Yield to Call vs Yield to Maturity: Worked Example and Yield to Worst
A callable bond has two quoted yields because it has two possible holding periods: you might hold it to maturity, or the issuer might redeem it early at the first call date. Yield to maturity (YTM) prices the first path; yield to call (YTC) prices the second. Most explanations give the definitions and stop there. Below, both yields are calculated for the same bond step by step, then the direction is tested against a discount bond to show it flips, and the whole thing is extended into yield to worst — the single number dealers and regulators actually require when a bond has several call dates.
What each yield assumes
Both calculations use the bond's actual market price today. They differ only in which future redemption event and time horizon they price to:
| Yield | Assumes you're paid off at… | Redemption value used | Holding period used |
|---|---|---|---|
| Yield to maturity (YTM) | the bond's final maturity date | face value | years to maturity |
| Yield to call (YTC) | a specific call date | that date's call price (often at or above par) | years to that call date |
Both use the same approximate-yield formula, just with different redemption values and time horizons plugged in: Yield ≈ [C + (Redemption − Price) ÷ n] ÷ [(Redemption + Price) ÷ 2], where C is the annual coupon, n is years to that redemption event, and Price is today's market price. This is the standard shortcut formula taught for both YTC and YTM before reaching for a financial calculator's exact IRR; it does not require the whole cash-flow schedule.
Why the direction flips: premium vs. discount
Whether YTC lands above or below YTM depends entirely on whether the bond trades at a premium or a discount to its redemption value:
| Bond trades at… | Relationship | Why |
|---|---|---|
| A premium (price > call/face value) | YTC < YTM | An early call cuts short the period over which the premium you paid gets amortized away, pulling the annualized yield down. |
| A discount (price < call/face value) | YTC > YTM | An early call returns you to par (or the call price) sooner, so the discount you bought at is recovered faster, pushing the annualized yield up. |
In practice this means issuers rarely call a discount bond — there's no refinancing benefit to redeeming debt that's trading below what they'd have to pay to retire it — so the discount-bond case above is a useful teaching contrast more than a common real event. Premium bonds, trading above their call price because rates have fallen since issuance, are the case where an issuer calling early is actually likely.
Worked example 1: a premium bond
A $1,000 face-value bond pays a 6% annual coupon ($60/year), matures in 10 years, and is callable in 5 years at $1,020. It currently trades at $1,075 because market rates have fallen below 6% since issuance.
| Yield | Redemption | n | Calculation | Result |
|---|---|---|---|---|
| YTM | $1,000 (face, year 10) | 10 | [60 + (1,000−1,075)÷10] ÷ [(1,000+1,075)÷2] = [60−7.50] ÷ 1,037.50 | 5.06% |
| YTC | $1,020 (call, year 5) | 5 | [60 + (1,020−1,075)÷5] ÷ [(1,020+1,075)÷2] = [60−11.00] ÷ 1,047.50 | 4.68% |
YTC (4.68%) comes in below YTM (5.06%), exactly as the premium-bond rule predicts: the $75 premium you paid gets amortized over 5 years instead of 10, so it drags the annualized return down harder.
Worked example 2: the same math on a discount bond
Now a $1,000 face-value bond pays a 5% annual coupon ($50/year), matures in 10 years, is callable in 5 years at par ($1,000), and currently trades at $950 because market rates have risen since issuance.
| Yield | Redemption | n | Calculation | Result |
|---|---|---|---|---|
| YTM | $1,000 (face, year 10) | 10 | [50 + (1,000−950)÷10] ÷ [(1,000+950)÷2] = [50+5.00] ÷ 975 | 5.64% |
| YTC | $1,000 (call, year 5) | 5 | [50 + (1,000−950)÷5] ÷ [(1,000+950)÷2] = [50+10.00] ÷ 975 | 6.15% |
The direction has flipped: YTC (6.15%) now sits above YTM (5.64%), because the $50 discount is recovered over 5 years instead of 10. This is the same formula, the same shape of bond, with only the price moved from above to below the redemption value.
Yield to worst: picking the minimum across every call date
Real callable bonds, especially municipal bonds, often carry several call dates rather than one. Yield to worst (YTW) is simply the lowest yield among YTM and the YTC at every one of those dates — the most conservative number, since it assumes whichever outcome pays you back the least gets exercised.
Take a $1,000 face-value, 15-year, 7% annual-coupon bond ($70/year) trading at $1,120, callable at three dates:
| Redemption event | Redemption value | n (years) | Approximate yield |
|---|---|---|---|
| Call, year 5 | $1,035 | 5 | 4.92% |
| Call, year 8 | $1,015 | 8 | 5.33% |
| Call, year 12 | $1,005 | 12 | 5.69% |
| Maturity, year 15 | $1,000 | 15 | 5.85% |
The yield rises steadily from the earliest call date to maturity — typical for a premium bond, since each later date amortizes the premium over more years. The lowest figure is the year-5 call at 4.92%, so that is this bond's yield to worst: if you're quoted a flat yield on this bond with no other detail, 4.92% is the number you can actually count on, not the 5.85% YTM.
Why this isn't just an academic distinction
The Municipal Securities Rulemaking Board requires dealers pricing a callable municipal bond on a yield basis to compute the dollar price to whichever of the call dates or maturity produces the lowest price for the customer, and to disclose which call date and price were used — the regulatory version of "quote the worst case, not the optimistic one." That's the same logic as yield to worst: a bond advertised at its YTM alone can overstate what a buyer will actually realize if it gets called early, so professional quoting conventions default to the conservative figure instead.
Quick reference
| Situation | What to expect |
|---|---|
| Bond trades at a premium | YTC < YTM; the earliest call date usually gives the lowest (worst) yield |
| Bond trades at a discount | YTC > YTM; calls are unlikely in practice, so yield to worst ≈ YTM |
| Multiple call dates exist | Compute the approximate yield to every date and to maturity; the smallest is the yield to worst |
This topic's practice questions cover both the callable-bond call-risk mechanic and the premium-bond YTC-vs-YTM relationship worked through above; try PassDrill's fixed-income practice questions to apply it.
This page is educational material to help you understand and practice bond-yield math; it is not investment, financial, or professional advice, and no specific security is recommended.
Source: CFA Institute Level I curriculum, Fixed Income topic area, yield-measures reading, for the standard yield-to-call/yield-to-maturity/yield-to-worst definitions and the approximate-yield formula (cross-checked against eFinanceManagement's and Achievable's worked treatments of the same formula and premium/discount direction, since the CFA Institute's own curriculum text sits behind a paywall); Municipal Securities Rulemaking Board, Rule G-15 interpretive guidance "Pricing to Call" (msrb.org/node/11893), for the dealer requirement to price callable municipal bonds to the lowest of call or maturity. All figures above are independently calculated for this example, not reproduced from either source.