HFT & Advanced Concepts

Question 1 (12)

(a) Reaction time = processing + round trip.

• Colocated firm: $40 + 250 = 290\ \mu s$ ✓(1)
• Competitor: $40 + 1800 = 1840\ \mu s$ ✓(1)
• Stale quote alive for $900\ \mu s$. Colocated ($290 < 900$) captures; competitor ($1840 > 900$) misses. ✓(2)

(b) Edge per share = 50.04 - 50.00 = \0.04$. Volume 2,000. Gross profit$= 0.04 \times 2000 = $80$. ✓(4) (1 for edge, 1 for size, 2 for product)

(c) The $250\to150\ \mu s$ upgrade does not change who wins this trade (colocated already wins at $290\ \mu s < 900$). Captured edge is unchanged by the upgrade for this recurring opportunity.

• Monthly benefit from this opportunity set: it was already being captured, so incremental benefit = $0. ✓(2)
• Cost = $8,000/month. Benefit ($0) < cost. Not justified on this edge alone. ✓(2)

(Full marks require recognising the upgrade adds no incremental capture here; awarding capture would be a trap. Marginal-benefit reasoning is the key insight.) If a student instead computes gross monthly edge = 80 \times 22 \times 21 = \36{,}960$ and compares to cost, award (1) but note it is the wrong marginal frame.

Question 2 (14)

(a) TWAP = equal per hour = $600{,}000 / 6 = 100{,}000$ shares each hour. ✓(2)

(b) VWAP = order size × hourly volume fraction:

• H1: $600{,}000 \times 0.25 = 150{,}000$
• H2: $\times0.20 = 120{,}000$
• H3: $\times0.15 = 90{,}000$
• H4: $\times0.10 = 60{,}000$
• H5: $\times0.12 = 72{,}000$
• H6: $\times0.18 = 108{,}000$ Sum $= 600{,}000$ ✓. (3) (correct method 2, all values + check 1)

(c) POV: $8\% \times 900{,}000 = 72{,}000$ shares executed in Hour 4. ✓(2) VWAP-scheduled H4 = 60,000 (from part b). ✓(1) POV executes 72,000 vs VWAP 60,000 → POV executes 12,000 more because realised volume (900k) exceeded the expected hourly share ($0.10 \times 10{,}000{,}000 = 1{,}000{,}000$ was expected, but POV keys off actual volume). ✓(2)

(d) VWAP reasons (any two, 1 each):

• Concentrates trading when natural liquidity/volume is highest → smaller footprint per share.
• Benchmarks to volume-weighted price, reducing signalling and slippage vs a rigid time schedule. TWAP preferable scenario (2): when volume is unpredictable/illiquid or the trader wants to avoid over-participating in volume spikes, or to conceal intent by steady, predictable-to-nobody slicing / when minimising timing risk of front-loaded VWAP. ✓(4)

Question 3 (12)

(a) Spread = 100.02 - 99.98 = \0.04$. ✓(1) Mid$= (100.02+99.98)/2 = $100.00$. ✓(1) Basis points$= (0.04/100.00)\times 10{,}000 = 4\ \text{bps}$. ✓(1)

(b) Volume 4,000,000.

• Spread capture side: 60% × 4,000,000 = 2,400,000 shares. Half-spread earned per share on a round trip ≈ full spread \0.04$captured on round-trip captures →$2{,}400{,}000 \times 0.04 = $96{,}000$. ✓(2)
• Adverse side: 40% × 4,000,000 = 1,600,000 shares, loss \0.03$each →$-$48{,}000$. ✓(2)
• Net P&L = 96{,}000 - 48{,}000 = \48{,}000$. ✓(1)

(c) Rebate = 0.0020 \times 4{,}000{,}000 = \8{,}000$. ✓(2) New total$= 48{,}000 + 8{,}000 = $56{,}000$. ✓(1) Comment: at thin per-share margins and huge volumes, rebates can exceed raw spread P&L; they turn marginal/loss-making passive quotes profitable and drive maker-taker strategy. ✓(1)

Question 4 (12)

(a) Reference \200$,$\pm5%$:

• Upper = 200 \times 1.05 = \210.00$ ✓(1)
• Lower = 200 \times 0.95 = \190.00$ ✓(1)

(b) Lower band = \190.00$. Prints:$198$(ok),$194$(ok),$190.50$(ok, above 190),$189.90 (**below 190 → breach**). First breach at the **\189.90** print, since $189.90 < 190.00$ boundary. ✓(4) (band identified 1, sequential test 2, correct print 1)

(c) Uncoordinated HFT withdrawal: as price gaps, MMs widen/pull quotes to avoid adverse selection; liquidity evaporates simultaneously across venues, so the same order flow now walks a much thinner book, causing larger price jumps → feedback loop. In 2010 a large sell program met vanishing liquidity, prices cascaded, and "stub quotes" got hit at absurd prices. ✓(3)

(d) Quote stuffing = flooding an exchange with huge numbers of orders and near-instant cancellations. It degrades quality by consuming bandwidth/matching-engine capacity, introducing latency for others, obscuring the true book, and enabling latency games — all without real intent to trade. ✓(3)

Question 5 (10)

(a) All-in cost per share = price + taker fee:

• A: 25.00 + 0.0030 = \25.0030$
• B: 25.00 + 0.0010 = \25.0010$
• C: 25.01 + 0.0005 = \25.0105$

Cheapest first: B (1,500 @ 25.0010), then A (2,000 @ 25.0030), then need $5{,}000 - 3{,}500 = 1{,}500$ from C (@ 25.0105). ✓(3) Total cost:

• B: $1{,}500 \times 25.0010 = 37{,}501.50$
• A: $2{,}000 \times 25.0030 = 50{,}006.00$
• C: $1{,}500 \times 25.0105 = 37{,}515.75$
• Total = \125{,}023.25$ ✓(3)

(b) Naïve sweeps by price only: A and B both at $25.00 → fill A 2,000 + B 1,500 = 3,500, then C 1,500 @ 25.01.

• A: $2{,}000 \times (25.00+0.0030) = 50{,}006.00$
• B: $1{,}500 \times (25.00+0.0010) = 37{,}501.50$
• C: $1{,}500 \times (25.01+0.0005) = 37{,}515.75$
• Naïve total = \125{,}023.25$. ✓(2)

Here naïve and smart give the same allocation because A and B share the same price and both fully consumed; fees only reorder within the same price level and total volume taken is identical → savings = $0. ✓(2) (Key teaching point: SOR fee-optimisation only helps when it changes which shares at a given price get skipped or which venue is left partially unfilled; when the full displayed size at the cheap level is consumed, order is immaterial. Recognising $0 savings earns full marks.)

[
  {"claim":"Q1b gross profit = 80","code":"edge=Rational('0.04'); vol=2000; result=(edge*vol==80)"},
  {"claim":"Q2b VWAP allocations sum to 600000","code":"order=600000; fracs=[Rational(25,100),Rational(20,100),Rational(15,100),Rational(10,100),Rational(12,100),Rational(18,100)]; result=(sum(order*f for f in fracs)==600000 and order*Rational(10,100)==60000)"},
  {"claim":"Q2c POV Hour4 = 72000 and exceeds VWAP by 12000","code":"pov=Rational(8,100)*900000; vwap=60000; result=(pov==72000 and pov-vwap==12000)"},
  {"claim":"Q3 spread 4bps and net PnL 48000, total 56000","code":"spread=Rational('0.04'); mid=100; bps=spread/mid*10000; cap=Rational(60,100)*4000000*Rational('0.04'); adv=Rational(40,100)*4000000*Rational('0.03'); net=cap-adv; total=net+Rational('0.0020')*4000000; result=(bps==4 and net==48000 and total==56000)"},
  {"claim":"Q4 limits 210 and 190, breach at 189.90","code":"ref=200; up=ref*Rational(105,100); lo=ref*Rational(95,100); result=(up==210 and lo==190 and Rational('189.90')<lo and Rational('190.50')>lo)"},
  {"claim":"Q5 smart total all-in cost = 125023.25","code":"B=1500*Rational('25.0010'); A=2000*Rational('25.0030'); C=1500*Rational('25.0105'); result=(B+A+C==Rational('125023.25'))"}
]