\times 28=\$1,120$.
• Warrants attached to straight bonds let holders buy common shares at a fixed price. They can be detached and traded separately.
• Contingent convertible bonds (CoCos) convert automatically into equity if a trigger occurs (e.g., a bank's equity capital falls below a required level).

A typical call schedule steps down toward par after a period of call protection:

Options are worth more when the underlying is more volatile. Higher interest rate volatility therefore raises the value of the call held by the issuer, so the callable bond's value falls. It also raises the value of the put held by the investor, so the putable bond's value rises.

LOS 52.b — Legal, regulatory and tax considerations

Where bonds are issued and traded

The "Euro" in Eurobond does not mean the bonds are denominated in euros, sold in Europe or issued by a European firm; the name comes from the market's origins in Europe, where most Eurobonds are still traded. Foreign bonds, global bonds and Eurobonds are collectively international bonds. Bearer bonds (ownership shown simply by possession, with no record kept by the issuer) were once the norm for Eurobonds. Today most bonds are registered bonds. Markets also differ in laws, regulation and conventions such as coupon frequency, but the currency of a bond is the factor that best explains yield differences across markets, because a bond's yield is driven by interest rates in the country of its currency. Sukuk are Sharia-compliant bonds whose payments are treated as rent on underlying assets.

Taxation of bond income

• Interest income is usually taxed as ordinary income. In the US, interest on municipal bonds is usually not subject to national income tax, and often not to state tax in the issuing state either.
• Gains or losses on selling a bond before maturity are capital gains or losses. They are often taxed at lower rates, and lower still if the gain is long-term.
• Original issue discount (OID) bonds (e.g., zero-coupon bonds): the rise in value toward par is really interest, so in many jurisdictions part of the discount is taxed each year as interest income even though no cash is received.
• Some jurisdictions give bonds issued at a premium the symmetric treatment: part of the premium is used to reduce the taxable portion of the coupon interest.