Unit ko samjho · NISM Series IV
Strategies Using Exchange Traded Interest Rate Futures and Options
24 questions is unit mein
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- A manager already owns fixed-rate government bonds and wants to reduce losses from a rise in yields. Assuming closely matching bond-price futures, which directional hedge is appropriate?
- A pension fund will receive cash in two months and then buy fixed-rate government bonds. It fears yields may fall before the purchase. Which hedge best addresses the resulting higher purchase price?
- A company expects floating-rate borrowing costs to rise. Its proposed futures hedge is quoted so that its price falls when the relevant rate rises. Ignoring basis risk, which position provides the desired offset?
- CASE H: A long bond portfolio has market value ₹10 crore and modified duration 4. Each available bond futures contract has PVBP ₹80. Assuming matching yield changes, how many futures contracts hedge the portfolio’s first-order rate sensitivity?
- CASE H: A ₹10 crore bond portfolio has modified duration 4. The manager wants duration 2, not a fully neutral position. Each bond futures contract has PVBP ₹80. With value fixed and matching yield changes, what adjustment is required?
- A portfolio has positive PVBP ₹10,350. Each short futures contract offsets ₹80 of PVBP. Only whole contracts are allowed. Which short position minimises the absolute residual PVBP?
- A cash portfolio has PVBP ₹50,000 per basis point of its own yield. Its yield is expected to change by 1.2 basis points for each one-basis-point change in the futures reference yield. One futures contract has PVBP ₹80 to its reference. What first-order short hedge count follows?
- Over a period, a bond portfolio loses ₹6,00,000. Its short futures hedge gains ₹5,50,000 and total hedge costs are ₹20,000. What is the combined net result?
- A futures hedge was initially PVBP-neutral. Since then bonds were sold from the cash portfolio and the remaining bonds’ duration changed. What should the manager do?
- Define basis as S − F. A trader buys one unit of a bond at S₀=100 and shorts matching futures at F₀=101. On closing both, S₁=98 and F₁=98.50. Ignoring carry, costs and multipliers, what is combined P/L per unit?
- A bond portfolio needs a hedge for another three months, but its existing short futures expire soon. Which transaction rolls the short hedge into a later expiry?
- An investor buys a bond at 100 and a put on the same bond with strike 98 for premium 0.70. Evaluate only the terminal bond price plus option payoff. Assume no coupons, financing or costs. What is the maximum loss per unit?
- An investor owns a bond bought at 100 and writes a call with strike 102 for premium 0.50 on the same amount. Ignore coupons and costs. If the bond finishes at 105, what is the combined profit per unit?
- A trader buys a bond-price call at strike 100 for 1.20 and sells an otherwise matching call at strike 103 for 0.40. What is the spread’s maximum expiry profit per unit, excluding costs?
- A trader buys a put with strike 102 for 1.50 and sells a put with strike 99 for 0.50. Both reference the same bond and expiry. If settlement is 100, what is net profit per unit?
- A trader buys a call and a put on the same bond, each with strike 100 and the same expiry. Premiums are 1.10 and 0.90. Ignoring costs, what are the expiry break-even prices?
- A trader writes a call and a put with the same strike and expiry on a bond. Which risk characteristic best describes this short straddle?
- A bond investor buys a protective put at strike 98 and writes a call at strike 103 on the same holding. Equal premiums make the net option premium zero. What does this arrangement achieve, ignoring coupons and costs?
- A deliverable bond forward is priced above the cost of buying the same bond and carrying it to delivery. Assume financing, purchase and forward sale can be locked in simultaneously with all costs included. Which trade exploits the discrepancy?
- A zero-coupon bond can be short-sold for 100. The sale proceeds can be invested to become 102 at forward maturity. A matching deliverable forward can be bought at 100.80, and all bond-borrowing and trading costs total 0.40 per unit. What profit can be locked in under these assumptions?
- A trader buys the near bond future at 100 and sells the far future at 101, one contract each. Later the near is 100.40 and the far is 101.10. Both multipliers are 2,000. What is the combined profit before costs?
- A trader holds long two-year bond-price futures with PVBP ₹1,000 and short ten-year bond-price futures with the same PVBP magnitude. The two-year yield rises 5 bp and the ten-year yield rises 15 bp. Under linear sensitivities, what is the combined P/L?
- A trader sees a favourable cash–futures spread and buys the cash bond, but the offsetting futures order does not execute before prices move. What risk has materialised?
- A corporate-bond portfolio is hedged against government yield movements using G-Sec futures. Government yields are unchanged, but the issuers’ credit spreads widen sharply. Which outcome remains possible?
Zaroori ideas
Practice bank se · 1
A manager already owns fixed-rate government bonds and wants to reduce losses from a rise in yields. Assuming closely matching bond-price futures, which directional hedge is appropriate?
The manager is economically long bond prices. To reduce that sensitivity, the hedge should have the opposite price exposure: short comparable futures. When yields rise and bond prices fall, futures gains can offset part of the cash loss. The size must still be set using relevant risk measures rather than direction alone. Remember: Determine the existing exposure before choosing hedge direction.
Hint Common mistake: Buying futures merely because the underlying portfolio consists of purchased bonds.
IV-083Practice bank se · 2
A pension fund will receive cash in two months and then buy fixed-rate government bonds. It fears yields may fall before the purchase. Which hedge best addresses the resulting higher purchase price?
The fund does not yet own the bonds. Its exposure is to the cost of a planned purchase. Falling yields raise that cost. A long bond-price future can earn a compensating gain while cash remains unavailable for the bond purchase. This is a different exposure from an existing long bond holding. Remember: An anticipated purchase often requires the opposite hedge from an existing asset holding.
Hint Common mistake: Confusing a forecast of falling yields with a forecast of falling bond prices.
IV-084Practice bank se · 3
A company expects floating-rate borrowing costs to rise. Its proposed futures hedge is quoted so that its price falls when the relevant rate rises. Ignoring basis risk, which position provides the desired offset?
The exposure is a higher borrowing rate, while the contract is inversely quoted to that rate. A short futures position therefore gains in the adverse borrowing scenario. With a futures contract quoted directly on a rate rather than inversely, the required direction could differ. The stated price convention governs. Remember: Trace the adverse exposure through the contract’s quotation before selecting long or short.
Hint Common mistake: Using a generic “rising rates means buy” rule for every interest-rate derivative.
IV-085Practice bank se · 4
CASE H: A long bond portfolio has market value ₹10 crore and modified duration 4. Each available bond futures contract has PVBP ₹80. Assuming matching yield changes, how many futures contracts hedge the portfolio’s first-order rate sensitivity?
Portfolio PVBP = ₹10 crore × 4 × 0.0001 = ₹40,000 per basis point. The hedge count is ₹40,000/₹80 = 500 contracts. Since the portfolio is long bond prices, use short futures. This first-order calculation assumes matching rate moves and does not eliminate convexity or basis risk. Remember: Size a duration hedge using comparable rupee sensitivities.
Hint Common mistake: Matching face amounts while ignoring differing price sensitivities.
IV-086Practice bank se · 5
CASE H: A ₹10 crore bond portfolio has modified duration 4. The manager wants duration 2, not a fully neutral position. Each bond futures contract has PVBP ₹80. With value fixed and matching yield changes, what adjustment is required?
Current PVBP is ₹10 crore × 4 × 0.0001 = ₹40,000. Target PVBP is ₹10 crore × 2 × 0.0001 = ₹20,000. Sell (40,000 − 20,000)/80 = 250 contracts. A target-duration hedge should preserve the intended residual exposure rather than automatically neutralising everything. Remember: Hedge the difference between current and desired sensitivity.
Hint Common mistake: Using the full-hedge quantity when the mandate specifies a non-zero risk target.
IV-087Practice bank se · 6
A portfolio has positive PVBP ₹10,350. Each short futures contract offsets ₹80 of PVBP. Only whole contracts are allowed. Which short position minimises the absolute residual PVBP?
The theoretical count is 10,350/80 = 129.375. Compare nearby integers rather than blindly rounding upward: 129 leaves 10,350 − 129×80 = +₹30. 130 leaves −₹50. Under the stated absolute-residual objective, 129 is better. A policy against any underhedge could lead to a different choice, but that is not the objective here. Remember: Rounding policy should follow the hedge objective.
Hint Common mistake: Assuming every fractional hedge ratio must be rounded upward.
IV-088Practice bank se · 7
A cash portfolio has PVBP ₹50,000 per basis point of its own yield. Its yield is expected to change by 1.2 basis points for each one-basis-point change in the futures reference yield. One futures contract has PVBP ₹80 to its reference. What first-order short hedge count follows?
The exposures must first be expressed against the same risk factor. A one-basis-point futures-reference move causes a 1.2-basis-point cash-yield move, so cash value sensitivity is ₹60,000. Offsetting it requires 60,000/80 = 750 short futures. The result is model-dependent because the stated yield relationship may change. Remember: Convert risk sensitivities to a common reference before taking their ratio.
Hint Common mistake: Assuming cash and futures yields always move one-for-one.
IV-089Practice bank se · 8
Over a period, a bond portfolio loses ₹6,00,000. Its short futures hedge gains ₹5,50,000 and total hedge costs are ₹20,000. What is the combined net result?
The relevant result combines cash asset, derivative and costs: −6,00,000 + 5,50,000 − 20,000 = −₹70,000. The hedge substantially reduced the unhedged loss but did not produce a perfect offset. That can reflect basis effects, sizing, costs or other imperfect matching. Remember: Assess the total economic exposure, not the derivative leg in isolation.
Hint Common mistake: Calling a hedge successful merely because its futures trade made money.
IV-090Practice bank se · 9
A futures hedge was initially PVBP-neutral. Since then bonds were sold from the cash portfolio and the remaining bonds’ duration changed. What should the manager do?
PVBP neutrality is a point-in-time condition. Changes in portfolio composition, prices, yields and time to maturity alter exposure. The futures sensitivity can also change. Rebalancing should be driven by current risk and the mandate, while considering transaction costs and trading constraints. Remember: A hedge ratio is an estimate to monitor, not a permanent label.
Hint Common mistake: Treating a hedge established once as maintenance-free.
IV-091Practice bank se · 10
Define basis as S − F. A trader buys one unit of a bond at S₀=100 and shorts matching futures at F₀=101. On closing both, S₁=98 and F₁=98.50. Ignoring carry, costs and multipliers, what is combined P/L per unit?
Combined P/L = (98 − 100) + (101 − 98.50) = +0.50. Equivalently, it equals (S₁−F₁) − (S₀−F₀) = −0.50 − (−1.00). Thus matching quantities does not remove basis risk. The basis can move favourably or adversely during the hedge. Remember: For equal units of long cash and short futures, net price P/L follows the change in the defined basis.
Hint Common mistake: Assuming quantity matching guarantees an exact price offset.
IV-092Practice bank se · 11
A bond portfolio needs a hedge for another three months, but its existing short futures expire soon. Which transaction rolls the short hedge into a later expiry?
Rolling replaces an expiring position with another maturity. For a short hedge, buy the old contract and sell the new one. The calendar spread, execution costs and altered contract sensitivity matter, so a roll is not necessarily costless and the new number of contracts may need recalculation. Remember: A roll has a closing leg and a new opening leg.
Hint Common mistake: Treating as an automatic extension of the same hedge.
IV-093Practice bank se · 12
An investor buys a bond at 100 and a put on the same bond with strike 98 for premium 0.70. Evaluate only the terminal bond price plus option payoff. Assume no coupons, financing or costs. What is the maximum loss per unit?
Terminal bond-plus-put value is S_T + max(98 − S_T, 0) = max(S_T, 98). The minimum is 98, while initial cost is 100 + 0.70 = 100.70. Maximum loss is therefore 2.70. The protection floor must be adjusted for the cost of acquiring it when discussing net results. Remember: A protective put provides a price floor, not a free guarantee of the original purchase price.
Hint Common mistake: Ignoring premium when measuring protected portfolio downside.
IV-094Practice bank se · 13
An investor owns a bond bought at 100 and writes a call with strike 102 for premium 0.50 on the same amount. Ignore coupons and costs. If the bond finishes at 105, what is the combined profit per unit?
Combined profit = (105 − 100) − max(105 − 102, 0) + 0.50 = 2.50. Writing the call exchanges some potential upside for premium. It does not remove the bond’s downside. The premium merely provides a small buffer against a price decline. Remember: A covered call limits upside while retaining substantial downside exposure.
Hint Common mistake: Calling a covered call a complete downside hedge.
IV-095Practice bank se · 14
A trader buys a bond-price call at strike 100 for 1.20 and sells an otherwise matching call at strike 103 for 0.40. What is the spread’s maximum expiry profit per unit, excluding costs?
The lower-strike long call and higher-strike short call create a bull call spread. Net debit = 1.20 − 0.40 = 0.80. At or above 103, the payoff difference is capped at 103 − 100 = 3, so maximum profit is 3 − 0.80 = 2.20. Below 100 both expire worthless and the debit is lost. Remember: For a debit vertical spread, maximum profit is width minus net premium paid.
Hint Common mistake: Ignoring the short option when extrapolating gains above its strike.
IV-096Practice bank se · 15
A trader buys a put with strike 102 for 1.50 and sells a put with strike 99 for 0.50. Both reference the same bond and expiry. If settlement is 100, what is net profit per unit?
At settlement 100, the 102 put is worth 2 and the 99 put is . Combined gross payoff is 2 − 0 = 2. The initial net debit is 1.50 − 0.50 = 1, producing profit 1. An expiry price between strikes requires evaluating each leg, not assuming the maximum spread payoff. Remember: Evaluate each option separately before combining a multi-leg payoff.
Hint Common mistake: Using maximum-profit formulas at settlement prices inside the strike interval.
IV-097Practice bank se · 16
A trader buys a call and a put on the same bond, each with strike 100 and the same expiry. Premiums are 1.10 and 0.90. Ignoring costs, what are the expiry break-even prices?
Total premium is 1.10 + 0.90 = 2. At expiry, straddle payoff is |S_T − 100|. requires |S_T − 100| = 2, giving 98 and 102. A large enough move in either direction can profit, but merely expecting volatility is insufficient if the movement does not cover the premium. Remember: A long straddle pays for two options and must recover both premiums.
Hint Common mistake: Using the call’s or put’s standalone break-even for the combined strategy.
IV-098Practice bank se · 17
A trader writes a call and a put with the same strike and expiry on a bond. Which risk characteristic best describes this short straddle?
A short straddle collects both premiums and performs best near the common strike at expiry. A large rise generates losses on the short call, while a large fall generates losses on the short put. The combined position is normally short and short . Premium income is not a substitute for risk capacity. Remember: Income strategies can hide adverse tail exposure behind frequent small gains.
Hint Common mistake: Describing premium collection as risk-free yield.
IV-099Practice bank se · 18
A bond investor buys a protective put at strike 98 and writes a call at strike 103 on the same holding. Equal premiums make the net option premium zero. What does this arrangement achieve, ignoring coupons and costs?
Combined terminal value is S_T + max(98−S_T,0) − max(S_T−103,0). It equals 98 below the put strike, S_T between strikes, and 103 above the call strike. Zero net premium means premiums offset. It does not mean zero economic trade-off or zero trading costs. Remember: Zero-cost usually refers to net upfront premium, not the absence of sacrificed opportunities.
Hint Common mistake: Calling a financed protective structure a free, unlimited-upside guarantee.
IV-100Practice bank se · 19
A deliverable bond forward is priced above the cost of buying the same bond and carrying it to delivery. Assume financing, purchase and forward sale can be locked in simultaneously with all costs included. Which trade exploits the discrepancy?
A replicating cash-and-carry portfolio funds the bond until delivery and receives interim cash flows. If the forward sale price exceeds its fully locked-in net cost, buying cash and selling forward captures the difference. The strong assumptions matter: unmatched settlement references, unavailable funding or execution can undermine a supposed arbitrage. Remember: Arbitrage compares executable complete strategies, not isolated screen prices.
Hint Common mistake: Calling a naked directional futures sale cash-and-carry arbitrage.
IV-101Practice bank se · 20
A zero-coupon bond can be short-sold for 100. The sale proceeds can be invested to become 102 at forward maturity. A matching deliverable forward can be bought at 100.80, and all bond-borrowing and trading costs total 0.40 per unit. What profit can be locked in under these assumptions?
Short the bond, invest the proceeds and buy the forward to obtain the bond needed to return the borrowed security. Terminal surplus = 102 − 100.80 − 0.40 = 0.80. The example assumes borrow availability and all cash flows locked in. Those assumptions cannot be omitted when evaluating a real reverse cash-and-carry trade. Remember: Include security-borrowing costs and delivery availability in reverse carry.
Hint Common mistake: Ignoring the practical cost of maintaining a short cash position.
IV-102Practice bank se · 21
A trader buys the near bond future at 100 and sells the far future at 101, one contract each. Later the near is 100.40 and the far is 101.10. Both multipliers are 2,000. What is the combined profit before costs?
Near-leg P/L = (100.40−100)×2,000 = ₹800. Far-leg P/L = (101−101.10)×2,000 = −₹200. Combined result is ₹600. The position profits because the far-minus-near spread narrows from 1.00 to 0.70, not merely because both outright prices rise. Remember: Spread positions depend on relative movement and the sign of each leg.
Hint Common mistake: Adding absolute price changes without considering long and short directions.
IV-103Practice bank se · 22
A trader holds long two-year bond-price futures with PVBP ₹1,000 and short ten-year bond-price futures with the same PVBP magnitude. The two-year yield rises 5 bp and the ten-year yield rises 15 bp. Under linear sensitivities, what is the combined P/L?
The long two-year position loses 1,000×5 = ₹5,000. The short ten-year position gains 1,000×15 = ₹15,000. Net profit is ₹10,000. Equal opposite PVBP would cancel a common parallel move, but the larger long-end rise creates a curve-steepening gain for this configuration. Remember: Parallel-shift neutrality is not yield-curve neutrality.
Hint Common mistake: Treating one aggregate PVBP number as a complete description of rate risk.
IV-104Practice bank se · 23
A trader sees a favourable cash–futures spread and buys the cash bond, but the offsetting futures order does not execute before prices move. What risk has materialised?
An arbitrage calculation assumes all necessary legs can be executed at the required prices. After only the cash purchase, the trader has directional bond exposure and financing needs. Changes in price or before the futures leg executes can eliminate the apparent profit or create a loss. Remember: The implementation of a multi-leg strategy is part of its risk analysis.
Hint Common mistake: Calling an opportunity riskless before both legs and financing are secured.
IV-105Practice bank se · 24
A corporate-bond portfolio is hedged against government yield movements using G-Sec futures. Government yields are unchanged, but the issuers’ credit spreads widen sharply. Which outcome remains possible?
A corporate yield includes a government benchmark plus credit and other spread components. A G-Sec futures hedge primarily tracks government-rate exposure. If credit spreads widen while the benchmark is unchanged, corporate prices can fall with little offset from the government futures. Residual risks should be identified before describing a portfolio as hedged. Remember: Name the risk being hedged and the risks left unhedged.
Hint Common mistake: Claiming a rate hedge also insures issuer credit deterioration.
IV-106Expiry day is the last day on which a derivative contract can be traded.
Aage padhoThe strike price is the level at which an option can be exercised.
Aage padhoMoneyness describes where an option's strike sits relative to the current level of the underlying.
Aage padhoBreakeven is the point at which a defined result is exactly zero.
Aage padhoGamma is the rate at which an option's delta changes as the underlying moves.
Aage padhoVega measures how much an option's theoretical price changes when implied volatility changes.
Aage padhoImpact cost is the difference between the price shown on screen and the price a trade is actually filled at.
Aage padhoLiquidity describes how easily a given quantity can be traded.
Aage padho