Unit ko samjho · NISM Series XXI-A
Investing in Fixed Income Securities
8 questions is unit mein
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- A bond with face value ₹1,000 pays an annual coupon of 8% and trades at ₹960. What is its current yield, rounded to two decimals?
- A zero-coupon bond will repay ₹1,210 in two years. At a required annual compound yield of 10%, what is its present value?
- For a conventional fixed-rate bond with unchanged promised cash flows, what is the usual effect of an increase in the required yield?
- A corporate bond is downgraded after the issuer’s debt-service capacity weakens. Market interest rates on comparable government bonds are unchanged. What is the most direct valuation concern?
- A callable bond may be redeemed by the issuer at the stated call price. If market rates fall substantially, which risk is particularly relevant to its holder?
- A bond has modified duration of 4.5. If its yield rises by 0.75 percentage points, what approximate percentage price change does duration alone indicate?
- A bond pays ₹10 after one year and ₹110 after two years. At a 10% annual yield, its price is ₹100. What is its Macaulay duration, to two decimals?
- A bond’s Macaulay duration is 2.4 years. Its nominal annual yield is 8%, compounded semi-annually. Using modified duration = Macaulay duration ÷ (1 + yield per period), what is modified duration?
Zaroori ideas
Practice bank se · 1
A bond with face value ₹1,000 pays an annual coupon of 8% and trades at ₹960. What is its current yield, rounded to two decimals?
Current yield relates annual coupon income to current market price. It is not a full yield-to-maturity calculation. Annual coupon = 8% × ₹1,000 = ₹80. Current yield = ₹80 ÷ ₹960 × 100 = 8.3333%, or 8.33%. The possible gain or loss at redemption is not included in this measure. Remember: Use market price for current yield and face value for the coupon payment.
Hint Common mistake: Confusing coupon rate, current yield and yield to maturity.
XXI-A-034Practice bank se · 2
A zero-coupon bond will repay ₹1,210 in two years. At a required annual compound yield of 10%, what is its present value?
A zero-coupon bond’s value is the present value of its single promised payment, subject to the chosen yield and credit assumptions. Use present value = maturity payment ÷ (1 + annual yield)^years. ₹1,210 ÷ 1.10² = ₹1,210 ÷ 1.21 = ₹1,000. There are no interim coupons to add. Remember: One future payment still requires the full compounding period in the discount factor.
Hint Common mistake: Discounting a two-year cash flow for only one year.
XXI-A-035Practice bank se · 3
For a conventional fixed-rate bond with unchanged promised cash flows, what is the usual effect of an increase in the required yield?
Bond valuation discounts future payments. Price and required yield move in opposite directions when those payments are held constant. Keep the coupon and redemption amounts fixed as instructed. A larger discount rate means each future payment has a lower present value, reducing the sum of those present values. Remember: Separate a change in market yield from a change in contractual cash flows.
Hint Common mistake: Assuming that a fixed coupon adjusts to preserve the bond’s market price.
XXI-A-036Practice bank se · 4
A corporate bond is downgraded after the issuer’s debt-service capacity weakens. Market interest rates on comparable government bonds are unchanged. What is the most direct valuation concern?
A corporate bond’s required yield reflects a reference rate and compensation for issuer-specific risks, among other factors. The risk-free or government reference is unchanged, so it does not explain a new valuation discount here. Deteriorating credit quality can widen the required spread. Discounting the same promised payments at that higher yield tends to lower price. Remember: A credit rating is an assessment of risk, not a repayment guarantee or a certain default forecast.
Hint Common mistake: Treating the rating symbol as a contractual cash-flow change.
XXI-A-037Practice bank se · 5
A callable bond may be redeemed by the issuer at the stated call price. If market rates fall substantially, which risk is particularly relevant to its holder?
An embedded issuer call can limit the investor’s benefit from falling rates and introduce early-reinvestment risk. A lower refinancing cost can make exercise attractive to the issuer, subject to the contract. If called, the investor receives the contractual call amount and must assess the rates available for reinvestment. Exercise is not assumed to be certain. Remember: Identify whose option is embedded in a bond and how exercise changes cash flows.
Hint Common mistake: Treating a callable bond as an option-free bond with identical cash-flow certainty.
XXI-A-038Practice bank se · 6
A bond has modified duration of 4.5. If its yield rises by 0.75 percentage points, what approximate percentage price change does duration alone indicate?
Modified duration estimates the proportional price response to a small yield change, with an inverse sign relationship. Use ΔP/P approximately equal to −modified duration × Δyield, with the yield change in decimal form. −4.5 × 0.0075 = −0.03375 = −3.375%, which rounds to −3.38%. Convexity and other changes are excluded. Remember: Convert a percentage-point yield change into a decimal before multiplying by duration.
Hint Common mistake: Using the right formula with the wrong yield units.
XXI-A-039Practice bank se · 7
A bond pays ₹10 after one year and ₹110 after two years. At a 10% annual yield, its price is ₹100. What is its Macaulay duration, to two decimals?
Macaulay duration is the present-value-weighted average time to receive a bond’s cash flows. Present values are ₹10/1.10 = ₹9.0909 and ₹110/1.10² = ₹90.9091. They total ₹100. Weighted time = (1 × 9.0909 + 2 × 90.9091)/100 = 1.9091 years, or 1.91 years. Remember: Use present-value cash-flow weights rather than equal weights or maturity alone.
Hint Common mistake: Confusing a weighted receipt time with a price-sensitivity measure.
XXI-A-040Practice bank se · 8
A bond’s Macaulay duration is 2.4 years. Its nominal annual yield is 8%, compounded semi-annually. Using modified duration = Macaulay duration ÷ (1 + yield per period), what is modified duration?
The conversion from Macaulay to modified duration must use the yield per compounding period consistent with the quoted yield. Semi-annual yield = 8%/2 = 4%. The duration is already stated in years. Modified duration = 2.4/(1 + 0.04) = 2.3077, or 2.31. Do not double the time measure. Remember: Keep annualised time and per-period yield conventions separate.
Hint Common mistake: Ignoring the compounding frequency embedded in a nominal yield.
XXI-A-041