Call Protection and the First Eligible Redemption Date

Why Call Protection Must Be Checked First

A yield calculation depends on the cash flows the bond could actually pay. For a callable bond, those cash flows depend on the redemption date. But a listed call price does not by itself make a date available: the contract may protect the bond from redemption for an initial period. The first step is therefore to read the protection clause and identify the eligible redemption dates. Only then should you calculate yields for call scenarios.

This order matters in an exam problem because a yield equation can be calculated for a date that is not contractually possible. Such a calculation may be algebraically correct and still answer the wrong question. The treatment here is aligned with the SOA Exam FM (Financial Mathematics) syllabus.

Definition: A bond has a call-protection period when its terms prohibit the issuer from redeeming it by call during a stated initial period. The first eligible redemption date is the earliest date on which the contract permits a call. A date at which a call price is specified is not eligible if it falls within the protection period. Maturity is a separate contractual redemption date and remains available even when earlier calls are protected.

Translate the Contract into a Timeline

Call-protection wording must be interpreted together with the dates on which the contract allows redemption. For example, “not callable before the second anniversary” excludes dates strictly before that anniversary, while “not callable on or before the second anniversary” excludes the anniversary itself as well. If calls are allowed only on coupon dates, a date between coupon dates is not made eligible merely because the protection period has ended.

There is no universal convention that resolves every possible wording. Use the stated contractual terms, including whether the boundary date is included, and do not infer an unstated call date. A reliable way to organize the information is to mark each date as protected, eligible for call, or maturity:

Protected: the issuer cannot redeem by call on this date.
Eligible for call: the contract permits a call on this date, at the stated call price.
Maturity: the contractual final date, when the stated maturity payment is due if the bond has not been called earlier.

The call price is the principal redemption amount for the relevant date; the coupon due on that date is an additional cash flow if the contract says it is paid. In a yield equation, include both when applicable. The yield is the annual effective rate that equates the purchase price with the present value of the cash flows for the specified, eligible redemption scenario.

Key procedure: Read the protection boundary, identify the contract’s permitted dates, remove protected call dates, and then set up a separate yield equation for each scenario the question asks you to evaluate.

Why the Yield Equation Uses Only Eligible Dates

For a fixed redemption scenario, let $P$ be the bond’s purchase price, let $C_k$ be the cash flow at time $k$, and let $i$ be the annual effective yield per year. The present value equation is

P=\sum_{k=1}^{n} C_k v^k, \qquad v=\frac{1}{1+i}.

This equation follows from the definition of yield: each future payment is discounted at the rate $i$, and the discounted payments must add to the observed price. A call scenario specifies which coupons are paid and the date and amount of the redemption payment. If a call date is protected, the issuer cannot produce that scenario under the contract. It therefore cannot be used as a valid call-yield scenario, even if substituting its stated price into the equation would produce a numerical answer.

For level annual coupons $C$ paid at the ends of years 1 through $n$, and a redemption payment $R$ at the end of year $n$, the equation can be written as

P=C a_{\overline{n}|}+R v^n, \qquad a_{\overline{n}|}=\frac{1-v^n}{i}.

The annuity factor represents the present value of the coupons, while $Rv^n$ represents the present value of the redemption payment. The same structure applies to a call scenario when $n$ is replaced by the eligible call year and $R$ by that date’s call price. This does not mean every eligible date must be evaluated in every question; calculate the scenarios the question requests, after filtering out dates the contract prohibits.

Worked Examples

Worked Example: Finding the First Eligible Call Date

A four-year bond has face value $1,000 and annual coupons of $40, paid at each year-end. Its schedule lists a call price of $1,050 at year 1, $1,025 at year 2, and $1,000 at year 3. The terms state that the bond is not callable on or before the second anniversary. It matures at year 4 for $1,000. The market price is $1,000. Find the first eligible call date and the yield to that date.

Method: establish eligibility before discounting. The call dates at years 1 and 2 are both prohibited: the first is before the second anniversary, and the second is on it. The first eligible call date is year 3, with call price $1,000. If called then, the investor receives three coupons of $40 and the $1,000 call payment at year 3.

Set $i$ equal to the annual effective yield to the eligible year-3 call. The yield equation is

1000=40a_{\overline{3}|}+1000v^3.

Test $i=0.04$. The discount factor is $v=1/1.04=0.96153846$. Thus $v^2=0.92455621$ and $v^3=0.88899636$. The annuity factor is $a_{\overline{3}|}=(1-0.88899636)/0.04=2.775091$. The coupon present value is $40(2.775091)=111.00364$, and the call-payment present value is $1000(0.88899636)=888.99636$. Their sum is $1,000.00 to the displayed precision.

The yield to the first eligible call is therefore 4.000% per year. The maturity date is also a contractual scenario, but it is not the first call date asked for here. The method avoids the common mistake of treating a listed year-1 call price as permission to call during the protected period.

Worked Example: Calculating Yield to a Call After Protection Ends

A four-year bond with face value $1,000 pays annual coupons of $60. The call schedule lists prices of $1,050 at year 1, $1,040 at year 2, and $1,020 at year 3. The bond is protected from call through the end of year 2. Its market price is $1,044.50923. Find the yield to the first eligible call date.

Method: use only the first unprotected call date. Protection through the end of year 2 makes years 1 and 2 ineligible. The first eligible call is at year 3, with a call price of $1,020. The investor receives three $60 coupons and the $1,020 redemption payment at year 3. In particular, the year-3 payment includes the coupon and call price, for a total cash flow of $1,080 at that date.

The equation for the yield $i$ is

1044.50923=60a_{\overline{3}|}+1020v^3.

Test $i=0.05$. Then $v=1/1.05=0.95238095$, $v^2=0.90702948$, and $v^3=0.86383760$. The annuity factor is $a_{\overline{3}|}=(1-0.86383760)/0.05=2.72324803$. The coupons have present value $60(2.72324803)=163.39488$. The call payment has present value $1020(0.86383760)=881.11435$. The total is $163.39488+881.11435=1044.50923$, matching the market price.

The yield to the first eligible call is 5.000% per year. The calculation is valid for year 3 because that date is permitted; yields based on the year-1 or year-2 call prices would describe prohibited scenarios. The common mistake is to calculate yields for every printed call price without first applying the protection clause.

Worked Example: Keeping Maturity Separate from Protected Call Dates

A five-year bond has face value $1,000, annual coupons of $60, and a market price of $1,000. It is protected from call through year 1. The schedule allows calls at year 2 for $1,030, year 3 for $1,020, and year 4 for $1,010; if not called, the bond pays $1,000 at maturity in year 5. Find the yield to maturity and state which dates are eligible call dates.

Method: identify scenarios, then calculate the requested one. The year-1 date is protected. The eligible call dates are years 2, 3, and 4. Year 5 is maturity, not an earlier call date. For the requested yield to maturity, the assumed cash flows are five coupons of $60 plus the $1,000 maturity payment at year 5.

The yield equation is

1000=60a_{\overline{5}|}+1000v^5.

At $i=0.06$, $v=1/1.06=0.94339623$, and $v^5=0.74725817$. Therefore, $a_{\overline{5}|}=(1-0.74725817)/0.06=4.21236383$. The coupons have present value $60(4.21236383)=252.74183$, and the maturity payment has present value $1000(0.74725817)=747.25817$. These add to $1,000.00.

The yield to maturity is 6.000% per year. No year-1 call yield is a valid call scenario because year 1 is protected. This example distinguishes two questions: whether a date is an eligible call date, and what yield follows from the maturity cash flows.

Common Exam Trap: A Listed Date Is Not Automatically Eligible

Suppose a bond’s terms say that it cannot be called on or before year 2, but the schedule lists call prices at years 1, 2, and 3. A tempting but incorrect approach is to use the year-1 price and set up a yield equation with one coupon and that redemption amount. That equation may have a solution, but the contract rules out the year-1 redemption. It is not a valid yield-to-call scenario.

The correction is to apply the boundary wording first: years 1 and 2 are excluded, and year 3 is the first possible call date if the contract permits calls then. The distinction between “before year 2” and “on or before year 2” can change the first eligible date. Read the exact phrase rather than relying on an assumed industry convention.

Read the protection boundary.
Determine whether the boundary anniversary itself is excluded and note any allowed call-date restrictions.

Mark the available dates.
Separate protected call dates from eligible call dates and maturity.

Build each requested cash-flow scenario.
Include coupons through the redemption date and the call or maturity payment due on that date.

Calculate only the requested valid yields.
Do not include a protected call date in a yield comparison or a yield-to-worst calculation.

This filtering step is useful beyond a single yield calculation. Any comparison across call scenarios must be based on scenarios the contract allows. Call protection can remove an otherwise plausible early redemption from consideration, changing which dates need to be analyzed. The relevant dates come from the bond’s actual terms, not from the arithmetic convenience of a yield equation.

Check Your Understanding

For each problem, determine the eligible date or calculate the requested yield using only the permitted scenario.

A bond matures at year 8. It lists annual call dates beginning at year 1, but the terms prohibit calls through the end of year 3. What is the first eligible call date? (Answer: Year 4.)
A seven-year bond pays coupons every six months. It is not callable on or before 18 months, and calls are permitted only on coupon dates. What is the first eligible call date, and how many eligible call dates are there through maturity? (Answer: The first eligible date is 2 years; there are 11 eligible dates from 2 years through 7 years, inclusive.)
A bond costs $999.546485 and pays a $40 coupon at each year-end. It is protected through year 1 and may be called at year 2 for $1,020. Find its yield to the first eligible call. (Answer: 5.000% per year, since $999.546485=40/1.05+1060/(1.05)^2$, to the stated price precision.)
A bond’s contract says “not callable on or before 30 months.” It pays coupons every six months, and calls can be made only on coupon dates. What is the first eligible call date? (Answer: 3 years.)
A six-year bond is protected through year 2. Its call schedule lists prices at years 1, 2, 3, 4, and 5, and it redeems at maturity in year 6 if not previously called. Which dates are eligible call dates, and which is the maturity date? (Answer: Years 3, 4, and 5 are eligible call dates; year 6 is maturity.)

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