Part A / An order with a price limit
A client wants to buy 2,000 shares. The displayed offer book is below; the best bid is $99.90. First assume an immediately executable market order, no fees, no hidden liquidity, no price movement and that all displayed offers remain available. Then compare a buy limit of $100.10.
| Offer price | Available shares |
|---|---|
| $100.00 | 500 |
| $100.10 | 800 |
| $100.25 | 1,200 |
- Calculate the market order's total cost and volume-weighted average price (VWAP).
- Calculate dollar and basis-point slippage relative to the arrival mid-price.
- For the $100.10 limit order, calculate immediate shares filled, average fill price and unfilled quantity.
- Explain the trade-off to the client without guaranteeing the remaining fill.
Fill by price level / total cost / VWAP
Arrival mid / dollar slippage / basis points
Limit-order filled / unfilled / average fill price
Use your own notes or the writing space in the downloadable PDF.
Part A / Worked execution
The mid-price is a stated benchmark for this exercise, not proof of an executable price. Real costs can include fees, spread, impact, latency and opportunity cost from unfilled orders.
Part B / A first-order rates hedge
A long bond position loses approximately $4,800 for a parallel 1 basis point rise in yield. A long futures contract loses approximately $60 for the same rate move. Define those as positive DV01 magnitudes for long exposures. Ignore convexity, carry, basis changes and delivery effects for the initial calculation.
- How many futures contracts, and in which direction, offset the first-order exposure?
- Estimate bond, futures and net P&L for a parallel 10 basis point rise.
- If the bond DV01 increases to $5,100 while the 80-contract hedge stays unchanged, what first-order exposure remains?
Hedge size and direction
P&L for +10 bps / residual after DV01 changes
Use your own notes or the writing space in the downloadable PDF.
Part B / Worked hedgeOpen worked answer
Short 80 futures: $4,800 / $60 = 80. A 10 bp rise produces approximately -$48,000 on the long bond position and +$48,000 on the short futures, for zero first-order net P&L under the stipulated mapping.
With bond DV01 at $5,100, the unchanged short futures offset $4,800, leaving $300 per bp long exposure. A 10 bp rise then implies approximately -$3,000 residual P&L. Under the same assumptions, five additional short contracts would offset that change.
A single DV01 hedge does not eliminate curve-shape, credit-spread, basis, convexity, liquidity or operational risk. The two instruments may not respond to the same underlying rate in practice.
Explain the limitation before the number becomes a promise
To practice the interview discussion, explain Part A to a client in plain language and Part B to a desk risk manager. They need different details even though both answers require careful assumptions.
- State whether a rate is in percent, decimal or basis points; 10 bps is 0.10 percentage points.
- Name the execution benchmark and distinguish an observed quote from an available fill.
- Keep hedge direction explicit: a short exposure gains when the corresponding long exposure loses, under the assumed sensitivity.
- Recalculate sensitivities when prices, time or the portfolio changes.
- For a real futures hedge, check the contract specification, conversion factors, deliverable basket and the relationship to the cash instrument.
Source notes
Sources support the underlying concepts. The worked cases, figures and examples are original teaching material with the assumptions stated in the resource.
Background on market and limit orders. The order book and first-order sensitivity inputs are original fictional examples; the hedge is defined mathematically by the supplied sensitivities.
Questions about this resource
Does a limit order guarantee a better execution?
It limits the acceptable price but may not fill. The case explicitly leaves 700 shares unfilled at the stated limit.
Does matching DV01 remove all bond risk?
No. It offsets the stipulated first-order parallel-rate sensitivity. Other risks, including basis, curve shape and convexity, remain.
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Explain execution costs and hedge direction without losing track of units.