Unit study guide · NISM Series V-D
Exchange Traded Interest Rate Futures
10 questions in this unit
What this unit covers
- A hypothetical short-term interest-rate futures contract is quoted as 100 minus its implied annual reference rate expressed in percent. If the futures quote is 93.60, what reference rate is implied by this quotation? Assumptions: The 100-minus-rate quotation is an illustrative contract convention, not a claim about a particular current Indian contract.
- An illustrative bond futures contract represents ₹2,00,000 face value and is quoted per ₹100 of face value. Its minimum price tick is 0.0025 quote points. What rupee change does one tick represent for one contract? Assumptions: All contract sizes and tick specifications are hypothetical.
- A trader buys two illustrative bond futures contracts, each representing ₹5,00,000 face value. Prices are quoted per ₹100 of face value. The position opens at 100.10 and closes at 100.40. Ignoring all costs, what is the total profit or loss? Assumptions: Contract terms are hypothetical and transaction costs are ignored.
- One short interest-rate futures contract is entered at 99.50. The first day’s settlement price is 99.80 and the second day’s settlement price is 99.20. Each one-point price change is worth ₹2,000 per contract. What is the second day’s mark-to-market cash flow, calculated from the previous day’s settlement? Assumptions: The multiplier is illustrative. The short remains open through both settlements.
- A fund holds bonds and shorts bond futures to reduce interest-rate exposure. During a rally, the bonds gain value but the short futures position incurs daily settlement losses. The fund does not sell the bonds that day. Which planning issue is most directly illustrated? Assumptions: The bonds are not sold and their unrealised gain is not automatically available as cash.
- A hypothetical bond’s full spot price is ₹100 per ₹100 of face value. It pays no coupon before a six-month futures maturity. Financing costs 6% per year on a simple-interest basis for the full six months. Ignoring margin-timing effects and other costs, what fair futures price follows this carry calculation? Assumptions: The financing rate is simple for six months. Daily-settlement timing and other costs are excluded.
- For an illustrative carry trade, a bond’s full spot price is ₹104 per ₹100 face value. A ₹2 coupon is paid after three months, and the futures horizon is six months. Finance the initial purchase for six months at 8% annual simple interest and reinvest the coupon for its remaining three months at the same annual simple rate. The fair full-price delivery amount equals financed purchase cost minus the coupon’s accumulated value. What is that amount? Assumptions: Both financing and reinvestment use the supplied simple-interest conventions. Full prices are used throughout. Ignore margin-funding effects, taxes, fees and credit risk.
- An illustrative cash-settled bond futures contract uses the underlying bond’s officially specified reference price on expiry for final settlement. Which price is relevant to that final settlement? Assumptions: The cash-settlement method is supplied for this illustrative contract.
- A borrower needs a rate hedge for an unusual loan amount starting on 15 October. A dealer offers a customised forward-rate agreement, while an exchange offers futures only in standard contract sizes and listed maturities. Which comparison is most accurate? Assumptions: The available contracts and requested loan terms are hypothetical.
- One-year and two-year spot rates are 5% and 6% per year, both with annual compounding. Under a no-arbitrage calculation, what one-year forward rate for the second year makes one year at 5%, followed by that forward rate, equivalent to two years at the 6% spot rate? Round to two decimals. Assumptions: Annual compounding and the supplied no-arbitrage relationship apply. Ignore risk and funding differences.
Key ideas
From the practice bank · 1
A hypothetical short-term interest-rate futures contract is quoted as 100 minus its implied annual reference rate expressed in percent. If the futures quote is 93.60, what reference rate is implied by this quotation? Assumptions: The 100-minus-rate quotation is an illustrative contract convention, not a claim about a particular current Indian contract.
The implied rate is 100 − 93.60 = 6.40%. Under this quotation convention, a higher implied rate corresponds to a lower futures quote. Remember: Know whether a contract is quoted as a bond price, a yield, or a transformation of a rate.
Hint Apply the quotation rule exactly as stated.
V-D-129From the practice bank · 2
An illustrative bond futures contract represents ₹2,00,000 face value and is quoted per ₹100 of face value. Its minimum price tick is 0.0025 quote points. What rupee change does one tick represent for one contract? Assumptions: All contract sizes and tick specifications are hypothetical.
Tick value = ₹2,00,000 × 0.0025/100 = ₹5. The division by 100 is required because the quote is a price per ₹100 of face value. Remember: Translate quote-point changes into money using the contract’s quotation base.
Hint Multiply face value by the tick and divide by 100.
V-D-130From the practice bank · 3
A trader buys two illustrative bond futures contracts, each representing ₹5,00,000 face value. Prices are quoted per ₹100 of face value. The position opens at 100.10 and closes at 100.40. Ignoring all costs, what is the total profit or loss? Assumptions: Contract terms are hypothetical and transaction costs are ignored.
Profit = (100.40 − 100.10)/100 × ₹5,00,000 × 2 = ₹3,000. A long position benefits from this increase in the futures price. Remember: Keep position direction, contract count and quote units consistent.
Hint Use the rise in price, face value per contract and number of contracts.
V-D-131From the practice bank · 4
One short interest-rate futures contract is entered at 99.50. The first day’s settlement price is 99.80 and the second day’s settlement price is 99.20. Each one-point price change is worth ₹2,000 per contract. What is the second day’s mark-to-market cash flow, calculated from the previous day’s settlement? Assumptions: The multiplier is illustrative. The short remains open through both settlements.
Second-day cash flow = (99.80 − 99.20) × ₹2,000 = ₹1,200 received. The first-day loss was ₹600, so cumulative profit is only ₹600, but that is a different question. Remember: Daily settlement uses the previous settlement price, not the original entry price.
Hint For the short, subtract today’s settlement from yesterday’s settlement.
V-D-132From the practice bank · 5
A fund holds bonds and shorts bond futures to reduce interest-rate exposure. During a rally, the bonds gain value but the short futures position incurs daily settlement losses. The fund does not sell the bonds that day. Which planning issue is most directly illustrated? Assumptions: The bonds are not sold and their unrealised gain is not automatically available as cash.
The bond gain may remain unrealised while futures losses must be settled in cash. The fund therefore needs planning in addition to an economically appropriate hedge. Remember: A sound hedge can still create interim cash-funding needs.
Hint Distinguish the total economic result from the timing of cash movements.
V-D-133From the practice bank · 6
A hypothetical bond’s full spot price is ₹100 per ₹100 of face value. It pays no coupon before a six-month futures maturity. Financing costs 6% per year on a simple-interest basis for the full six months. Ignoring margin-timing effects and other costs, what fair futures price follows this carry calculation? Assumptions: The financing rate is simple for six months. Daily-settlement timing and other costs are excluded.
Fair futures price = ₹100 × (1 + 0.06 × 0.5) = ₹103.00. With no interim income, the financing cost is added to the spot price under the supplied assumptions. Remember: Carry pricing connects spot cost, financing and income over the contract period.
Hint Finance the spot purchase for half a year.
V-D-134From the practice bank · 7
For an illustrative carry trade, a bond’s full spot price is ₹104 per ₹100 face value. A ₹2 coupon is paid after three months, and the futures horizon is six months. Finance the initial purchase for six months at 8% annual simple interest and reinvest the coupon for its remaining three months at the same annual simple rate. The fair full-price delivery amount equals financed purchase cost minus the coupon’s accumulated value. What is that amount? Assumptions: Both financing and reinvestment use the supplied simple-interest conventions. Full prices are used throughout. Ignore margin-funding effects, taxes, fees and credit risk.
Financed cost = 104 × (1 + 0.08 × 0.5) = 108.16. The coupon grows to 2 × (1 + 0.08 × 0.25) = 2.04, giving 108.16 − 2.04 = ₹106.12 per ₹100 face value. Remember: Interim bond income offsets carry cost, and its timing affects the amount of that offset.
Hint Use six months for financing and only three months for reinvesting the coupon.
V-D-135From the practice bank · 8
An illustrative cash-settled bond futures contract uses the underlying bond’s officially specified reference price on expiry for final settlement. Which price is relevant to that final settlement? Assumptions: The cash-settlement method is supplied for this illustrative contract.
Final settlement follows the contract’s specified expiry reference. The entry-day spot price or a trader’s own estimate does not replace that agreed benchmark. Remember: Read the precise final-settlement reference rather than assuming every contract settles at par.
Hint The settlement methodology is a contract term.
V-D-136From the practice bank · 9
A borrower needs a rate hedge for an unusual loan amount starting on 15 October. A dealer offers a customised forward-rate agreement, while an exchange offers futures only in standard contract sizes and listed maturities. Which comparison is most accurate? Assumptions: The available contracts and requested loan terms are hypothetical.
A tailored agreement can align closely with a particular exposure. Standard futures can still be useful, but the borrower must assess contract rounding, timing differences and any remaining basis risk. Remember: A closer contractual match and a safer counterparty arrangement are separate considerations.
Hint Ask which contract allows negotiated terms and which uses standard specifications.
V-D-137From the practice bank · 10
One-year and two-year spot rates are 5% and 6% per year, both with annual compounding. Under a no-arbitrage calculation, what one-year forward rate for the second year makes one year at 5%, followed by that forward rate, equivalent to two years at the 6% spot rate? Round to two decimals. Assumptions: Annual compounding and the supplied no-arbitrage relationship apply. Ignore risk and funding differences.
The forward rate is (1.06²/1.05 − 1) × 100 = 7.0095%, or 7.01%. The equation equates investments over the same two-year horizon. It is not a guarantee of the actual future short rate. Remember: A forward rate is implied by relative discount factors, not by simple subtraction of spot yields.
Hint Set (1.05) × (1 + forward rate) equal to 1.06².
V-D-138Liquidity in the stock market means how easily a quantity can be bought or sold.
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