How to Trade — Execution & Platforms

Question 1

(a) Risk per share = $P_e - P_s$. Rupee risk budget $= f\cdot E$. Setting $Q(P_e-P_s)=fE$: $Q=\frac{fE}{P_e-P_s}$ (2 marks derivation) Numbers: $fE = 0.015\times500000 = 7500$. Risk/share $=820-803.50=16.50$. $Q=\frac{7500}{16.50}=454.5\Rightarrow 454\text{ shares}.$ (3 marks)

(b) Leverage does not change the risk-based quantity — risk is defined by stop distance and rupee risk, independent of how much margin funds the notional. (2 marks)

• Risk constraint: limits loss if stop hit ($Q\le fE/(P_e-P_s)$).
• Margin constraint: limits notional you can hold given capital: notional $\le E/m$ where $m=0.20$ (5×). (2 marks) Margin-max notional $= 500000/0.20 = 2{,}500{,}000$; max shares $=2500000/820=3048.7\to3048$. (1 mark) Actual $Q=\min(454,3048)=\mathbf{454}$ — risk constraint binds. (1 mark)

(c) Total loss at stop = price loss + spread (entry) + round-trip cost: $Q(P_e-P_s) + Qs + c\,Q(P_e+P_s)=fE$ where $s=0.20$, $c=0.0005$ (0.05% on combined turnover ≈ $c(P_e+P_s)$ per share). $Q\big[(P_e-P_s)+s+c(P_e+P_s)\big]=fE$ $Q=\frac{fE}{(P_e-P_s)+s+c(P_e+P_s)}$ (4 marks setup+derivation) Denominator $=16.50+0.20+0.0005\times1623.50 = 16.50+0.20+0.81175=17.51175$. $Q=\frac{7500}{17.51175}=428.29\Rightarrow \mathbf{428}\text{ shares}.$ (2 marks) Comment: costs (₹1.01175/share here) are ~6% of the 16.50 stop distance — for tight stops the cost term is a larger fraction of risk/share, shrinking $Q$ materially; ignoring it over-sizes and breaches the risk budget. (1 mark)

(d) $Q=428$. Gross move $=849.00-820=29.00$/share → gross $=428\times29=12{,}412$. Costs: spread $=428\times0.20=85.60$; round-trip proportional $=0.0005\times428\times(820+849)=0.0005\times428\times1669=357.166$. Net P&L $=12412-85.60-357.17=\mathbf{₹11{,}969.23}$. (2 marks) Margin deployed $=0.20\times428\times820=70{,}192$. Return on margin $=11969.23/70192=17.05\%$. Return on equity $=11969.23/500000=2.39\%$. (1 mark) Divergence: leverage magnifies return on the deployed capital (5×) vs the whole account; only 14% of equity was posted as margin, so the same rupee gain is a large % of margin but small % of equity. (1 mark)

Question 2

(a) Peak exposure $=\max(\text{snapshots})=310000$. Required peak margin $=0.20\times310000=\mathbf{62{,}000}$. (3 marks) Collateral $=60000<62000$ → non-compliant. Shortfall $=62000-60000=\mathbf{2{,}000}$. (2 marks) Penalty $=1\%\times2000=\mathbf{₹20.00}$. (1 mark)

(b) Equity in a long on margin: $\text{Equity}=Q P - \text{Debt}$. Debt (borrowed) $=QP_e(1-m)$ (initial equity fraction $m$). At current price $P$: equity $=QP - QP_e(1-m)$. Maintenance requires equity $\ge m_m\cdot QP$. At square-off equality: $QP_{liq}-QP_e(1-m)=m_m QP_{liq}$ $P_{liq}(1-m_m)=P_e(1-m)$ $\boxed{P_{liq}=P_e\frac{1-m}{1-m_m}}$ (4 marks derivation) Numbers: $P_{liq}=300\times\frac{0.80}{0.90}=300\times0.8889=\mathbf{₹266.67}$. (3 marks)

(c)

def peak_margin_penalty(snapshots, margin_rate, collateral, penalty_rate):
    """Return peak-margin penalty (0 if compliant).
    Peak = max snapshot notional; required = peak*margin_rate."""
    peak = max(snapshots)
    required = peak * margin_rate
    shortfall = max(0.0, required - collateral)
    return shortfall * penalty_rate
 
assert peak_margin_penalty([250000,310000,295000,200000],0.20,60000,0.01) == 20.0
 
def liquidation_price(Pe, m, mm):
    """Long square-off price where equity == maintenance margin.
    P_liq = Pe*(1-m)/(1-mm)."""
    return Pe * (1 - m) / (1 - mm)
 
assert abs(liquidation_price(300,0.20,0.10) - 266.666666) < 1e-3

(Function correctness 4, docstrings/tests 3)

Question 3

(a) Per round trip: spread cost $=sQ$ (crossing once effectively per side; model as $sQ$ per RT), proportional cost $=c\cdot QP$ each side $\times2 = 2cQP$. Cost per trade $=sQ+2cQP$. Total: $C(N)=N\,Q(s+2cP).$ Break-even gross edge $g^*$ (₹/share) satisfies $gQ=Q(s+2cP)$: $g^*=s+2cP.$ (3 derivation + 3 result)

(b) $2cP=2\times0.0003\times1200=0.72$. Cost/share $=s+2cP=0.15+0.72=0.87$. Net/share $=0.90-0.87=0.03$. Net/trade $=0.03\times200=₹6.00$. (2) Daily ($N=40$): $40\times6=\mathbf{₹240.00}$. (2) Break-even gross move $=g^*=\mathbf{₹0.87/share}$. (2)

(c) State machine (each position independent):

• FLAT →(fill buy)→ LONG
• LONG →(price ≤ stop trigger)→ ALERT_STOP →(square-off)→ CLOSED
• LONG →(price ≥ target trigger)→ ALERT_TARGET →(book)→ CLOSED
• ALERT_STOP/ALERT_TARGET → LONG only if user cancels/adjusts. (3)

Pseudocode dispatcher:

for pos in positions:
    if pos.state == LONG:
        if price <= pos.stop and not pos.alerted_stop:
            notify(pos, "STOP"); pos.state = ALERT_STOP; pos.alerted_stop = True
        elif price >= pos.target and not pos.alerted_target:
            notify(pos, "TARGET"); pos.state = ALERT_TARGET; pos.alerted_target = True

The per-position boolean flag (alerted_stop/alerted_target) guarantees at most one notification per position per trigger, preventing repeated firing on every tick — this deduplication is the key anti-alert-fatigue choice. (3)

[
 {"claim":"Raw risk-based Q = 454 (floor of 7500/16.5)","code":"result = int(7500/16.5)==454"},
 {"claim":"Cost-aware Q = 428","code":"den=16.5+0.20+0.0005*(820+803.5); result = int(7500/den)==428"},
 {"claim":"Net P&L cost-aware = 11969.23","code":"Q=428; g=Q*29; sp=Q*0.20; rt=0.0005*Q*(820+849); pnl=g-sp-rt; result = abs(pnl-11969.23)<0.5"},
 {"claim":"Peak margin penalty = 20.0","code":"peak=max([250000,310000,295000,200000]); req=0.20*peak; sf=max(0,req-60000); result = sf*0.01==20.0"},
 {"claim":"Liquidation price = 266.67","code":"result = abs(300*(1-0.20)/(1-0.10)-266.6667)<0.01"},
 {"claim":"Break-even edge 0.87 and net daily 240","code":"gstar=0.15+2*0.0003*1200; net=(0.90-gstar)*200*40; result = abs(gstar-0.87)<1e-9 and abs(net-240)<1e-6"}
]