Quick Answer
Bond prices move opposite to interest rates: prices rise above par when rates fall, and fall below par when rates rise. Par value is normally
Quick Answer: Bond prices move opposite to interest rates: prices rise above par when rates fall, and fall below par when rates rise. Par value is normally $1,000. The four yield measures, coupon, current yield, yield to maturity, and yield to call, follow a strict order on discount and premium bonds, and are equal at par.
,000. The four yield measures, coupon, current yield, yield to maturity, and yield to call, follow a strict order on discount and premium bonds, and are equal at par.Now that you know the major bond types (Treasuries, agencies, corporates, munis, money market), it's time to understand how bonds are priced and how yields are measured. These concepts appear frequently on the SIE exam.
Par Value (Face Value)
- The amount the issuer promises to repay at maturity
- Corporate and government bonds: standard par value of $1,000
- Municipal bonds: par value of $1,000 per bond, but a standard minimum denomination of $5,000 (five bonds)
- Bonds are quoted as a percentage of par
- A quote of 98 = 98% of par = $980 for a $1,000 bond
- A quote of 102 = 102% of par = $1,020 for a $1,000 bond
Pricing Terminology
Bond prices and yields move in opposite directions. When market interest rates fall below a bond's fixed coupon rate, investors pay above par (a premium) to own it, because it offers higher fixed payments than newly issued bonds. Paying more for the same fixed coupon reduces their effective yield below the coupon rate.
The reverse is also true. When rates rise above the coupon rate, the bond's price falls to a discount, and the lower price raises the effective yield above the coupon rate.
| Term | Price vs. Par | What it means for yield |
|---|---|---|
| Premium | Above par (>100) | Market yield is lower than the coupon rate |
| Discount | Below par (<100) | Market yield is higher than the coupon rate |
| Par | Equal to par (100) | Market yield equals the coupon rate |
Think of it this way: A bond pays $50 per year (5% coupon on $1,000 par). If new bonds now yield only 3%, this bond is more attractive, so investors bid its price up to $1,100 (a premium). The annual payment is still $50, but $50 ÷ $1,100 ≈ 4.5%. The effective yield dropped below the 5% coupon because the investor paid more for the same fixed payments. Flip the scenario: if new bonds yield 7%, no one wants this 5% bond at $1,000, so the price falls to $900. Now $50 ÷ $900 ≈ 5.6%, higher than the coupon. Lower price, higher yield.
Exam Tip: Gotchas
- A bond quoted at 98 means $980, not $98. Quotes are percentages of par, so 98 = 98% of $1,000.
- "Above 100" means above $1,000, not above $100. In bond pricing, 100 represents 100% of par ($1,000 for a corporate bond). A quote of 105 means 105% of $1,000 = $1,050 (a premium). The number 100 in a bond quote is not a dollar price of $100.
- Corporate and municipal par are both $1,000. Municipals trade in a $5,000 minimum denomination (five bonds); do not confuse the block size with the par value of one bond. These values come up frequently on the exam.
Coupon (Nominal Yield)
- The annual interest rate stated on the bond at issuance
- Fixed for the life of a fixed-rate bond (does not change)
- Determines the dollar amount of interest payments
- Formula: Annual interest = Coupon rate x Par value
- The coupon rate is always expressed as an annual rate; the bond's maturity determines how many annual payments you receive, not the size of each payment
Example: A bond with a 5% coupon and $1,000 par:
- Annual interest = 5% x $1,000 = $50
- Semiannual payment = $25
Exam Tip: Gotchas
- Coupon yield never changes. It is fixed at issuance, regardless of what happens to the bond's market price.
- Current yield changes daily as the market price moves, but nominal yield stays the same for the life of the bond.
The Four Yield Measures
These four yields and their relationships are frequently tested:
| Yield Type | Formula | What It Measures |
|---|---|---|
| Nominal (coupon) yield | Annual coupon / Par value | The stated interest rate |
| Current yield | Annual coupon / Current market price | Income return at today's price |
| Yield to Maturity (YTM) | Total return if held to maturity | Includes coupon + price gain or loss |
| Yield to Call (YTC) | Total return if called early | Uses call price and call date instead of par and maturity |
The Yield Hierarchy
The relationship between yields depends on whether the bond trades at a discount, premium, or par:
Discount Bond (price below par)
The investor earns a capital gain at maturity, so yields that account for this gain are higher:
Coupon yield < Current yield < YTM < YTC
- YTC is highest because the discount is earned over a shorter period (to the call date), amplifying the annualized return
Premium Bond (price above par)
The investor takes a capital loss at maturity, so yields that account for this loss are lower:
Coupon yield > Current yield > YTM > YTC
- YTC is lowest because the premium loss is compressed into a shorter period
Par Bond
When a bond trades at par, all four yields are equal:
Coupon yield = Current yield = YTM = YTC
Memory Aid: Discount Climbs, Premium Dips
Read the ladder by the comparison signs, not just by the left-to-right order:
- Discount bond: yields climb as you move right: Nominal < Current < YTM < YTC
- Premium bond: yields dip as you move right: Nominal > Current > YTM > YTC
- Par bond: yields stay flat: Coupon = Current = YTM
Exam Tip: Gotchas
- The yield hierarchy is frequently tested. For discount bonds, yields get progressively higher as you account for more factors (coupon < current < YTM < YTC). For premium bonds, the pattern reverses completely.
- At par, all four yields are equal. If the exam describes a bond trading at par, every yield measure gives the same answer.
Accrued Interest
When a bond trades between its scheduled interest payment dates, the buyer owes the seller the interest that has built up since the last coupon payment. This built-up interest is called accrued interest.
- The buyer pays the accrued interest to the seller at settlement, in addition to the bond's price
- The buyer is made whole at the next coupon date, when they receive the full interest payment
- Accrued interest is added to the buyer's cost of the bond
Day-count Conventions
How the days are counted depends on the type of bond:
| Bond Type | Day-count Basis | How Days Are Counted |
|---|---|---|
| Corporate, municipal, and agency | 30/360 | Every month counts as 30 days; the year counts as 360 days |
| U.S. government (Treasuries) | Actual/365 | The actual number of days; the year counts as 365 days |
Think of it this way: A 30/360 bond treats every month as if it had exactly 30 days, so the math is simple and predictable. U.S. government bonds skip that shortcut and count the real number of days on the calendar.
Exam Tip: Gotchas
- Corporate, municipal, and agency bonds use 30/360. Only U.S. government securities (Treasuries) use actual days (actual/365).
- The buyer pays accrued interest to the seller, not the other way around. The seller earned that interest while holding the bond, so the buyer reimburses it at settlement and collects it back at the next coupon payment.
What Should You Check on Exam Day?
- Can you explain why a bond quoted at 98 means $980, not $98?
- Do you know how the four yields rank on a discount bond versus a premium bond?
- Can you state which yield measure never changes after a bond is issued?
- Do you know who pays accrued interest at settlement, the buyer or the seller?
- Can you explain which bonds use the 30/360 day-count and which use actual/365?