Question 1

Spot is 1.1960 dollars per euro. The 12-month dollar rate is 4.12% and the 12-month euro rate is 3.96%, both simple. The 12-month outright forward is quoted at 1.1915. What locks a profit on EUR 5,000,000 of notional? Options: Buy euros forward, and cover by borrowing euros, selling them spot and depositing dollars: $31,703.54; Nothing, the forward is away from spot only because the two interest rates differ; Buy euros forward and hold the rate gap: $9,568.00; Buy euros forward and bank the forward points: $22,500.00; Sell euros forward, and cover by borrowing dollars, buying euros spot and depositing them: $31,703.54.

Accepted Answer

Buy euros forward, and cover by borrowing euros, selling them spot and depositing dollars: $31,703.54. Covered interest parity sets F = S x (1 + r_dom x T)/(1 + r_for x T) = 1.1960 x 1.041200 / 1.039600 = 1.197841. The market quotes 1.1915, so the euro forward is too cheap by 0.006341, which is 63.4 pips. Buy EUR 5,000,000 forward at 1.1915, and offset it by borrowing euros at 3.96%, selling them spot and depositing the dollars at 4.12%. The dollar deposit grows to 1.197841 per euro. The difference is $31,703.54 and it is certain at trade time. The raw rate gap of 0.16% comes to $9,568.00 over the period, but that is not profit, it is exactly what the forward points already pay for.

Question 2

You quote a market 4 ticks wide and trade 38 round turns in a day, buying on the bid and selling on the offer. Each tick is worth $5. What is the day's theoretical edge, in dollars?

Accepted Answer

760. A round turn captures the whole 4-tick width, worth $20. Across 38 round turns that is $760. Half the width is the edge per SIDE, not per round turn.

Question 3

The $120/$130 box expiring in 3 months is quoted at $10.23, on options with a 100 multiplier. The 3-month rate is 4.87% continuously compounded and there are no dividends. What is the trade on 20 boxes? Options: Buy the box: $702.02 of present value; Nothing, a box is worth whatever the four option prices say it is worth; Sell the box: $7.02 of present value; Sell the box: $702.02 of present value; Sell the box: $460.00 of present value.

Accepted Answer

Sell the box: $702.02 of present value. A box is long the $120 call, short the $130 call, long the $130 put and short the $120 put. At expiry it pays exactly $10 at every terminal price, so it is a zero coupon bond and nothing else: worth $10 x e^(-0.0487 x 0.2500) = $10 x 0.987899 = $9.8790 today. It is quoted at $10.23, above that by $0.3510. Sell it and hold to expiry: take $10.23 now, pay $10 then. On 20 boxes at a 100 multiplier that is $0.3510 x 100 x 20 = $702.02. Comparing the quote with the undiscounted $10 gives $460.00, which counts the interest as profit. Dropping the 100 multiplier gives $7.02, a hundredth of the real size. A box has no delta, no vega and no view in it, which is why it is quoted as a funding instrument.

Question 4

The $80/$90 box expiring in 9 months is quoted at $8.73, on options with a 100 multiplier. The 9-month rate is 5.63% continuously compounded and there are no dividends. What is the trade on 200 boxes? Options: Buy the box: $25,400.00 of present value; Sell the box: $17,130.81 of present value; Buy the box: $17,130.81 of present value; Nothing, a box is worth whatever the four option prices say it is worth; Buy the box: $171.31 of present value.

Accepted Answer

Buy the box: $17,130.81 of present value. A box is long the $80 call, short the $90 call, long the $90 put and short the $80 put. At expiry it pays exactly $10 at every terminal price, so it is a zero coupon bond and nothing else: worth $10 x e^(-0.0563 x 0.7500) = $10 x 0.958654 = $9.5865 today. It is quoted at $8.73, below that by $0.8565. Buy it and hold to expiry: pay $8.73 now, collect $10 then. On 200 boxes at a 100 multiplier that is $0.8565 x 100 x 200 = $17,130.81. Comparing the quote with the undiscounted $10 gives $25,400.00, which counts the interest as profit. Dropping the 100 multiplier gives $171.31, a hundredth of the real size. A box has no delta, no vega and no view in it, which is why it is quoted as a funding instrument.

Question 5

A routing change lifts the fill rate on 170,000 daily orders from 75% to 86%. Each extra fill is worth $0.25 of gross profit. What is the daily gain, in dollars?

Accepted Answer

4675. The lift is 11 percentage points on 170,000 orders, which is 18,700 extra fills, worth $4,675 a day.

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