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: standard par value of $5,000
- 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.
- Corporate par = $1,000; municipal par = $5,000. These standard 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
For a discount bond, each yield measure climbs higher (Nominal → Current → YTM → YTC). For a premium bond, each measure dips lower in the same order. Par sits flat (all four equal).
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.