Unit study guide · NISM Series V-D
Strategies Using Interest Rate Derivatives
6 questions in this unit
What this unit covers
- A bond portfolio loses approximately ₹15,000 when yields rise by one basis point. One selected bond futures contract gains approximately ₹250 for a one-basis-point yield rise when held short. Under this fixed sensitivity approximation, which position offsets the portfolio’s interest-rate sensitivity? Assumptions: Sensitivities are fixed illustrative values. Basis and convexity effects are ignored.
- During a stress period a corporate-bond portfolio loses ₹2,00,000, while its short government-bond futures hedge earns ₹1,60,000. Ignore costs and all other cash flows. What is the combined result, and what does it show about the hedge? Assumptions: The two supplied profit-and-loss amounts are the only components of the result.
- An investor buys a bond for 100 price units and simultaneously buys a European put on the same bond with strike 98 for a premium of 1 price unit. Both are held to the put’s expiry. The put pays max(98 − final bond price, 0). Ignore coupons, costs and premium financing. What is the maximum loss of the combined position per bond under these assumptions? Assumptions: The put exactly matches the bond and is held to expiry. No coupon or other cash flow occurs.
- A trader builds three identical bull call spreads on the same hypothetical interest-rate futures contract and expiry. Each spread buys a 98-strike call for 2.50 points and sells a 102-strike call for 0.80 points. Each point is worth ₹2,000 per option contract. Ignoring costs and financing, what is the maximum total expiry profit? Assumptions: The two option legs share the same underlying, multiplier and expiry.
- A trader buys five near-month bond futures at 98.00 and sells five far-month futures at 99.00. Each one-point change is worth ₹1,000 per contract for either maturity. Both legs are closed when the near-month price is 99.00 and the far-month price is 99.40. Ignoring costs, what is the spread’s total profit? Assumptions: The two illustrative futures contracts have identical point values and all positions are closed together.
- A bond costs ₹98 per ₹100 face value and pays no income during the next three months. A trader can finance this purchase for three months at 12% annual simple interest. A cash-settled futures contract on the same bond is priced at 102.50 and settles to the bond’s market price on that date. The trader buys ₹10,00,000 face value of the bond, shorts matching futures and sells the bond at expiry. Assume perfect price matching and ignore all fees, margin-funding costs and constraints. What profit is locked in under these assumptions? Assumptions: The cash bond and final futures settlement reference match exactly. Borrowing and trading are assumed permitted and available. Margin timing, costs, credit risk and constraints are excluded.
Key ideas
From the practice bank · 1
A bond portfolio loses approximately ₹15,000 when yields rise by one basis point. One selected bond futures contract gains approximately ₹250 for a one-basis-point yield rise when held short. Under this fixed sensitivity approximation, which position offsets the portfolio’s interest-rate sensitivity? Assumptions: Sensitivities are fixed illustrative values. Basis and convexity effects are ignored.
Required contracts = ₹15,000/₹250 = 60. The short side gains when yields rise, offsetting the portfolio’s stated loss under the approximation. Remember: A hedge must match both the size and direction of the risk sensitivity.
Hint Divide portfolio sensitivity by contract sensitivity and choose the offsetting direction.
V-D-145From the practice bank · 2
During a stress period a corporate-bond portfolio loses ₹2,00,000, while its short government-bond futures hedge earns ₹1,60,000. Ignore costs and all other cash flows. What is the combined result, and what does it show about the hedge? Assumptions: The two supplied profit-and-loss amounts are the only components of the result.
Combined result = −₹2,00,000 + ₹1,60,000 = −₹40,000. A government-bond futures hedge may leave risks such as changing credit spreads or imperfect sensitivity matching in a corporate-bond portfolio. Remember: Assess the combined hedge result and identify the risk that remains.
Hint Add the underlying loss and the hedge gain with their correct signs.
V-D-146From the practice bank · 3
An investor buys a bond for 100 price units and simultaneously buys a European put on the same bond with strike 98 for a premium of 1 price unit. Both are held to the put’s expiry. The put pays max(98 − final bond price, 0). Ignore coupons, costs and premium financing. What is the maximum loss of the combined position per bond under these assumptions? Assumptions: The put exactly matches the bond and is held to expiry. No coupon or other cash flow occurs.
The initial outlay is 100 + 1 = 101 units. The bond plus put is worth at least 98 at expiry, so the maximum loss is 101 − 98 = 3 units. Remember: A protective put creates a floor, but its strike gap and premium still determine the maximum loss.
Hint Compare total initial outlay with the minimum combined expiry value.
V-D-147From the practice bank · 4
A trader builds three identical bull call spreads on the same hypothetical interest-rate futures contract and expiry. Each spread buys a 98-strike call for 2.50 points and sells a 102-strike call for 0.80 points. Each point is worth ₹2,000 per option contract. Ignoring costs and financing, what is the maximum total expiry profit? Assumptions: The two option legs share the same underlying, multiplier and expiry.
The strike width is 102 − 98 = 4 points and net premium is 2.50 − 0.80 = 1.70 points. Maximum profit = (4 − 1.70) × ₹2,000 × 3 = ₹13,800. Remember: A debit spread’s maximum profit equals its capped payoff less the initial net debit.
Hint Subtract net premium from strike width, then multiply by point value and number of spreads.
V-D-148From the practice bank · 5
A trader buys five near-month bond futures at 98.00 and sells five far-month futures at 99.00. Each one-point change is worth ₹1,000 per contract for either maturity. Both legs are closed when the near-month price is 99.00 and the far-month price is 99.40. Ignoring costs, what is the spread’s total profit? Assumptions: The two illustrative futures contracts have identical point values and all positions are closed together.
The long leg gains (99 − 98) × ₹1,000 × 5 = ₹5,000. The short leg loses (99.40 − 99) × ₹1,000 × 5 = ₹2,000, leaving a net profit of ₹3,000. Remember: A calendar spread depends on the relative movement of its maturities, not just their common direction.
Hint Calculate each leg separately before adding them.
V-D-149From the practice bank · 6
A bond costs ₹98 per ₹100 face value and pays no income during the next three months. A trader can finance this purchase for three months at 12% annual simple interest. A cash-settled futures contract on the same bond is priced at 102.50 and settles to the bond’s market price on that date. The trader buys ₹10,00,000 face value of the bond, shorts matching futures and sells the bond at expiry. Assume perfect price matching and ignore all fees, margin-funding costs and constraints. What profit is locked in under these assumptions? Assumptions: The cash bond and final futures settlement reference match exactly. Borrowing and trading are assumed permitted and available. Margin timing, costs, credit risk and constraints are excluded.
The financed cost per ₹100 face value is 98 × (1 + 0.12 × 3/12) = 100.94. The bond sale and matching short-futures settlement together realise 102.50, giving (102.50 − 100.94) × ₹10,00,000/100 = ₹15,600. Remember: An arbitrage calculation must include financing and state the assumptions that make the cash flows match.
Hint The cash sale plus short-futures settlement locks in 102.50 per ₹100 face. Subtract the financed purchase cost.
V-D-150