How do investors measure what they actually earn on a bond? This unit covers the six yield measures you need for the Series 7 and, more importantly, how they rank for premium and discount bonds.
Yield Measures
| Yield | Formula / Description | When to Use |
|---|---|---|
| Coupon yield (nominal yield) | Annual Coupon / Par Value | Stated rate on the bond; never changes |
| Current yield | Annual Coupon / Current Market Price | Measures current income return only |
| Yield to maturity (YTM) | Total return if held to maturity (coupon + price gain/loss + time) | Most comprehensive yield for non-callable bonds |
| Yield to call (YTC) | Total return if held to the first call date | Use for callable bonds trading at a premium |
| Yield to worst | The lowest of YTM and all possible YTCs | Most conservative measure; use for callable bonds |
| Discount yield | (Par - Price) / Par x (360 / days to maturity) | Used for money market instruments (T-bills, commercial paper) |
Exam Tip: Gotchas
- Yield to maturity (YTM) is the most comprehensive yield for non-callable bonds. It accounts for coupon income, price gain or loss, and time to maturity.
- Discount yield uses a 360-day year (not 365). This convention applies to money market instruments like T-bills and commercial paper.
Yield Relationships for Premium and Discount Bonds
This ranking is essential to memorize:
Premium bond (price > par):
Coupon Yield > Current Yield > YTM > YTC (lowest)
Discount bond (price < par):
Coupon Yield < Current Yield < YTM < YTC (highest)
Par bond (price = par):
Coupon Yield = Current Yield = YTM
| Bond Type | Nominal Yield (NY) vs. Current Yield (CY) | CY vs. YTM | YTM vs. YTC |
|---|---|---|---|
| Premium | NY > CY | CY > YTM | YTM > YTC |
| Discount | NY < CY | CY < YTM | YTM < YTC |
| Par | NY = CY | CY = YTM | All yields equal |
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: Nominal = Current = YTM
Think of it this way: For a premium bond, you paid more than you will get back. The sooner the bond is called, the less time you have to spread that loss, so yield to call (YTC) is the lowest yield. For a discount bond, the opposite is true: the sooner you get called, the faster you pocket the gain, so YTC is the highest yield.
Exam Tip: Gotchas
- For premium bonds, yields decrease as you move right: NY > CY > YTM > YTC. YTC is the lowest because the capital loss is concentrated over fewer years.
- For discount bonds, yields increase as you move right: NY < CY < YTM < YTC. YTC is the highest because the capital gain is concentrated over fewer years.
- Current yield ignores capital gains and losses. It only measures income return (annual coupon / market price).
Yield to Worst
Yield to worst is always the lowest possible yield for a callable bond:
| Bond Type | Yield to Worst Equals |
|---|---|
| Premium callable bond | YTC (issuer is incentivized to call and refinance at lower rates) |
| Discount callable bond | YTM (issuer has no incentive to call when rates are higher) |
Exam Tip: Gotchas
- For a premium callable bond, yield to worst = YTC. The issuer will likely call the bond to refinance at lower rates, so the investor's worst case is early redemption.
- For a discount callable bond, yield to worst = YTM. The issuer has no incentive to call, so the investor holds to maturity at the lower yield.
- Yield to worst is always the lowest possible yield among YTM and all possible YTCs.
The Inverse Relationship Between Price and Yield
Bond prices and yields always move in opposite directions:
- Market interest rates rise → bond prices fall (yields rise)
- Market interest rates fall → bond prices rise (yields fall)
Why does this happen? If you own a bond paying 3% and new bonds start paying 5%, no one wants your 3% bond at full price. You would have to sell at a discount. That is why rising rates push bond prices down.
Price sensitivity factors:
- Longer maturity = greater price sensitivity to rate changes
- Lower coupon = greater price sensitivity to rate changes
- Zero-coupon bonds have the greatest price sensitivity (all cash flow at maturity)
Exam Tip: Gotchas
- Zero-coupon bonds are the most price-sensitive. With no interim coupon payments, the entire return depends on the final payment at maturity, so rate changes have the maximum impact.
- Longer maturity + lower coupon = maximum sensitivity. If asked which bond is most affected by a rate change, pick the one with the longest maturity and lowest coupon.