Matching a liability with a bond and a reserve
Series X-A case study · set 2, case 7 of 9 · 5 questions · 2 marks each
Question 1 of 5Case practice
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A trust must pay ₹12.1 lakh exactly two years from today. A zero-coupon instrument promises ₹12.1 lakh at that date and is priced to yield 10% annually. Assume it is default-free for this exercise and will be held to maturity. The trust has ₹11 lakh available today, of which ₹1 lakh must remain liquid for operating emergencies. It cannot borrow. A salesperson instead suggests using the entire amount in a long-duration fund whose value is not guaranteed on the payment date. The trust’s principal objective for this allocation is to meet the dated liability, rather than maximise an uncertain return. Ignore taxes and transaction costs.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
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The case and its answers
Every question of this case, with its answer and why each other option is wrong.
A trust must pay ₹12.1 lakh exactly two years from today. A zero-coupon instrument promises ₹12.1 lakh at that date and is priced to yield 10% annually. Assume it is default-free for this exercise and will be held to maturity. The trust has ₹11 lakh available today, of which ₹1 lakh must remain liquid for operating emergencies. It cannot borrow. A salesperson instead suggests using the entire amount in a long-duration fund whose value is not guaranteed on the payment date. The trust’s principal objective for this allocation is to meet the dated liability, rather than maximise an uncertain return. Ignore taxes and transaction costs.
All people, firms, prices and contract terms are fictional.
Ignore taxes and transaction costs unless the case explicitly includes them.
Q1What is the present price of the zero-coupon instrument?
Option A. ₹9 lakh
Why it is wrong: This subtracts simple interest rather than discounting.
Option B. ₹11 lakh
Why it is wrong: This discounts for only one year.
Option C. ₹10 lakh — Correct answer
Option D. ₹12.1 lakh
Why it is wrong: This is the maturity cash flow.
Answer: C. ₹12.1 lakh ÷ 1.10² = ₹10 lakh. Remember: A zero-coupon bond’s value is the discounted maturity amount.
Hint, shown before you answer in practice mode: Discount the maturity payment over two years.
XA-S2-C07-Q1mediumnumerical
Q2How much may the trust allocate after preserving its operating reserve?
Option A. ₹9 lakh
Why it is wrong: This deducts the reserve twice.
Option B. ₹11 lakh
Why it is wrong: This uses the reserved operating cash.
Option C. ₹12.1 lakh
Why it is wrong: This is the future liability, not cash available today.
Option D. ₹10 lakh — Correct answer
Answer: D. ₹11 lakh − ₹1 lakh = ₹10 lakh. Remember: Portfolio construction must respect separately earmarked liquidity.
Hint, shown before you answer in practice mode: Remove the reserved ₹1 lakh from today’s available money.
XA-S2-C07-Q2mediumnumerical
Q3What is the funding shortfall today if the bond is purchased at the calculated price?
Option A. ₹2.1 lakh
Why it is wrong: This compares today’s cash directly with a future liability.
Option B. ₹10 lakh
Why it is wrong: This ignores all available investible cash.
Option C. ₹1 lakh
Why it is wrong: The operating reserve is already excluded from investible cash.
Option D. ₹0 — Correct answer
Answer: D. Both the bond price and investible amount are ₹10 lakh. The present funding gap is zero. Remember: A liability can be fully funded today with less than its future amount.
Hint, shown before you answer in practice mode: Compare the present cost with the investible money at the same date.
XA-S2-C07-Q3mediumnumerical
Q4Why does holding the assumed default-free bond to the matched date fit the stated objective?
Option A. Its maturity cash flow and date match the required payment. — Correct answer
Option B. It guarantees the highest possible return among all products.
Why it is wrong: The case only specifies its payment and yield.
Option C. It removes the need for the operating reserve.
Why it is wrong: The separate reserve remains required.
Option D. Its market price cannot change before maturity.
Why it is wrong: A bond’s market price can still change if yields change.
Answer: A. The promised maturity amount is the exact liability, payable at the required time. Interim market fluctuations need not force a sale under these assumptions. Remember: Cash-flow matching reduces dependence on future selling prices.
Hint, shown before you answer in practice mode: Focus on the liability’s amount and date.
XA-S2-C07-Q4mediumapplication
Q5What is the main weakness of the salesperson’s proposal for this allocation?
Option A. A long-duration fund must default.
Why it is wrong: Duration risk does not establish default.
Option B. The fund is certain to earn zero.
Why it is wrong: The case does not specify its return.
Option C. It uses reserved liquidity and leaves the liability dependent on an uncertain future fund value. — Correct answer
Option D. The trust has no dated cash need.
Why it is wrong: The payment date and amount are explicitly stated.
Answer: C. Using all ₹11 lakh breaches the reserve instruction. The proposed fund also does not provide the matched, assumed-certain payment of the zero-coupon instrument. Remember: A higher-return story does not override a binding cash-flow objective.
Hint, shown before you answer in practice mode: Check both the reserve constraint and certainty of the dated payment.
XA-S2-C07-Q5mediumapplication
Two assets whose risks do not move together
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