Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market
30 questions. Each answer is explained.
Question 1 of 10Practice · Series IV — Interest Rate Derivatives
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Learn these topics
More units in NISM Series IV
- Interest Rate Derivatives10
- Exchange Traded Interest Rate Futures20
- Exchange Traded Interest Rate Options22
- Strategies Using Exchange Traded Interest Rate Futures and Options24
- Trading Mechanism in Exchange Traded Interest Rate Derivatives10
- Clearing, Settlement and Risk Management of Interest Rate Derivatives16
- Regulatory Framework for Interest Rate Derivatives8
- Accounting and Taxation of Interest Rate Derivatives4
- Code of Conduct and Investor Protection Measures in Interest Rate Derivatives6
Exam format
| Questions | 100 · 1 mark each |
|---|---|
| Duration | 120 min · 2 hours |
| Pass mark | 60% · 60 of 100 marks |
| Negative marking | 25% · 0.25 marks off per wrong answer |
| Certificate validity | 3 years · from the date of the examination |
| Marks for this unit | Not published by NISM |
NISM Series IV Interest Rate Derivatives
Exam rules read on NISM's site on 3 October 2026. Check the current rules on NISM's site (opens in a new tab)
What these answers assume, and when it was last checked
Each question uses the rules listed below. We last checked them on 5 September 2026. A Budget or SEBI circular can change a rate, lot size or expiry day. If a rule changes before your exam, treat the linked questions as out of date and check NISM's current workbook.
- NSE uses Tuesday expiry and BSE uses Thursday expiry. This applies from 1 September 2025.
- The January 2026 index lot sizes are NIFTY 65, BANKNIFTY 30, FINNIFTY 60, MIDCPNIFTY 120 and NIFTYNXT50 25.
- The October 2024 SEBI framework sets a minimum index contract value of Rs 15–20 lakh. Each exchange may list one weekly benchmark index.
- Option buyers pay the premium upfront from 1 February 2025. A short index option has an extra 2% Extreme Loss Margin on expiry day from 20 November 2024.
- Equity short-term capital gains are taxed at 20%. Long-term gains are taxed at 12.5% above Rs 1.25 lakh. Both rates apply from 23 July 2024.
- F&O income is non-speculative business income in ITR-3. NSE equity derivatives trade from 9:15 a.m. to 3:40 p.m.
- The final ten-minute session began on 3 August 2026. It aligns with the cash market Closing Auction Session.
- Most Securities Transaction Tax questions test the base and who pays. On an option sale, it is the premium and the seller pays. On a futures sale, it is the traded value and the seller pays.
- On exercise, Securities Transaction Tax uses intrinsic value: settlement price minus strike price. The buyer pays it.
- Two questions test the current rate. From 1 April 2026, option sales carry 0.15% on the premium and futures sales carry 0.05% on traded price. The earlier rates were 0.10% and 0.02% from 1 October 2024.
- This section uses the T+1 rolling settlement cycle. Obligations are fixed on T+1. A short delivery goes to buy-in auction on T+1 and settles on T+2.
- The trade-for-trade surveillance segment uses direct close-out. Funds pay in by 10:30 a.m. and pay out on or after 1:30 p.m. on settlement day.
- Securities pay in to the settlement pool by 10:30 a.m. They pay out directly to the client’s demat account by 3:30 p.m.
- The 3:30 p.m. deadline replaced 1:30 p.m. under SEBI’s 10 October 2024 circular. Direct client credit was required by SEBI’s 5 June 2024 circular.
- The optional T+0 cycle trades until 1:30 p.m. Obligations are fixed by 2:30 p.m. on the trade day. An early pay-in shortage is closed out directly.
- Cash-market Value at Risk margin is six times exponentially weighted moving-average volatility. It has a 9% floor for Group I, a 21.5% floor for Group II, and a fixed 50% or 75% level for Group III.
- Extreme Loss Margin is 3.5% for a share and 2% for a broad-market-index exchange traded fund. Mark-to-market margin is collected before the next day’s trading. The trade-for-trade segment has 100% upfront margin.
- Close-out uses the higher of the highest price from trade day to auction day and 20% above the auction day’s official close.
- A funds shortage costs 0.07% a day. The trading facility is withdrawn at a shortage of Rs 5 lakh or more.
- SCORES allows 21 calendar days, then two 15-day review levels. Online Dispute Resolution moves from conciliation to arbitration after the market participant and SCORES steps.
- At NSE, the Investor Protection Fund limit is Rs 35 lakh per investor for each defaulting or expelled member. This applies to claims arising after 13 August 2024.
- A Basic Services Demat Account has no annual maintenance charge up to Rs 4 lakh of holdings. It costs up to Rs 100 above that, until the Rs 10 lakh eligibility ceiling. These slabs apply from 1 September 2024.
- The rupee pairs are USD-INR, EUR-INR, GBP-INR and JPY-INR. The cross-currency pairs are EUR-USD, GBP-USD and USD-JPY.
- Each contract covers 1,000 units of the foreign currency, except JPY-INR. JPY-INR covers 100,000 yen and is quoted in rupees per 100 yen.
- The tick is 0.25 paise, or Rs 0.0025. It equals Rs 2.50 a contract.
- Rupee pairs trade from 9:00 a.m. to 5:00 p.m. A monthly contract stops trading at 12:30 p.m. two working days before the expiry month’s last business day.
- Final settlement is in cash at the FBIL reference rate on expiry day. FBIL, Financial Benchmarks India, has published this rate in place of the Reserve Bank since 2018. Premium-style European options are quoted in rupees. The buyer pays the premium in cash on T+1.
- Daily settlement is on T+1 and final settlement is on T+2.
- NSE Clearing circular 026/2020 sets SPAN margin plus Extreme Loss Margin. The futures margin is 0.50% for USD-INR, 0.15% for EUR-INR, 0.25% for GBP-INR and 0.35% for JPY-INR. A short option has 0.75%. These figures apply from 1 June 2020.
- A USD-INR client may hold 6% of total open interest or USD 20 million, whichever is higher. A trading member may hold 15% or USD 100 million.
- A resident user has one USD 100 million equivalent limit across all rupee pairs and exchanges. No document is needed below that limit, but a valid underlying contracted exposure must still exist. This clarification applies from 3 May 2024.
- The currency segment has no Securities Transaction Tax.
The exam figures (questions, time, pass mark, negative marking and certificate validity) come from NISM's own pages, read on 3 October 2026. Timed practice uses the same figures. Study with the official workbook as well.
The written-out answers on this page are hidden while your timed set runs.
All 30 questions on Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market, with answers
Q1An investor buys a company’s plain fixed-rate bond rather than its ordinary shares. Which entitlement follows from the bond investment?
Option A. A right to have the coupon raised whenever the company’s yearly profits go up
Why it is wrong: A fixed-rate coupon follows the contract, not annual profit growth.
Option B. Contractual interest and principal payments, subject to the issuer not defaulting — Correct answer
Option C. A shareholder-style vote at company meetings for each rupee of bond face value
Why it is wrong: Ordinary debt does not carry the shareholder voting rights implied here.
Option D. A residual claim on all of the company’s profits left after its creditors are paid
Why it is wrong: Residual ownership is characteristic of equity, not a plain bond.
Answer: B. A plain bond creates a contractual creditor relationship. Its coupon and redemption amount are specified, while ordinary equity holders receive the residual economic outcome after prior claims. Credit risk can prevent the promised cash flows from being paid, so “fixed income” does not mean a guaranteed realised return. Remember: Distinguish contractual debt cash flows from residual equity ownership.
Hint, shown before you answer in practice mode: Common mistake: Interpreting a promised coupon as a guaranteed investment outcome.
IV-001easyconceptual
Q2A ₹5,00,000 face-value bond carries an 8% annual coupon, payable semi-annually in equal instalments. What is one coupon payment?
Option A. ₹40,000
Why it is wrong: This is the annual coupon, not one semi-annual instalment.
Option B. ₹4,000
Why it is wrong: This applies an incorrect principal scale.
Option C. ₹10,000
Why it is wrong: This incorrectly divides the annual coupon into four payments.
Option D. ₹20,000 — Correct answer
Answer: D. Annual coupon cash flow = ₹5,00,000 × 8% = ₹40,000. With two equal payments each year, the payment is ₹40,000 ÷ 2 = ₹20,000. Coupon frequency changes the size and timing of payments, not the quoted annual coupon rate. Remember: Convert an annual coupon rate into the specified payment frequency.
Hint, shown before you answer in practice mode: Common mistake: Treating an annual coupon percentage as a per-half-year rate.
IV-002easynumerical
Q3A floating-rate bond resets its annual coupon to the reference rate plus 75 basis points. If the reference rate at the reset date is 6.20%, what annual coupon applies for the next period?
Option A. 6.275%
Why it is wrong: This treats 75 basis points as 0.075 percentage point.
Option B. 7.50%
Why it is wrong: This is neither the reference rate nor the contractual spread calculation.
Option C. 5.45%
Why it is wrong: This subtracts a spread that the contract says to add.
Option D. 6.95% — Correct answer
Answer: D. The coupon is reset using the contract’s benchmark and spread: 6.20% + 0.75% = 6.95% per annum. The cash amount for a coupon period still depends on notional, accrual fraction and payment terms. A floating coupon does not imply a fixed rupee interest payment. Remember: One basis point is 0.01 percentage point.
Hint, shown before you answer in practice mode: Common mistake: Mixing basis points with percent or ignoring the reset rule.
IV-003mediumnumerical
Q4A Treasury bill is purchased below its redemption value and makes no periodic interest payments. Where does the investor’s return arise if it is held to redemption and paid in full?
Option A. Only a change in a floating coupon benchmark
Why it is wrong: There is no resetting coupon on the stated instrument.
Option B. A semi-annual coupon plus the same purchase price at maturity
Why it is wrong: This describes a coupon structure absent from the question.
Option C. A dividend declared by the government each year
Why it is wrong: A Treasury bill is debt, not an ownership instrument paying discretionary dividends.
Option D. The difference between redemption proceeds and purchase price — Correct answer
Answer: D. A discount instrument has a smaller initial outflow than the final redemption receipt. For example, paying ₹98 and receiving ₹100 generates ₹2 before costs without any intervening coupon. The holding-period return is measured on the ₹98 invested, and annualisation requires the specified tenor convention. Remember: No coupon does not mean no yield.
Hint, shown before you answer in practice mode: Common mistake: Assuming all fixed-income returns must be received as periodic interest.
IV-004easyconceptual
Q5A rupee government bond is used as a low-credit-risk benchmark. An investor plans to sell it well before maturity. Which risk still directly matters?
Option A. It must trade at face value on every day before maturity
Why it is wrong: A benchmark government bond can trade above or below par.
Option B. Its contractual fixed coupon automatically falls when market yields rise
Why it is wrong: Market yields change valuation, not the fixed contractual coupon.
Option C. Its sale proceeds are fixed at the original purchase price
Why it is wrong: The secondary-market sale price is not contractually locked in.
Option D. Its market price may fall if required yields rise — Correct answer
Answer: D. Risk-free rate is a benchmark concept, not a claim that every government-security investment has a riskless holding-period return. For a fixed cash-flow bond, rising discount rates reduce present value. A sale before maturity exposes the investor to that market-price change even when repayment credit risk is treated as negligible. Remember: Match the meaning of “risk-free” to currency, horizon and type of risk.
Hint, shown before you answer in practice mode: Common mistake: Confusing low default risk with zero market-price risk.
IV-005mediumconceptual
Q6Using simple interest and Actual/365, what interest accrues on ₹10,00,000 at 7.30% per annum for exactly 50 days?
Option A. ₹10,000 — Correct answer
Option B. ₹5,000
Why it is wrong: This halves the required 50-day accrual.
Option C. ₹10,138.89
Why it is wrong: This uses a 360-day denominator instead of the stated 365.
Option D. ₹73,000
Why it is wrong: This charges a full year of interest.
Answer: A. The agreed day-count convention determines the fraction of a year. Interest = principal × annual rate × days/365 = ₹10,00,000 × 0.073 × 50/365 = ₹10,000. The rate is used as a decimal and the 50-day fraction is applied only once. Remember: Accrual conventions are inputs, not interchangeable shortcuts.
Hint, shown before you answer in practice mode: Common mistake: Using Actual/360 merely because the instrument is short-term.
IV-006mediumnumerical
Q7An investment quotes a nominal annual interest rate of 8%, compounded semi-annually. Its effective annual rate is:
Option A. 8.16% — Correct answer
Option B. 8.00%
Why it is wrong: This ignores interest earned on the first half-year’s interest.
Option C. 4.00%
Why it is wrong: This is the half-year rate rather than the annual effective rate.
Option D. 16.64%
Why it is wrong: This incorrectly applies 8% in each half-year.
Answer: A. With semi-annual compounding, the periodic rate is 8%/2 = 4%. ₹1 becomes 1.04 × 1.04 = 1.0816 over the year, giving 8.16%. Rates with different compounding frequencies should be converted to a consistent basis before comparison. Remember: Nominal annual rate and effective annual rate are different quantities.
Hint, shown before you answer in practice mode: Common mistake: Compounding the quoted annual rate once for each payment period.
IV-007mediumnumerical
Q8A default-free zero-coupon bond pays ₹100 exactly two years from now. With a 5% annual-compounded two-year spot rate, its value today is closest to:
Option A. ₹90.70 — Correct answer
Option B. ₹95.24
Why it is wrong: This discounts for only one year.
Option C. ₹110.25
Why it is wrong: This compounds the future receipt forward instead of discounting it.
Option D. ₹90.00
Why it is wrong: This subtracts two years of simple interest from face value.
Answer: A. Present value = ₹100/(1.05)^2 = ₹90.7029. A spot rate discounts a single cash flow at its matching maturity. Using only one discount period or subtracting an interest amount from redemption value does not produce the compound present value. Remember: Use the spot rate and compounding frequency that match the cash-flow date.
Hint, shown before you answer in practice mode: Common mistake: Confusing discounting with simple-interest subtraction.
IV-008mediumnumerical
Q9Annual-compounded one-year and two-year spot rates are 5% and 6%, respectively. Under no-arbitrage compounding, the implied one-year forward rate starting in one year is closest to:
Option A. 1.00%
Why it is wrong: The difference between spot rates is not the implied one-year forward rate.
Option B. 7.01% — Correct answer
Option C. 11.00%
Why it is wrong: Adding the two spot rates does not equate investment paths.
Option D. 6.00%
Why it is wrong: This is the two-year spot rate for the whole two-year horizon.
Answer: B. The two-year growth factor must equal the one-year spot growth factor multiplied by the second-year forward growth factor: (1.06)^2 = 1.05(1 + f). Therefore f = 1.1236/1.05 − 1 = 7.0095%. This is a rate implied by current prices, not a guaranteed forecast of next year’s realised short rate. Remember: Forward rates equate compounded investment paths.
Hint, shown before you answer in practice mode: Common mistake: Reading a forward rate as a certain future policy or borrowing rate.
IV-009hardnumerical
Q10A ₹100 face-value bond pays a 6% annual coupon in two equal instalments. Exactly 60 of the 180 convention-days in the current coupon period have accrued. What is accrued interest per ₹100 face value?
Option A. ₹2.00
Why it is wrong: This applies the accrual fraction to the full annual coupon.
Option B. ₹3.00
Why it is wrong: This is the full half-year coupon, not the accrued portion.
Option C. ₹0.50
Why it is wrong: This halves the coupon once more than required.
Option D. ₹1.00 — Correct answer
Answer: D. The next coupon is ₹100 × 6%/2 = ₹3. The elapsed fraction is 60/180 = 1/3, so accrued interest = ₹3 × 1/3 = ₹1. The question provides convention-days explicitly, avoiding any ambiguity about actual calendar-day treatment. Remember: Apply elapsed-period fraction to one coupon payment.
Hint, shown before you answer in practice mode: Common mistake: Applying the fraction to annual interest instead of the relevant period’s coupon.
IV-010mediumnumerical
Q11A bond’s clean price is ₹101.40 and accrued interest is ₹1.25, both per ₹100 face value. Ignoring charges, how much cash is payable for ₹10,00,000 face value?
Option A. ₹10,26,500 — Correct answer
Option B. ₹10,14,000
Why it is wrong: This omits accrued interest.
Option C. ₹10,01,500
Why it is wrong: This subtracts accrued interest rather than adding it.
Option D. ₹1,02,650
Why it is wrong: This uses only one-tenth of the required face-value multiplier.
Answer: A. Dirty price = clean price + accrued interest = 101.40 + 1.25 = ₹102.65 per ₹100 face. The position contains 10,00,000/100 = 10,000 quoted units, so settlement cash is ₹10,26,500. Accrued interest compensates the seller for the part of the coupon period already elapsed. Remember: Separate quotation conventions from the cash settlement amount.
Hint, shown before you answer in practice mode: Common mistake: Paying only the displayed clean price for a coupon-bearing bond.
IV-011mediumnumerical
Q12A bond pays ₹7 annually per ₹100 face value and is quoted at ₹95. Using the quoted price for current yield, the current yield is closest to:
Option A. 7.37% — Correct answer
Option B. 7.00%
Why it is wrong: This is the coupon rate on face value.
Option C. 12.63%
Why it is wrong: This combines coupon and redemption gain without a holding-period framework.
Option D. 5.00%
Why it is wrong: This is the discount to face value, not coupon income yield.
Answer: A. Current yield measures annual coupon income relative to the stated market price: 7/95 = 7.3684%. It does not incorporate the timing of redemption gain or reinvestment of coupons. Accordingly, current yield is not a substitute for yield to maturity. Remember: Coupon rate uses face value. Current yield uses market price.
Hint, shown before you answer in practice mode: Common mistake: Treating current yield as the bond’s complete holding-to-maturity return.
IV-012easynumerical
Q13A conventional fixed-coupon bond has a positive coupon, trades below par on a coupon date and redeems at par. Assuming positive yields and comparable annualised conventions, which ordering is generally correct?
Option A. Coupon rate = current yield = yield to maturity
Why it is wrong: Equality holds for a conventional par bond under consistent conventions.
Option B. Yield to maturity < current yield < coupon rate
Why it is wrong: This is the usual premium-bond ordering, not the stated discount-bond case.
Option C. Coupon rate < current yield < yield to maturity — Correct answer
Option D. Current yield < coupon rate < yield to maturity
Why it is wrong: At a below-par price, coupon divided by price exceeds coupon divided by face value.
Answer: C. For a discount bond, the same coupon is divided by a price smaller than face value, so current yield exceeds coupon rate. Holding to par redemption adds a capital-gain component, making YTM greater than current yield in this conventional setting. The coupon-date and convention assumptions avoid accrued-interest distortions. Remember: Use price relative to par to reason about yield measures.
Hint, shown before you answer in practice mode: Common mistake: Applying a premium-bond relationship to a discount bond.
IV-013mediumconceptual
Q14A bond pays an annual coupon of ₹8 and redeems ₹100 in exactly two years. The first coupon is due in one year. At a 10% annual-compounded required yield, its price is closest to:
Option A. ₹89.26
Why it is wrong: This discounts only the final ₹108 and omits the first coupon.
Option B. ₹96.53 — Correct answer
Option C. ₹98.18
Why it is wrong: This discounts the coupon-yield difference over only part of the cash-flow schedule.
Option D. ₹100.00
Why it is wrong: Par would be consistent with an 8% yield, not the stated 10%.
Answer: B. The first cash flow is ₹8 after one year. The second is ₹108 after two years. Price = 8/1.10 + 108/1.21 = ₹96.5289. The price below par is consistent with the required yield being above the coupon rate. Remember: List every cash-flow date before discounting.
Hint, shown before you answer in practice mode: Common mistake: Forgetting the final coupon or an intermediate coupon.
IV-014mediumnumerical
Q15An investor buys a coupon bond at its quoted YTM and holds it to redemption. Even if every promised payment is made, what can cause the realised compound return to differ from that initial YTM?
Option A. Coupons are reinvested at rates different from the initial YTM — Correct answer
Option B. The bond ceases to have a redemption cash flow once a coupon is paid
Why it is wrong: A coupon payment does not cancel the principal redemption obligation.
Option C. The contractual coupon rate changes with every market quote
Why it is wrong: A fixed coupon does not reset with its secondary-market yield.
Option D. The initial purchase price is retrospectively revised each day
Why it is wrong: Market repricing does not alter the actual acquisition outflow.
Answer: A. YTM is the discount rate equating price with promised cash flows. Realising the same compound wealth growth over the entire maturity horizon also depends on how interim coupons are reinvested. Holding to maturity avoids having to sell at an uncertain price, but it does not remove reinvestment-rate uncertainty. Remember: Promised cash-flow IRR and realised compound wealth growth need not coincide.
Hint, shown before you answer in practice mode: Common mistake: Assuming holding to maturity removes every source of return uncertainty.
IV-015mediumconceptual
Q16A bond is purchased for a dirty price of ₹99. During the holding period it pays a ₹3 coupon and is then sold for a dirty price of ₹100.50. Ignoring reinvestment and costs, the holding-period return is closest to:
Option A. 4.55% — Correct answer
Option B. 3.03%
Why it is wrong: This includes only coupon income, ignoring the price change.
Option C. 1.52%
Why it is wrong: This includes only the price gain, ignoring the coupon.
Option D. 4.50%
Why it is wrong: This treats ₹100 rather than the actual ₹99 investment as the denominator.
Answer: A. Total gain = sale proceeds + coupon − purchase price = 100.50 + 3 − 99 = ₹4.50. Return = 4.50/99 = 4.5455%. Using dirty prices on both sides prevents omitting or double-counting accrued interest. This is a holding-period return, not an annualised yield. Remember: Combine coupon receipts with price change, then divide by the actual investment.
Hint, shown before you answer in practice mode: Common mistake: Mixing clean-price capital gains with unadjusted coupon receipts.
IV-016mediumnumerical
Q17A government yield curve slopes upward. Which interpretation is most defensible?
Option A. Longer maturities yield more today, perhaps reflecting expected short rates and term premiums — Correct answer
Option B. All outstanding government bonds have contractual coupon rates that keep increasing over time
Why it is wrong: The yield curve concerns required yields by maturity, not fixed contractual coupon changes.
Option C. Every future short-term rate is now certain to be higher than today’s short-term rate
Why it is wrong: An observed curve does not remove uncertainty or term-premium effects.
Option D. Longer-maturity bonds necessarily have lower price sensitivity to a change in yields
Why it is wrong: Longer maturity commonly increases sensitivity when other characteristics are similar.
Answer: A. A yield curve relates comparable yields to maturity. An upward slope means longer-term yields exceed shorter-term yields at that time. It may be consistent with expectations of higher future short rates, but liquidity and term-risk premiums can also matter. It is not a deterministic forecast. Remember: Distinguish the observed term structure from a forecast about realised rates.
Hint, shown before you answer in practice mode: Common mistake: Attributing the entire yield-curve slope to one explanation.
IV-017mediumconceptual
Q18The two-year government yield rises from 6.00% to 6.20%, while the ten-year yield rises from 6.50% to 7.00%. How has the ten-year minus two-year spread changed?
Option A. It has steepened by 70 basis points
Why it is wrong: Adding the two yield changes does not measure the slope change.
Option B. It has steepened by 30 basis points — Correct answer
Option C. It is unchanged because both yields rose
Why it is wrong: Equal direction is not the same as an equal-sized parallel shift.
Option D. It has flattened by 30 basis points
Why it is wrong: This reverses the spread change.
Answer: B. Initial spread = 6.50% − 6.00% = 0.50 percentage point. New spread = 7.00% − 6.20% = 0.80 percentage point. The spread widens by 0.30 percentage point, or 30 basis points. Because the long yield rises more, this is a bear steepening. Remember: Curve shape depends on relative yield changes, not only their direction.
Hint, shown before you answer in practice mode: Common mistake: Calling every across-the-curve rate increase a parallel shift.
IV-018mediumnumerical
Q19A default-free zero-coupon bond has exactly four years remaining to redemption. Its Macaulay duration is:
Option A. Less than 4 years because the bond is discounted
Why it is wrong: Discounting changes value, but not the timing of its only cash flow.
Option B. Zero because there are no coupon payments
Why it is wrong: Redemption is itself a cash flow and creates interest-rate sensitivity.
Option C. 4 years — Correct answer
Option D. More than 4 years because no coupons are paid
Why it is wrong: A weighted average of one cash-flow date equals that date.
Answer: C. Macaulay duration is the present-value-weighted average time of a bond’s cash flows. A zero-coupon bond has just one payment, so its entire weight is at maturity. This does not imply its modified duration is also exactly four. Modified duration depends on yield and compounding. Remember: Cash-flow timing, not coupon presence alone, determines Macaulay duration.
Hint, shown before you answer in practice mode: Common mistake: Confusing Macaulay duration with modified duration.
IV-019easyconceptual
Q20A bond has Macaulay duration of 5.20 years and an 8% nominal annual yield compounded semi-annually. Its modified duration is:
Option A. 4.81
Why it is wrong: This divides by 1.08 and ignores the semi-annual yield convention.
Option B. 5.41
Why it is wrong: This multiplies rather than divides by the yield adjustment.
Option C. 5.20
Why it is wrong: This leaves Macaulay duration unadjusted.
Option D. 5.00 — Correct answer
Answer: D. Modified duration = Macaulay duration/(1 + y/m). Here m = 2, so 5.20/1.04 = 5.00. It gives the approximate percentage-price sensitivity to a unit change in yield expressed as a decimal, with the minus sign supplied in the price-change formula. Remember: Use the same compounding convention in duration and yield.
Hint, shown before you answer in practice mode: Common mistake: Applying an annual-compounding denominator to a semi-annual yield.
IV-020mediumnumerical
Q21A bond portfolio has dirty market value of ₹80,00,000 and modified duration of 4.5. Its approximate price value of one basis point (PVBP) is:
Option A. ₹36,000 per basis point
Why it is wrong: This uses a ten-basis-point rather than one-basis-point change.
Option B. ₹360 per basis point
Why it is wrong: This understates the one-basis-point decimal factor by ten.
Option C. ₹3,60,000 per basis point
Why it is wrong: This applies a one-percentage-point change, equal to 100 basis points.
Option D. ₹3,600 per basis point — Correct answer
Answer: D. PVBP measures the approximate rupee magnitude of a price change for a one-basis-point yield move. PVBP ≈ dirty value × modified duration × 0.0001 = ₹3,600. A yield rise normally creates a loss on this long, option-free bond portfolio. The quoted PVBP is a positive magnitude. Remember: Keep PVBP units explicit: rupees per basis point.
Hint, shown before you answer in practice mode: Common mistake: Using 0.01 instead of 0.0001 for a one-basis-point move.
IV-021mediumnumerical
Q22A bond’s dirty price is ₹102 and modified duration is 6. For a 25-basis-point rise in yield, the duration-only estimated new price is:
Option A. ₹103.53
Why it is wrong: This gives a gain for a yield rise and reverses the duration sign.
Option B. ₹86.70
Why it is wrong: This treats 25 basis points as 2.5 percentage points.
Option C. ₹100.47 — Correct answer
Option D. ₹100.50
Why it is wrong: This incorrectly applies the percentage change to par rather than the ₹102 price.
Answer: C. Approximate proportional change = −modified duration × change in yield = −6 × 0.0025 = −1.5%. The rupee change is −₹102 × 1.5% = −₹1.53, giving ₹100.47. Convexity and other changes are expressly excluded by the duration-only instruction. Remember: Duration gives an approximate percentage change, which must be applied to the actual price.
Hint, shown before you answer in practice mode: Common mistake: Dropping the negative sign in the price–yield relation.
IV-022mediumnumerical
Q23For an option-free bond with positive convexity, what happens to the duration-only price estimate when a positive convexity correction is included for a small yield rise?
Option A. The estimated price fall becomes larger
Why it is wrong: This would require a negative rather than positive convexity correction.
Option B. The coupon payment automatically increases
Why it is wrong: Convexity describes valuation curvature, not contractual coupon changes.
Option C. The estimated price fall becomes smaller — Correct answer
Option D. The first-order duration term becomes exactly zero
Why it is wrong: Adding a second-order correction does not erase the first-order exposure.
Answer: C. The approximation is ΔP/P ≈ −DmodΔy + ½C(Δy)^2. For positive convexity, the squared-yield term is positive whether yields rise or fall. Thus, relative to the tangent-line duration estimate, a yield rise produces a somewhat smaller price loss. This statement assumes the same cash flows and local approximation. Remember: Positive convexity raises the estimated price relative to a duration-only tangent.
Hint, shown before you answer in practice mode: Common mistake: Treating the convexity term as having the same sign as the yield change.
IV-023hardconceptual
Q24A portfolio holds ₹30 lakh market value in Bond A with modified duration 2 and ₹70 lakh in Bond B with modified duration 6. For a common small parallel yield shift, portfolio modified duration is:
Option A. 3.2
Why it is wrong: This reverses the market-value weights.
Option B. 4.0
Why it is wrong: This equally weights the two durations despite unequal market values.
Option C. 8.0
Why it is wrong: Adding durations ignores position sizes and portfolio value.
Option D. 4.8 — Correct answer
Answer: D. Under a common parallel shift, sum each holding’s rupee sensitivity and divide by total market value. Portfolio duration = (30 × 2 + 70 × 6)/100 = 4.8. Face-value weights are not a general substitute for market-value weights, and a single duration does not describe every non-parallel curve move. Remember: Aggregate risk in rupees before converting back to a portfolio sensitivity.
Hint, shown before you answer in practice mode: Common mistake: Using a simple average when holdings are unequally sized.
IV-024mediumnumerical
Q25An institution has fixed-rate assets with PVBP ₹12,000 and fixed-rate liabilities with PVBP ₹8,000. Both values fall when yields rise. For a parallel 10-basis-point rise, what is the approximate change in economic equity, assets minus liabilities?
Option A. A loss of ₹40,000 — Correct answer
Option B. A gain of ₹40,000
Why it is wrong: This reverses the sign of the net asset sensitivity.
Option C. A loss of ₹2,00,000
Why it is wrong: This adds the two value declines instead of subtracting liabilities from assets.
Option D. No change because both sides have fixed rates
Why it is wrong: Fixed coupons do not imply equal rupee duration exposures.
Answer: A. Equity = assets − liabilities, so Δequity = −₹12,000 × 10 − (−₹8,000 × 10) = −₹40,000. The liability’s decline is favourable to economic equity because the present value of what is owed decreases. Matching nominal asset and liability amounts alone would not necessarily match PVBP. Remember: For net worth, liability price changes enter with the opposite accounting sign.
Hint, shown before you answer in practice mode: Common mistake: Adding asset and liability PVBP without considering economic direction.
IV-025hardnumerical
Q26Two option-free bonds have the same maturity, face value and positive yield. One pays a low fixed coupon and the other a higher fixed coupon. Which normally has greater Macaulay duration?
Option A. The bond with the higher number of outstanding units
Why it is wrong: Issue size does not by itself determine per-bond cash-flow duration.
Option B. The high-coupon bond
Why it is wrong: Larger interim payments move the weighted average cash-flow date earlier.
Option C. The low-coupon bond — Correct answer
Option D. Both must have identical duration because maturity is identical
Why it is wrong: Coupon timing and size matter as well as final maturity.
Answer: C. Macaulay duration weights each cash-flow date by present value. A higher coupon distributes more of the bond’s value through earlier payments, reducing the weighted-average date relative to a lower-coupon bond with the same maturity and yield. Maturity is therefore not a complete measure of interest-rate sensitivity. Remember: Equal maturity does not imply equal duration.
Hint, shown before you answer in practice mode: Common mistake: Ignoring coupon structure when comparing bond price risk.
IV-026mediumconceptual
Q27An investor buys a newly issued government bond at auction and later sells it to another investor. Which transaction directly provides the original borrowing proceeds to the issuer?
Option A. Only the later secondary-market sale
Why it is wrong: Secondary proceeds normally go to the selling investor, not the issuer.
Option B. The purchase at the new-issue auction — Correct answer
Option C. Neither transaction, because bonds only redistribute existing funds
Why it is wrong: Primary bond issuance is a means of raising finance.
Option D. Both transactions provide the full sale price to the issuer
Why it is wrong: This incorrectly treats a transfer of an outstanding bond as new borrowing.
Answer: B. Primary markets connect issuers raising funds with investors. Secondary markets allow existing claims to be transferred, adding liquidity and price discovery. A secondary sale can influence the issuer’s future funding conditions, but its immediate proceeds belong to the seller of the existing security. Remember: New financing and transfer of an existing security are different market functions.
Hint, shown before you answer in practice mode: Common mistake: Assuming every trade in government debt finances a new fiscal borrowing.
IV-027easyconceptual
Q28A dealer sells government securities under a repo and agrees to repurchase them on a specified date at an agreed price. From the dealer’s economic perspective, the transaction primarily provides:
Option A. Permanent equity capital without a repayment obligation
Why it is wrong: A repo has a repurchase obligation and is not an equity issue.
Option B. A final outright disposal with no subsequent contractual leg
Why it is wrong: The repurchase leg distinguishes repo from an ordinary outright sale.
Option C. An option to repay only if market yields rise
Why it is wrong: The standard repo obligation is not an option conditional on yields.
Option D. Secured short-term funding against the securities — Correct answer
Answer: D. A repo combines a sale with a commitment to repurchase. Economically, it enables the cash recipient to finance securities on a secured basis. The repurchase price incorporates the agreed funding economics. It is not simply a bet on the bond’s future market price. Repo funding is relevant to bond carry and futures arbitrage. Remember: Understand the financing function behind the two legal transaction legs.
Hint, shown before you answer in practice mode: Common mistake: Treating the initial repo sale as an unconnected outright sale.
IV-028mediumconceptual
Q29Two otherwise identical simple-interest contracts use the same annual rate, principal and 90 actual accrual days. One uses Actual/360 and the other Actual/365. Which accrues more interest?
Option A. They accrue equal interest because both use actual days
Why it is wrong: The denominator is also part of the convention.
Option B. Actual/365
Why it is wrong: Its larger denominator produces a smaller accrual fraction.
Option C. Actual/360 — Correct answer
Option D. The comparison cannot be made without knowing the coupon frequency
Why it is wrong: The question already specifies simple-interest accrual on identical inputs.
Answer: C. Accrued interest is P × r × day-count fraction. With P, r and the actual day count held constant, 90/360 exceeds 90/365, so Actual/360 produces more interest. This is a convention comparison, not a claim that one convention applies universally to Indian interest-rate products. Remember: The denominator of a day-count fraction changes the cash amount.
Hint, shown before you answer in practice mode: Common mistake: Focusing only on the “Actual” part of the convention.
IV-029mediumconceptual
Q30A contract defines modified following as: move a non-business-day payment to the next business day, unless that crosses into a new month, in which case use the preceding business day. Payment is due on a non-business-day month-end. The next business day is in the next month. Which date applies?
Option A. The original date regardless of whether settlement is possible
Why it is wrong: The contract requires a business-day adjustment.
Option B. The same calendar date one month later
Why it is wrong: The adjustment convention does not add a full month.
Option C. The preceding business day in the original month — Correct answer
Option D. The next business day in the next month
Why it is wrong: This applies following but ignores the stated modification.
Answer: C. The supplied convention has two steps: first look forward, then test whether that adjustment changes the month. Because it does here, the fallback is the preceding business day. Actual calendars and product-specific conventions must be checked in practice. This item tests the rule explicitly provided, not an assumed exchange holiday schedule. Remember: Apply the complete contractual date convention, including its exceptions.
Hint, shown before you answer in practice mode: Common mistake: Using a familiar convention instead of the one written in the contract.
IV-030mediumconceptual
Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market: common questions
How many practice questions are there on Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market?
30 questions, all written out on this page with the correct answer and why each other option is wrong. This unit is one of the 10 practice topics for NISM Series IV, which has 150 questions in total.
Are these real NISM Series IV questions on Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market?
No. LearnNifty wrote every question from NISM's public syllabus. NISM does not publish its question bank, so nobody can offer you the real paper. Use these questions to check that an idea has gone in. Use the official NISM workbook to see what is examined.
Does negative marking apply to NISM Series IV?
Yes. NISM takes off 25% of a question's marks for a wrong answer. On a 1-mark question that is 0.25 marks off. A blank question earns nothing and loses nothing, so a wrong guess costs marks on this paper. Timed practice here uses the same rule.
Are these practice questions kept up to date?
Each question is written against the rules printed on this page, last checked on 5 September 2026. A Budget or a SEBI circular can change a rate, a lot size or an expiry day. If one of those rules changes before your exam, treat the questions that use it as out of date. Then check NISM's current workbook.
Interest Rate Derivatives
10 questions on Interest Rate Derivatives. Its quiz opens on that unit.
Open Interest Rate Derivatives