A bond portfolio faces a parallel yield rise
Series IV practice case · 4 questions · 1 mark each
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A treasury desk owns a bond portfolio worth ₹1,00,00,000. Its modified duration is 4.5. The desk uses the first-order approximation percentage price change = −modified duration × yield change, with yield change written as a decimal. It considers a parallel rise in yields of 0.50 percentage points. A selected bond futures contract has a price value of one basis point, or PVBP, of ₹150 per contract. A long futures position loses about ₹150 when yields rise by one basis point, while a short position gains that amount. Ignore convexity, basis changes, transaction costs and changes in the hedge ratio.
The portfolio duration and contract PVBP are given assumptions.
Results are first-order estimates, not exact price forecasts.
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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 treasury desk owns a bond portfolio worth ₹1,00,00,000. Its modified duration is 4.5. The desk uses the first-order approximation percentage price change = −modified duration × yield change, with yield change written as a decimal. It considers a parallel rise in yields of 0.50 percentage points. A selected bond futures contract has a price value of one basis point, or PVBP, of ₹150 per contract. A long futures position loses about ₹150 when yields rise by one basis point, while a short position gains that amount. Ignore convexity, basis changes, transaction costs and changes in the hedge ratio.
The portfolio duration and contract PVBP are given assumptions.
Results are first-order estimates, not exact price forecasts.
Q1What is the estimated percentage change in the bond portfolio value?
Option A. −2.25% — Correct answer
Option B. −0.225%
Why it is wrong: This understates the yield shock by a factor of ten.
Option C. −225%
Why it is wrong: This treats 0.50 percentage points as a decimal of 0.50 instead of 0.005.
Option D. +2.25%
Why it is wrong: A conventional fixed-rate bond portfolio falls in price when yields rise.
Answer: A. Estimated price change = −4.5 × 0.005 × 100 = −2.25%. The negative sign is essential. Remember: Distinguish percentage points from decimal yield changes.
Hint, shown before you answer in practice mode: Convert the yield move to 0.005 before multiplying.
IV-P-C01-Q1mediumnumerical
Q2What is the estimated loss in rupees before hedging?
Option A. ₹22,500
Why it is wrong: This is only 0.225% of portfolio value.
Option B. ₹2,25,000 — Correct answer
Option C. ₹2,250
Why it is wrong: This omits two zeros when applying the percentage to the portfolio.
Option D. ₹4,50,000
Why it is wrong: This corresponds to a one-percentage-point yield rise.
Answer: B. Estimated loss = ₹1,00,00,000 × 4.5 × 0.005 = ₹2,25,000. Convexity is deliberately excluded. Remember: A duration percentage must be applied to market value.
Hint, shown before you answer in practice mode: Multiply the portfolio value by 2.25%.
IV-P-C01-Q2mediumnumerical
Q3What is the portfolio PVBP under the same approximation?
Option A. ₹150
Why it is wrong: This is the futures contract PVBP, not the portfolio PVBP.
Option B. ₹450
Why it is wrong: This understates exposure by ten times.
Option C. ₹45,000
Why it is wrong: This overstates exposure by ten times.
Option D. ₹4,500 per basis point — Correct answer
Answer: D. Portfolio PVBP = ₹1,00,00,000 × 4.5 × 0.0001 = ₹4,500. It is the approximate price sensitivity to a one-basis-point yield move. Remember: Match portfolio and hedge sensitivities in the same units.
Hint, shown before you answer in practice mode: One basis point is 0.0001 in decimal yield.
IV-P-C01-Q3mediumnumerical
Q4Which futures hedge approximately offsets this portfolio PVBP?
Option A. Sell 3 futures contracts
Why it is wrong: Three contracts cover only ₹450 per basis point.
Option B. Buy 30 futures contracts
Why it is wrong: A long position loses when yields rise, adding to the portfolio loss.
Option C. Sell 30 futures contracts — Correct answer
Option D. Sell 300 futures contracts
Why it is wrong: This would hedge ten times the portfolio PVBP.
Answer: C. Required contracts = 4,500 ÷ 150 = 30. A short futures position gains when yields rise, offsetting the portfolio’s approximate loss. Remember: A hedge needs both the right size and the right direction.
Hint, shown before you answer in practice mode: Divide ₹4,500 by ₹150 and choose the offsetting direction.
IV-P-C01-Q4hardnumerical
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