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Unit study guide · NISM Series IV

Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Market

30 questions in this unit

What this unit covers

Key ideas

From the practice bank · 1

An investor buys a company’s plain fixed-rate bond rather than its ordinary shares. Which entitlement follows from the bond investment?

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 Common mistake: Interpreting a promised coupon as a guaranteed investment outcome.

IV-001

From the practice bank · 2

A ₹5,00,000 face-value bond carries an 8% annual coupon, payable semi-annually in equal instalments. What is one coupon payment?

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 Common mistake: Treating an annual coupon percentage as a per-half-year rate.

IV-002

From the practice bank · 3

A 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?

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 Common mistake: Mixing basis points with percent or ignoring the reset rule.

IV-003

From the practice bank · 4

A 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?

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 Common mistake: Assuming all fixed-income returns must be received as periodic interest.

IV-004

From the practice bank · 5

A 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?

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 Common mistake: Confusing low default risk with zero market-price risk.

IV-005

From the practice bank · 6

Using simple interest and Actual/365, what interest accrues on ₹10,00,000 at 7.30% per annum for exactly 50 days?

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 Common mistake: Using Actual/360 merely because the instrument is short-term.

IV-006

From the practice bank · 7

An investment quotes a nominal annual interest rate of 8%, compounded semi-annually. Its effective annual rate is:

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 Common mistake: Compounding the quoted annual rate once for each payment period.

IV-007

From the practice bank · 8

A 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:

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 Common mistake: Confusing discounting with simple-interest subtraction.

IV-008

From the practice bank · 9

Annual-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:

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 Common mistake: Reading a forward rate as a certain future policy or borrowing rate.

IV-009

From the practice bank · 10

A ₹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?

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 Common mistake: Applying the fraction to annual interest instead of the relevant period’s coupon.

IV-010

From the practice bank · 11

A 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?

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 Common mistake: Paying only the displayed clean price for a coupon-bearing bond.

IV-011

From the practice bank · 12

A 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:

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 Common mistake: Treating current yield as the bond’s complete holding-to-maturity return.

IV-012

From the practice bank · 13

A 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?

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 Common mistake: Applying a premium-bond relationship to a discount bond.

IV-013

From the practice bank · 14

A 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:

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 Common mistake: Forgetting the final coupon or an intermediate coupon.

IV-014

From the practice bank · 15

An 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?

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 Common mistake: Assuming holding to maturity removes every source of return uncertainty.

IV-015

From the practice bank · 16

A 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:

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 Common mistake: Mixing clean-price with unadjusted coupon receipts.

IV-016

From the practice bank · 17

A government yield curve slopes upward. Which interpretation is most defensible?

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 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 Common mistake: Attributing the entire yield-curve slope to one explanation.

IV-017

From the practice bank · 18

The 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?

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 Common mistake: Calling every across-the-curve rate increase a parallel shift.

IV-018

From the practice bank · 19

A default-free zero-coupon bond has exactly four years remaining to redemption. Its Macaulay duration is:

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 Common mistake: Confusing Macaulay duration with modified duration.

IV-019

From the practice bank · 20

A bond has Macaulay duration of 5.20 years and an 8% nominal annual yield compounded semi-annually. Its modified duration is:

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 Common mistake: Applying an annual-compounding denominator to a semi-annual yield.

IV-020

From the practice bank · 21

A 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:

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 Common mistake: Using 0.01 instead of 0.0001 for a one-basis-point move.

IV-021

From the practice bank · 22

A 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:

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 Common mistake: Dropping the negative sign in the price–yield relation.

IV-022

From the practice bank · 23

For 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?

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 Common mistake: Treating the convexity term as having the same sign as the yield change.

IV-023

From the practice bank · 24

A 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:

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 Common mistake: Using a simple average when holdings are unequally sized.

IV-024

From the practice bank · 25

An 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?

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 Common mistake: Adding asset and liability PVBP without considering economic direction.

IV-025

From the practice bank · 26

Two 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?

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 Common mistake: Ignoring coupon structure when comparing bond price risk.

IV-026

From the practice bank · 27

An 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?

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 Common mistake: Assuming every trade in government debt finances a new fiscal borrowing.

IV-027

From the practice bank · 28

A 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:

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 Common mistake: Treating the initial repo sale as an unconnected outright sale.

IV-028

From the practice bank · 29

Two 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?

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 Common mistake: Focusing only on the “Actual” part of the convention.

IV-029

From the practice bank · 30

A 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?

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 Common mistake: Using a familiar convention instead of the one written in the contract.

IV-030
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