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Unit study guide · NISM Series X-A

Investing in Fixed Income Securities

25 questions in this unit

What this unit covers

Key ideas

From the practice bank · 1

A bond has face value ₹2,000 and a fixed annual coupon rate of 9%, paid in two equal instalments every year. It currently trades at ₹1,920. What is each six-month coupon payment?

₹90 correctly divides the annual face-value-based coupon into two equal payments. Annual coupon = ₹2,000 × 9% = ₹180. This annual contractual amount does not change merely because the bond trades below face value. Two equal payments divide ₹180 by two, giving ₹90 every six months. The question asks for one instalment, not the whole year’s interest. The market price would matter when calculating the investor’s yield. It is not the base for the fixed coupon specified here. Remember: Keep face value, market price, annual coupon rate and payment frequency separate.

Hint Common mistake: Using the purchase price as the base for a contractual coupon.

X-A-076

From the practice bank · 2

A non-callable bond has face value ₹1,000, pays an annual coupon of ₹80 and redeems at ₹1,000 in three years. Valuation is immediately after a coupon date, with the next coupon in one year. At an annual required yield of 8%, assuming all payments occur, what is its value?

₹1,000 correctly values the matched coupon and yield at par. The coupon rate is ₹80 ÷ ₹1,000 = 8%, equal to the required annual yield. There is no accrued interest at the specified valuation time. Discount ₹80 in year one, ₹80 in year two, and ₹1,080 in year three at 8%. Their present values total ₹1,000. The final ₹1,080 contains the last coupon plus principal. That future receipt alone is not today’s price, and all receipts must be discounted. Remember: For a plain par-redemption bond, matching coupon and yield implies par value at a coupon date.

Hint Common mistake: Comparing undiscounted future receipts with a price paid today.

X-A-077

From the practice bank · 3

A bond will pay ₹80 one year from today and ₹1,080 two years from today, after which it ends. The second payment includes principal. At a required yield of 10% per year, compounded annually, what is its value today, rounded to two decimal places?

₹965.29 discounts both dated receipts separately and adds their present values. The year-one payment has present value ₹80 ÷ 1.10 = ₹72.7273. The year-two payment has present value ₹1,080 ÷ 1.10² = ₹892.5620. Add the unrounded values to obtain ₹965.2893, or ₹965.29. An 8% coupon on ₹1,000 face value is below the assumed 10% required yield, so a price below ₹1,000 is a sensible cross-check. Remember: Draw the cash-flow dates before selecting discount factors.

Hint Common mistake: Discounting every cash flow for the same number of years.

X-A-078

From the practice bank · 4

A hypothetical zero-coupon bond makes no interim payments and pays ₹12,100 exactly two years from today. At a required yield of 10% per year, compounded annually, what is its current value?

₹10,000 discounts the single redemption payment over both years correctly. There is one cash flow, ₹12,100, and it is two years away. Use two annual discounting periods. Present value = ₹12,100 ÷ 1.10² = ₹10,000. A reverse check gives ₹10,000 × 1.10 × 1.10 = ₹12,100. The ₹2,100 difference is the total two-year accumulation under the assumed yield, not a separate coupon to add to redemption. Remember: No coupon means no interim cash flow, not no potential return.

Hint Common mistake: Subtracting a multiple of the yield instead of reversing compound growth.

X-A-079

From the practice bank · 5

A bond has face value ₹1,000, an 8% annual coupon paid in equal half-yearly instalments, and exactly two years to maturity. It redeems at par. The required yield is 10% nominal per year compounded semi-annually. Valuation is immediately after a coupon payment. What is the price, rounded to two decimals?

₹964.54 uses ₹40 coupons, a 5% half-year yield and four periods. Each coupon is ₹1,000 × 8% ÷ 2 = ₹40. The half-year yield is 10% ÷ 2 = 5%. There are four half-years. Price = ₹40/1.05 + ₹40/1.05² + ₹40/1.05³ + ₹1,040/1.05⁴ = ₹964.5405. Round only the final total to ₹964.54. Treating the 10% as a rate for every half-year would greatly over-discount the payments. Remember: Convert both the coupon and yield consistently before valuing more-than-annual payments.

Hint Common mistake: Halving the coupon while leaving the annual discount rate unchanged.

X-A-080

From the practice bank · 6

A bond with face value ₹1,000 pays ₹90 of coupons a year and trades at ₹900. What is its current yield?

10.00% correctly measures ₹90 annual coupon income on a ₹900 purchase price. Use the annual coupon ₹90 as the numerator and the market price ₹900 as the denominator. Current yield = ₹90 ÷ ₹900 × 100 = 10%. The coupon rate, in contrast, is ₹90 ÷ ₹1,000 = 9%. The discount to face value cannot simply be added to 9% or 10% as a yearly return because the remaining maturity and redemption timing also matter. Remember: Use current price for current yield and face value for the coupon rate.

Hint Common mistake: Treating current yield as the investor’s complete to maturity.

X-A-081

From the practice bank · 7

A bond costs ₹960 today and will make its only remaining payment of ₹1,060 exactly one year later. That payment consists of ₹60 coupon and ₹1,000 redemption. Assuming payment in full, what is its annual yield to maturity, rounded to two decimals?

10.42% includes both components relative to the actual initial cost. The cash gain is ₹1,060 − ₹960 = ₹100. It includes ₹60 coupon plus ₹40 recovery of the discount to redemption. Annual yield = ₹100 ÷ ₹960 × 100 = 10.4167%, rounded to 10.42%. Equivalently, ₹960 × (1 + y) = ₹1,060. There are no intermediate coupons to reinvest in this one-period example. The result still depends on receiving the stated payment in full. Remember: For a one-year final payment, include coupon and redemption before comparing with purchase price.

Hint Common mistake: Mistaking the coupon rate or current yield for yield to maturity.

X-A-082

From the practice bank · 8

A bond with face value ₹1,000 is quoted at a clean price of ₹98.50 per ₹100 face value. Accrued interest is ₹12 per bond. For this transaction, settlement cash equals clean value plus accrued interest. Ignoring other charges, what cash is paid for one bond?

₹997 correctly scales the quotation and then adds the stated per-bond accrued interest. ₹1,000 face value contains ten blocks of ₹100. Clean value = 10 × ₹98.50 = ₹985. Add the ₹12 accrued interest specified per whole bond: settlement cash = ₹985 + ₹12 = ₹997. Accrued interest is not multiplied by ten here because it is already given for one bond. Nor is the coupon or principal separately added at settlement. Remember: Read both the quotation unit and the accrued-interest unit before adding them.

Hint Common mistake: Combining a per-₹100 quote with a per-bond amount without unit conversion.

X-A-083

From the practice bank · 9

A fixed-cash-flow corporate bond’s required yield equals a same-maturity benchmark yield plus a credit spread. The benchmark stays at 6%. The spread rises from 1.5 to 2.5 percentage points, while promised cash flows remain unchanged. What happens to required yield and present value?

8.5% is the new benchmark-plus-spread yield, and higher discounting lowers present value. Initial required yield is 6% + 1.5% = 7.5%. The new yield is 6% + 2.5% = 8.5%, a one-percentage-point increase. Every unchanged payment is divided by a larger compound discount factor. Adding those smaller present values therefore produces a lower price. This result holds under the stated fixed-cash-flow model. It does not assume that the benchmark itself moved or that the issuer has already defaulted. Remember: Separate benchmark-rate movements from spread movements when explaining bond-price changes.

Hint Common mistake: Looking only at the benchmark and overlooking changes in the additional yield demanded.

X-A-084

From the practice bank · 10

A bond investor receives every promised coupon on time. The first coupon can now be reinvested only at a lower rate than the rate assumed in the investor’s original accumulation plan. Which risk most directly explains the resulting shortfall in terminal wealth?

Reinvestment risk directly matches a reduction in the return available on interim cash receipts. The question explicitly states that coupons arrive on time, so the cash-flow shortfall is not caused by a missed contractual payment. The lower rate affects how much the received coupon grows between receipt and the final horizon. The coupon itself can be unchanged while terminal wealth falls short. For example, a ₹100 coupon reinvested for one year at 4% becomes ₹104, rather than ₹108 at an assumed 8%. This illustrates the mechanism, not a current interest-rate forecast. Remember: Timely coupon receipt does not fix the return obtainable by reinvesting that coupon.

Hint Common mistake: Assuming that receiving every payment automatically guarantees the planned compound return.

X-A-085

From the practice bank · 11

A bond gives its issuer the contractual right to redeem it early at a specified call price. Other terms are unchanged. Market yields fall substantially, allowing the issuer to refinance more cheaply. Which consequence should the bondholder specifically consider?

Early termination of the higher-coupon investment is the call risk described here. Falling yields can make replacing existing higher-coupon borrowing attractive to the issuer. The contractual call provides a possible way to do so. If the issuer calls the bond, the holder receives the specified redemption amount but loses the remaining scheduled investment in that bond. Replacement investments may offer lower yields. Calling is a possibility, not an assertion that the issuer must exercise. Call dates, prices and conditions remain those of the hypothetical contract. Remember: Identify who owns an embedded option before evaluating the bondholder’s risk.

Hint Common mistake: Confusing the issuer’s call right with a holder’s put right.

X-A-086

From the practice bank · 12

A zero-coupon bond has a single payment exactly four years from today. What is its Macaulay duration?

Four years is the weighted average when the only weight is attached to year four. All of the bond’s present value comes from the sole payment in year four. There are no earlier receipts with positive weight. Duration = (4 years × present value of the only payment) ÷ the same present value = 4 years. Discounting changes the payment’s value today, but not the date on which it arrives. This question asks for Macaulay duration, not modified duration or a price-change estimate. Remember: For a single-payment bond, Macaulay duration equals time to that payment.

Hint Common mistake: Interchanging Macaulay duration, modified duration and remaining principal.

X-A-087

From the practice bank · 13

A bond is valued at ₹2,000 and has a modified duration of 6. If its yield rises by 0.50 percentage point, what is its approximate new price, ignoring convexity?

₹1,940 correctly applies the estimated 3% price decline to ₹2,000. A rise of 0.50 percentage point is Δy = +0.005, not 0.50 or 0.05. Estimated proportional price change = −6 × 0.005 = −0.03, or −3%. The rupee change is −3% × ₹2,000 = −₹60. Approximate new price = ₹2,000 − ₹60 = ₹1,940. This is a first-order estimate. It is not a full repricing or an exact promise for larger yield moves. Remember: Convert yield changes carefully and label duration-based prices as approximations.

Hint Common mistake: Confusing a percentage-point yield change with a proportional change in price.

X-A-088

From the practice bank · 14

At one observation time, otherwise comparable bonds show yields of 7.0% at one year, 6.5% at three years and 6.0% at ten years. Based only on these observations, how is the yield curve best described?

The declining yields across increasing maturities establish the inverted shape. Order the observations by maturity: one year, three years, ten years. The yields decline from 7.0% to 6.5% to 6.0%. That downward sequence is an inverted curve over the stated observations. A flat curve would have equal yields, while a hump would have a middle yield above both ends. These three numbers describe a shape. They do not establish that a particular economic outcome must follow or provide a complete forecast of future interest rates. Remember: Describe the observed curve separately from any explanation or forecast about its cause.

Hint Common mistake: Treating a yield-curve shape as a guaranteed prediction.

X-A-089

From the practice bank · 15

A corporate issuer cannot make a scheduled bond coupon payment because it lacks the funds. The holder has not attempted to sell the bond, and there is no foreign-currency exposure. Which risk is most directly realised?

Failure to make the scheduled payment directly illustrates default risk, a form of credit risk. The event is a failure of the issuer to make the due coupon. It therefore directly affects the contractual cash flow the lender was expecting. No secondary-market sale is attempted, so the question is not describing a difficulty finding buyers. No currency change is involved either. The cause is the stated inability to pay. This classification does not determine the later recovery amount or claim that every market-price decline indicates default. Remember: Distinguish failure of promised payment from fluctuations in price or reinvestment opportunities.

Hint Common mistake: Labelling every bond-related loss as interest-rate risk.

X-A-090

From the practice bank · 16

Over one year a fixed-income investment earns an 8% nominal total return, while the relevant cost-of-living index rises by 10%. Using exact purchasing-power adjustment, what is the real return, rounded to two decimals?

−1.82% correctly measures the decline in purchasing power. Nominal money grows by a factor of 1.08, while the assumed price index grows by 1.10. Real return = (1.08 ÷ 1.10 − 1) × 100 = −1.8182%, or −1.82%. A ₹100 starting amount becomes ₹108 but purchases only ₹98.18 of the original-price basket. Subtracting inflation from nominal return gives −2%, a useful approximation in some settings but not the exact adjustment expressly requested here. Remember: Positive nominal returns can coexist with negative real returns.

Hint Common mistake: Adding inflation to investment return or treating the subtraction approximation as exact.

X-A-091

From the practice bank · 17

A hypothetical floating-rate bond pays annual interest on ₹10,000 face value. At the start of each annual period its coupon resets to the observed benchmark plus 1.30 percentage points, with no cap or floor. The benchmark at the new reset is 6.20%. What coupon is payable for that full year?

₹750 uses both rate components and the full annual face-value amount. At this reset the annual coupon rate becomes 6.20% + 1.30% = 7.50%. For the complete annual period, interest = ₹10,000 × 7.50% = ₹750. No partial-period adjustment is needed. The formula uses the benchmark observed at the start of the period. A later benchmark change does not alter this period’s already-reset coupon under the terms stated here. Remember: Apply the contract’s reset date, benchmark and spread before computing floating interest.

Hint Common mistake: Treating a percentage-point spread as a percentage of the benchmark.

X-A-092

From the practice bank · 18

A bond is purchased for ₹1,020 immediately after a coupon date. Assume it is called exactly one year later for ₹1,010 and also pays an ₹80 coupon on that date. No other payments occur. What is the annual yield to that assumed call, rounded to two decimals?

6.86% includes the coupon and actual assumed redemption relative to purchase cost. The sole receipt in one year is ₹1,010 call proceeds + ₹80 coupon = ₹1,090. The gain over the ₹1,020 purchase cost is ₹70. One-year yield = ₹70 ÷ ₹1,020 × 100 = 6.8627%, or 6.86%. The price loss of ₹10 between purchase and call offsets part of the coupon. Ignoring it overstates the return. The computation does not predict that an actual issuer will call. Remember: Use the call price and call horizon when computing yield to an assumed call.

Hint Common mistake: Substituting current yield for the full return to early redemption.

X-A-093

From the practice bank · 19

A short-term zero-coupon instrument costs ₹98,000 and redeems for ₹1,00,000 in 180 days. What is its simple annualised yield on the price paid, using a 365-day year?

4.14% uses purchase price in the denominator and the specified annualisation factor. The 180-day gain is ₹1,00,000 − ₹98,000 = ₹2,000. Relative to money invested, its period return is ₹2,000 ÷ ₹98,000 = 2.0408%. Multiply that period return by 365 ÷ 180 under the stated simple annualisation convention: 4.1383%, rounded to 4.14%. This is not a compounded effective annual return or a claim about the quotation convention of any actual Indian instrument. The 365-day basis is supplied for this exercise only. Remember: Identify the denominator, day-count basis and simple-versus-compound convention in yield calculations.

Hint Common mistake: Mixing a discount quote with an investment-yield calculation.

X-A-094

From the practice bank · 20

A bond is bought for ₹1,000 and pays ₹100 at the end of year one, then ₹1,100 at the end of year two, including redemption. The first coupon is reinvested for one year at 4%. Assuming all payments occur, what total wealth is available at the end of year two?

₹1,204 correctly combines the accumulated first coupon with the final payment. The year-one ₹100 coupon earns one year of 4% interest and becomes ₹104 by the end of year two. The year-two bond payment is ₹1,100. Adding it to ₹104 gives terminal wealth of ₹1,204. The original bond cash flows priced at ₹1,000 imply a 10% annual yield, but reinvesting the first coupon at only 4% produces less terminal wealth than reinvestment at 10%. Remember: Reinvest only the cash that has actually been received, for its remaining time to the horizon.

Hint Common mistake: Assuming the bond’s purchase yield automatically determines the coupon reinvestment rate.

X-A-095

From the practice bank · 21

CASE: A two-year bond with face value ₹1,000 pays a ₹100 coupon at the end of each year and repays its face value at the end of year two. What does the issuer pay at the end of year two?

At the end of year two the issuer pays the last ₹100 coupon plus the ₹1,000 face value, which is ₹1,100. Remember: Keep contractual issuer cash flows separate from the later earnings on reinvested receipts.

Hint Common mistake: Adding an earlier coupon a second time at redemption.

X-A-096

From the practice bank · 22

CASE: A bond will pay ₹1,100 exactly two years from today. At a 10% annual yield, what is the present value of that payment alone?

₹1,100 ÷ 1.10² = ₹1,100 ÷ 1.21 = ₹909.09. Remember: Identify whether the required valuation covers one receipt or the complete cash-flow stream.

Hint Common mistake: Using a correct whole-bond price to answer a question about just one component.

X-A-097

From the practice bank · 23

CASE: Right after its first coupon, a bond has one payment left, ₹1,100 due in one year. The market yield is now 8%. What is the bond's price?

₹1,100 ÷ 1.08 = ₹1,018.52. Remember: Update the cash-flow horizon and remove paid coupons when moving the valuation date.

Hint Common mistake: Counting a coupon both as cash received and as part of the ex-coupon price.

X-A-098

From the practice bank · 24

CASE: An investor buys a bond for ₹1,000. After one year the investor receives a ₹100 coupon and sells the bond for ₹1,018.52. What is the one-year holding-period return?

Return = (₹100 + ₹1,018.52 − ₹1,000) ÷ ₹1,000 = 11.85%. Remember: Distinguish the new buyer’s required yield from the seller’s realised holding-period return.

Hint Common mistake: Substituting a market yield directly for the investor’s cash-flow-based return.

X-A-099

From the practice bank · 25

CASE: An investor buys a two-year bond for ₹1,000. The ₹100 first-year coupon is reinvested at 8% for one year, and the bond pays ₹1,100 at the end of year two. What is the annual compound return over the two years?

Final wealth = ₹100 × 1.08 + ₹1,100 = ₹1,208. Annual return = √1.208 − 1 = 9.91%. Remember: Accumulate all receipts to one date, then annualise the total growth factor.

Hint Common mistake: Equating promised yield to a realised compound outcome regardless of reinvestment.

X-A-100
CAGR (Compound Annual Growth Rate)

CAGR expresses the change between a starting value and an ending value as a single constant annual rate.

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