CFA Level I Exam · Yield and Yield Spread Measures for Fixed-Rate Bonds

Yield to Call, Yield to Worst and Callable Bonds

Updated 7 October 2026 · Fact-checked

Yield to call is the discount rate that equates a callable bond's price to its coupons up to a call date plus the call price. Yield to worst is the lowest of the yield to maturity and the yields to every call date. Set N to the call date, FV to the call price, then compute the rate.

Understand Yield to Call, Yield to Worst and Callable Bonds

A callable bond gives the issuer the right to redeem the bond early at a set call price, usually on or after stated call dates. Issuers use this right when rates fall, so they can refinance more cheaply. The investor bears this risk, so a callable bond pays a higher yield than a similar option-free bond.

Yield to maturity (YTM) assumes you hold the bond to its final maturity date. For a callable bond that may not happen. Yield to call (YTC) assumes the issuer redeems the bond on a specific call date. You use the same pricing equation as YTM. The only changes are that the number of periods runs to the call date and the final payment is the call price, not par.

A call schedule can have many dates, for example a first call at 103, then 102, then a par call date at 100. You can compute a yield for each date. Yield to worst (YTW) is the lowest of all these yields, including YTM. It is the most conservative return you can earn if the issuer acts in its own interest and the bond does not default. A bond trading above its call price usually has YTC below YTM, so the worst case is an early call. A bond trading at a discount to the call price is unlikely to be called, because the issuer would pay more than market value to redeem it. Its YTW is usually the YTM, but check.

For a putable bond, the investor holds the option. The same logic gives a yield to put: use the put date and put price. The investor is likely to exercise the put when the bond price is below the put price, and then you compute the yield to put.

For mortgage-backed and other amortizing securities, the principal can be repaid early by borrowers. The cash flow yield is the internal rate of return on the projected cash flows, which include an assumed prepayment speed. If you change the prepayment assumption, the yield changes. All of these yields are still promised-style measures: they ignore how rate changes would affect the option's value. Spread measures such as OAS handle that.

Key formulas to remember

Yield to call pricing equation: Price = Σ PMT ÷ (1 + r)^t, t = 1 to n, + Call price ÷ (1 + r)^n; n is the number of periods to the call date and r is the periodic yield. Use the call price, not par, as the final redemption value.
Annualizing the periodic yield: Annual yield (bond-equivalent) = r × number of periods per year; For semiannual coupons, double the periodic rate. Do not compound it unless the question asks for an effective annual yield.
Yield to worst: YTW = minimum of (YTM, YTC at each call date); Include every call date in the schedule. For a putable bond, compute the yield to put separately when put exercise is expected.
Cash flow yield: Price + accrued interest = Σ CFt ÷ (1 + y)^t; CFt are projected interest and principal, including prepayments under an assumed speed. y is the periodic (usually monthly) rate, then annualized.
TVM keys for yield to call: N = periods to call; PMT = coupon per period; FV = call price; PV = –price; CPT I/Y; The price entered as PV must be negative if PMT and FV are positive.

How to solve Yield to Call, Yield to Worst and Callable Bonds questions

Use the same routine for yield to call, yield to put and yield to worst. You are only changing the end date and the final payment.

1List every possible redemption date: each call date, each put date if any, and maturity. Note the redemption price for each.
2For each date, count the number of periods from today. Convert years to periods using the coupon frequency, for example 3 years × 2 = 6 for semiannual coupons.
3Find the coupon per period: annual coupon rate × par ÷ frequency.
4Enter N, PMT, FV (the call price, put price or par at maturity) and PV (the negative of the price). Compute I/Y.
5Annualize by multiplying the periodic rate by the number of periods per year, unless told otherwise.
6Compare the yields. Yield to worst is the lowest yield across the call dates and maturity. Compute a yield to put when put exercise is expected; the lowest-yield rule is not applied to it.
7Do a reasonableness check: a bond trading at a premium to the call price has YTC below YTM, and a discount bond has YTC above YTM when the call price is at least par.

Quickest way: Premium or discount shortcut to pick the likely worst date

When to use it: Use this when a question asks which yield is the yield to worst, or when you have little time and need to eliminate options.

Compare the price with the redemption price. If the bond trades above the call price, early redemption loses you the premium, so expect YTC to be lowest.
If the bond trades well below the call price, early redemption is a gain, so the call is unlikely to be the worst case and YTM is usually the lowest. Verify by calculation if the numbers are close.
Use the coupon rate as a check, with care. A bond priced above the call price will have YTC below its coupon rate. If the call price is above par, a bond priced at a modest premium to par can have a YTC above the coupon, as in the second worked example (price 100, call 102).
Compute only the one or two yields that could be lowest, not every date. Under the three-option format, a check against the coupon rate and the current yield often eliminates two answers.

Common mistakes in Yield to Call, Yield to Worst and Callable Bonds

Using par as the final payment when calculating yield to call.
Habit from YTM questions, where FV is always par.
Fix: Read the call price in the stem. Put the call price in FV and the number of periods to the call date in N.
Forgetting to double or halve for semiannual coupons.
N is entered in years and PMT as the annual coupon.
Fix: Convert N to periods and PMT to the coupon per period. Then multiply the result by the frequency to annualize.
Choosing the yield to the first call date as the YTW without comparing other dates.
The first call date is often lowest, so students treat it as a rule.
Fix: A step-down call schedule or a discount price can change the result. Calculate or sensibly compare each date, and include YTM.
Entering price as a positive PV with a positive PMT and FV.
Calculators expect a cash-flow sign convention.
Fix: Enter PV as a negative number, or enter PMT and FV as negatives. The calculator then returns a positive I/Y.
Treating yield to call as a sure return.
The word 'yield' suggests a guaranteed outcome.
Fix: It assumes the bond is called on that date, that there is no default and that coupons are reinvested at the same yield. Say it is a measure, not a promise.
Thinking cash flow yield is a fixed number for a mortgage security.
Students treat it like YTM on a bullet bond.
Fix: Cash flow yield depends on the assumed prepayment speed. Faster or slower prepayments give different projected cash flows and a different yield.

Worked examples

Example 1

A bond pays an 8% annual coupon on par of 100 and has 3 years to maturity. It is callable in one year at 100, and that is the only call date. The price is 106. Which is the yield to worst? A. 1.89% B. 5.77% C. 7.55%

Show the solution

List redemption dates: call in 1 year at 100, and maturity in 3 years at 100.
Yield to call: in one year you receive the coupon of 8 plus the call price of 100, so 106 = 108 ÷ (1 + r).
Then r = 108 ÷ 106 – 1 = 0.01887, or 1.89%.
Yield to maturity: solve 106 = 8 ÷ (1 + r) + 8 ÷ (1 + r)² + 108 ÷ (1 + r)³. At r = 5.77%, the value is about 105.99, so YTM is about 5.77%.
Option C, 7.55%, is the current yield (8 ÷ 106), which is not a redemption yield.
YTW is the lowest of 1.89% and 5.77%.

Answer: A. The yield to worst is 1.89%, the yield to the call date.

Example 2

A bond pays a 5% annual coupon on par of 100 and is first callable in 2 years at 102. It trades at 100. What is the yield to call? A. 5.00% B. 5.97% C. 7.00%

Show the solution

Set up: N = 2, PMT = 5, FV = 102, PV = –100.
Equation: 100 = 5 ÷ (1 + r) + 107 ÷ (1 + r)², where 107 is the final coupon plus the call price.
Let x = 1 ÷ (1 + r). Then 107x² + 5x – 100 = 0, so x = (–5 + √42,825) ÷ 214 = 0.94365.
Then r = 1 ÷ 0.94365 – 1 = 0.0597, or 5.97%.
Check: 5 × 0.94365 = 4.718 and 107 × 0.89047 = 95.28, which sum to about 100.
Calculator: 2 [N], 5 [PMT], 102 [FV], –100 [PV], [CPT] [I/Y] gives 5.97. On the HP 12C: 2 [n], 5 [PMT], 102 [FV], 100 [CHS] [PV], [i].
Option A is the coupon rate, which would be the yield only if the call price were par. Option C is too high for a bond at par.

Answer: B. The yield to call is about 5.97%, higher than the 5% coupon because the bond is redeemed at a premium.

Exam tips

Read the stem for the call price, the call date and the coupon frequency before you touch the calculator. Most errors come from the wrong FV or N.
If a question says the bond is trading at a premium to the call price, expect the answer to be a yield to call. If it trades at a discount, test YTM first.
Use the coupon rate as a check, with care. A premium bond's yield should be below the coupon rate and a discount bond's above it for YTM, and for YTC when the call price is par or the bond trades above the call price. If the call price is above par, YTC can exceed the coupon even at par, as in the second worked example.
For cash flow yield, remember it is an IRR on projected cash flows that depends on the prepayment assumption. The wording 'assumed prepayment speed' is the cue.
In ethics-free calculation items, leave the price negative on the calculator and clear the TVM registers between questions so old values do not carry over.

Practice questions from Yield and Yield Spread Measures for Fixed-Rate Bonds

Yield to Call, Yield to Worst and Callable Bonds: frequently asked questions

What is the difference between yield to call and yield to maturity?

Both solve the same pricing equation. Yield to maturity uses the maturity date and par as the final payment. Yield to call uses a call date and the call price instead. The two differ because the cash flows and the time to redemption differ.

How do I calculate yield to worst on the CFA Level I exam?

Calculate the yield for every possible redemption date, including maturity and each call date. Then choose the lowest. In practice, test the dates that are most likely to be lowest, based on whether the bond trades at a premium or discount.

What is the par call date?

It is the first date when the issuer can redeem the bond at par, 100. Before that date, the call price may be above par. After it, the bond can be called at par. Yields are tested at each date in the schedule.

Is yield to worst always the yield to the first call date?

No. It is often the first call for a premium bond, but not always. A call schedule with changing prices, or a bond at a discount, can give a lower yield at another date or at maturity. Compare them.

What is cash flow yield?

It is the internal rate of return on a security's projected cash flows, such as a mortgage-backed security with an assumed prepayment speed. Because the projected cash flows change when prepayments change, the cash flow yield is not fixed.