QF5213 Chap.9 Bond Pricing, Coupons and Yields
Bond Pricing, Coupons and Yields
What a bond actually promises
Every bond in this topic reduces to a short list of promised payments. The issuer borrows money and agrees to send a fixed coupon at regular intervals plus the face value, usually $1,000, when the bond matures.
The coupon rate is just the annual coupon expressed as a share of face value, so a 6% bond with $1,000 face pays $60 a year in total, split into two $30 cheques when coupons are semiannual. Nothing in that schedule changes after issue, and that rigidity is why bonds are grouped as fixed income.
What does change is the return investors demand for holding those payments, and that single moving input drives almost everything else in the chapter.
Two complications sit on top of the basic promise.
The issuer might not pay, which is default risk, and the contract can carry extra clauses: a call option that lets the issuer repay early, a sinking fund that retires debt gradually, covenants that restrict borrowing or payouts, seniority that ranks one creditor ahead of another, or a right to convert the bond into shares.
Each clause shifts risk between issuer and investor and therefore moves the yield investors require.
From promised cash to a market price
The price of any bond is the present value of its remaining coupons and face value, discounted at the yield the market currently demands for that risk.
Written out, the coupons form an annuity and the face value is a single lump sum, so the valuation needs only two familiar present value pieces.
A spreadsheet PV function or a financial calculator does the same job in one line, provided the rate, the number of periods and the coupon all refer to the same time interval.
Because the yield sits in the denominator, price and yield always move in opposite directions, and the relationship is curved rather than straight.
Comparing the coupon rate with the market yield tells you instantly whether the bond trades above face value, at it, or below it, and as maturity approaches every bond drifts back to face value if yields stay put.
Yield to maturity, current yield and the coupon rate then line up in a predictable order depending on which of those three situations applies, which is one of the fastest checks available in a multiple choice question.
Where the risk in a bond comes from
Holding a bond exposes you to three separate risks. Price risk is the loss in value when yields rise, and it is larger for long maturities and small coupons.
Reinvestment risk is the danger that coupons and principal must be reinvested at lower rates, and it bites hardest on short maturities and large coupons. Credit risk is captured by agency ratings that run from AAA down through investment grade into speculative territory.
The class ties these ideas to Singapore examples, including a national airline that raised pandemic funding partly through convertible bonds, so expect questions that ask you to reason about features as well as to compute prices.
What this chapter covers
- 01
Bond terminology: par value, coupon rate, periodic coupon and maturity
- 02
Pricing a bond as the present value of coupons plus par
- 03
Premium, discount and par bonds and their drift towards par over time
- 04
Yield to maturity, current yield and their ordering
- 05
Semiannual coupons, effective annual rate and yield to call
- 06
Price risk, reinvestment risk and credit ratings
- 07
Bond features and the airline's 2020 rights shares and mandatory convertibles
Worked example · free
Finding the YTM of a semiannual discount bond
- 1Set up the periodic inputs: number of periods and coupon per period.
- 2Solve for the six-month rate that prices the bond at $920 and annualise it.
- 1Convert the quoted YTM into an effective annual rate.
- 2Compute the current yield and check the discount bond ordering.
Key terms
- Par Value
- The face amount of a bond, typically $1,000, that the issuer repays on the maturity date and on which the coupon rate is calculated.
- Coupon Rate
- Expresses the total annual coupon as a percentage of par value; it is fixed at issue and does not change with market yields.
- Yield to Maturity
- The discount rate that makes the present value of all remaining coupons and par equal to the bond's current market price.
- Current Yield
- Measures the annual coupon divided by the current price, capturing income only and ignoring any gain or loss as price moves to par.
- Yield to Call
- The return earned if a callable bond is redeemed at the first call date for the call price instead of being held to maturity.
- Premium Bond
- A bond trading above par because its coupon rate exceeds the yield the market currently requires for its risk.
- Discount Bond
- A bond trading below par because its coupon rate is lower than the yield the market currently requires for its risk.
- Reinvestment Rate Risk
- Describes the chance that coupons and principal received must be reinvested at lower rates, which reduces future income for the holder.
- Mandatory Convertible Bond
- A debt security that must convert into ordinary shares at maturity unless the issuer redeems it earlier on agreed terms.
Bond Pricing, Coupons and Yields FAQ
How do you know if a bond trades at a premium or a discount?
Compare the coupon rate with the yield investors currently demand. If the coupon pays more than that yield, buyers bid the price above face value; if it pays less, the price drops below face value. When the two rates match the bond sells at exactly face value.
Why do bond prices fall when interest rates rise?
A bond's price is a present value, so the market yield acts as the discount rate. Raising it shrinks the value of every fixed coupon and the final repayment at the same time. The cash amounts never change, so the only way the bond can offer the new, higher return is through a lower purchase price.
Is current yield the same as yield to maturity?
No. Current yield divides one year of coupons by today's price and stops there. Yield to maturity also counts the gain or loss as the price converges to face value by the final date, so the two agree only when the bond trades at face value.
How do I calculate YTM for a bond with semiannual coupons in Excel?
Enter the number of half-year periods, the half-year coupon, the price as a negative number and the face value into RATE. The result is a six-month rate, so double it to get the quoted annual YTM, and use the effective annual formula when comparing with other investments.
Which bond is riskier when rates change, a long one or a short one?
For price swings the longer bond is riskier: its distant cash flows are discounted over more years, so a yield change moves its value much further. Short bonds carry the opposite exposure, since their principal returns soon and may have to be reinvested at whatever lower rate prevails.
Exam move
Build a one-row spreadsheet that prices a bond from coupon rate, years, payments per year and yield, then change one input at a time. Raise the yield by one point at two maturities to see price risk, set the yield equal to the coupon to watch the price land on par, and solve backwards with RATE for a quoted price. Finish by writing down the coupon, current yield and YTM ordering for each case before checking it.
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