{ "notice": "Deterministic educational arithmetic for trading-bot capital, sizing and costs; no market backtest, forecast, optimization, live trading or performance claim.", "assumption_provenance": "Every fee, execution allowance, price, quantity increment, minimum notional, monthly cost, trade count and return is explicitly assumed for this exercise. None is a current quote or verified rule from a broker, exchange, hosting service or market dataset.", "currency": "USD accounting units; no foreign-exchange, stablecoin or custody model", "position_sizing": [ { "equity": 100.0, "risk_budget": 0.5, "risk_fraction": 0.005, "risk_budget_notional_before_rounding": 21.73913043478261, "cash_affordable_notional_before_rounding": 99.85017481269355, "candidate_quantity_rounded_down": 0.43, "candidate_reference_notional": 21.5, "status": "EXECUTE_IN_MODEL", "quantity": 0.43, "reference_notional": 21.5, "reference_notional_over_equity": 0.215, "entry_cash_required": 21.53226075, "cash_remaining_after_entry": 78.46773925, "conservative_planned_gap_free_loss": 0.4945, "planned_loss_over_equity": 0.004945, "unused_risk_budget": 0.0055, "modeled_gap_free_stop_loss_with_multiplicative_costs": 0.493855215, "assumed_stopped_exit_notional_before_exit_fee": 21.059465, "meets_assumed_same_minimum_on_stopped_exit": true }, { "equity": 500.0, "risk_budget": 2.5, "risk_fraction": 0.005, "risk_budget_notional_before_rounding": 108.69565217391305, "cash_affordable_notional_before_rounding": 499.2508740634678, "candidate_quantity_rounded_down": 2.17, "candidate_reference_notional": 108.5, "status": "EXECUTE_IN_MODEL", "quantity": 2.17, "reference_notional": 108.5, "reference_notional_over_equity": 0.217, "entry_cash_required": 108.66280425, "cash_remaining_after_entry": 391.33719575, "conservative_planned_gap_free_loss": 2.4955, "planned_loss_over_equity": 0.004991, "unused_risk_budget": 0.0045, "modeled_gap_free_stop_loss_with_multiplicative_costs": 2.492246085, "assumed_stopped_exit_notional_before_exit_fee": 106.276835, "meets_assumed_same_minimum_on_stopped_exit": true }, { "equity": 2000.0, "risk_budget": 10.0, "risk_fraction": 0.005, "risk_budget_notional_before_rounding": 434.7826086956522, "cash_affordable_notional_before_rounding": 1997.0034962538712, "candidate_quantity_rounded_down": 8.69, "candidate_reference_notional": 434.5, "status": "EXECUTE_IN_MODEL", "quantity": 8.69, "reference_notional": 434.5, "reference_notional_over_equity": 0.21725, "entry_cash_required": 435.15196725, "cash_remaining_after_entry": 1564.84803275, "conservative_planned_gap_free_loss": 9.9935, "planned_loss_over_equity": 0.00499675, "unused_risk_budget": 0.0065, "modeled_gap_free_stop_loss_with_multiplicative_costs": 9.980469345, "assumed_stopped_exit_notional_before_exit_fee": 425.597095, "meets_assumed_same_minimum_on_stopped_exit": true }, { "equity": 10000.0, "risk_budget": 50.0, "risk_fraction": 0.005, "risk_budget_notional_before_rounding": 2173.913043478261, "cash_affordable_notional_before_rounding": 9985.017481269355, "candidate_quantity_rounded_down": 43.47, "candidate_reference_notional": 2173.5, "status": "EXECUTE_IN_MODEL", "quantity": 43.47, "reference_notional": 2173.5, "reference_notional_over_equity": 0.21735, "entry_cash_required": 2176.76133675, "cash_remaining_after_entry": 7823.23866325, "conservative_planned_gap_free_loss": 49.9905, "planned_loss_over_equity": 0.00499905, "unused_risk_budget": 0.0095, "modeled_gap_free_stop_loss_with_multiplicative_costs": 49.925316735, "assumed_stopped_exit_notional_before_exit_fee": 2128.964985, "meets_assumed_same_minimum_on_stopped_exit": true } ], "minimum_executable_capital": { "main_grid": { "assumed_reference_price": 50.0, "assumed_quantity_increment": 0.01, "assumed_minimum_reference_notional": 10.0, "minimum_executable_quantity": 0.2, "minimum_executable_reference_notional": 10.0, "risk_budget_minimum_equity": 46.0, "entry_cash_minimum_equity": 10.015005, "minimum_equity_satisfying_both": 46.0, "binding_constraint": "risk_budget", "constraint_scope": "entry-only minimum, conservative planned loss budget, and funded entry cash", "assumed_full_quantity_stop_exit_minimum_diagnostic": { "assumed_adversely_adjusted_stop_exit_price_before_fee": 48.9755, "minimum_entry_quantity_also_meeting_stated_stop_exit_minimum": 0.21, "corresponding_entry_reference_notional": 10.5, "corresponding_stop_exit_notional_before_exit_fee": 10.284855, "risk_budget_minimum_equity": 48.3, "entry_cash_minimum_equity": 10.51575525, "minimum_equity_for_entry_and_assumed_stop_exit_minimum": 48.3, "meaning": "Additional assumed same-quantity notional check; not a full order-lifecycle or guaranteed-exit model" } }, "coarse_grid": { "assumed_reference_price": 51.0, "assumed_quantity_increment": 0.03, "assumed_minimum_reference_notional": 10.0, "minimum_executable_quantity": 0.21, "minimum_executable_reference_notional": 10.71, "risk_budget_minimum_equity": 49.266, "entry_cash_minimum_equity": 10.726070355, "minimum_equity_satisfying_both": 49.266, "binding_constraint": "risk_budget", "constraint_scope": "entry-only minimum, conservative planned loss budget, and funded entry cash", "assumed_full_quantity_stop_exit_minimum_diagnostic": { "assumed_adversely_adjusted_stop_exit_price_before_fee": 49.95501, "minimum_entry_quantity_also_meeting_stated_stop_exit_minimum": 0.21, "corresponding_entry_reference_notional": 10.71, "corresponding_stop_exit_notional_before_exit_fee": 10.4905521, "risk_budget_minimum_equity": 49.266, "entry_cash_minimum_equity": 10.726070355, "minimum_equity_for_entry_and_assumed_stop_exit_minimum": 49.266, "meaning": "Additional assumed same-quantity notional check; not a full order-lifecycle or guaranteed-exit model" } } }, "monthly_cost_impact": [ { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 0.0, "status": "NO_FIXED_COST_THRESHOLD_TRADING_CONSTRAINTS_REMAIN", "equity": 100.0, "round_trip_reference_notional_sum": 500.0, "assumed_gross_monthly_pnl": 2.0, "assumed_variable_monthly_friction": 1.5, "linear_monthly_pnl_before_fixed_cost": 0.5, "linear_monthly_pnl_after_fixed_cost": 0.5, "linear_monthly_return_after_fixed_cost": 0.005, "fixed_monthly_cost_over_equity": 0.0, "required_gross_notional_return_per_round_trip_for_break_even": 0.003 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 3000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 100.0, "round_trip_reference_notional_sum": 500.0, "assumed_gross_monthly_pnl": 2.0, "assumed_variable_monthly_friction": 1.5, "linear_monthly_pnl_before_fixed_cost": 0.5, "linear_monthly_pnl_after_fixed_cost": -14.5, "linear_monthly_return_after_fixed_cost": -0.145, "fixed_monthly_cost_over_equity": 0.15, "required_gross_notional_return_per_round_trip_for_break_even": 0.033 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 50.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 10000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 100.0, "round_trip_reference_notional_sum": 500.0, "assumed_gross_monthly_pnl": 2.0, "assumed_variable_monthly_friction": 1.5, "linear_monthly_pnl_before_fixed_cost": 0.5, "linear_monthly_pnl_after_fixed_cost": -49.5, "linear_monthly_return_after_fixed_cost": -0.495, "fixed_monthly_cost_over_equity": 0.5, "required_gross_notional_return_per_round_trip_for_break_even": 0.103 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 0.0, "status": "NO_FIXED_COST_THRESHOLD_TRADING_CONSTRAINTS_REMAIN", "equity": 500.0, "round_trip_reference_notional_sum": 2500.0, "assumed_gross_monthly_pnl": 10.0, "assumed_variable_monthly_friction": 7.5, "linear_monthly_pnl_before_fixed_cost": 2.5, "linear_monthly_pnl_after_fixed_cost": 2.5, "linear_monthly_return_after_fixed_cost": 0.005, "fixed_monthly_cost_over_equity": 0.0, "required_gross_notional_return_per_round_trip_for_break_even": 0.003 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 3000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 500.0, "round_trip_reference_notional_sum": 2500.0, "assumed_gross_monthly_pnl": 10.0, "assumed_variable_monthly_friction": 7.5, "linear_monthly_pnl_before_fixed_cost": 2.5, "linear_monthly_pnl_after_fixed_cost": -12.5, "linear_monthly_return_after_fixed_cost": -0.025, "fixed_monthly_cost_over_equity": 0.03, "required_gross_notional_return_per_round_trip_for_break_even": 0.009 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 50.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 10000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 500.0, "round_trip_reference_notional_sum": 2500.0, "assumed_gross_monthly_pnl": 10.0, "assumed_variable_monthly_friction": 7.5, "linear_monthly_pnl_before_fixed_cost": 2.5, "linear_monthly_pnl_after_fixed_cost": -47.5, "linear_monthly_return_after_fixed_cost": -0.095, "fixed_monthly_cost_over_equity": 0.1, "required_gross_notional_return_per_round_trip_for_break_even": 0.023 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 0.0, "status": "NO_FIXED_COST_THRESHOLD_TRADING_CONSTRAINTS_REMAIN", "equity": 2000.0, "round_trip_reference_notional_sum": 10000.0, "assumed_gross_monthly_pnl": 40.0, "assumed_variable_monthly_friction": 30.0, "linear_monthly_pnl_before_fixed_cost": 10.0, "linear_monthly_pnl_after_fixed_cost": 10.0, "linear_monthly_return_after_fixed_cost": 0.005, "fixed_monthly_cost_over_equity": 0.0, "required_gross_notional_return_per_round_trip_for_break_even": 0.003 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 3000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 2000.0, "round_trip_reference_notional_sum": 10000.0, "assumed_gross_monthly_pnl": 40.0, "assumed_variable_monthly_friction": 30.0, "linear_monthly_pnl_before_fixed_cost": 10.0, "linear_monthly_pnl_after_fixed_cost": -5.0, "linear_monthly_return_after_fixed_cost": -0.0025, "fixed_monthly_cost_over_equity": 0.0075, "required_gross_notional_return_per_round_trip_for_break_even": 0.0045 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 50.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 10000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 2000.0, "round_trip_reference_notional_sum": 10000.0, "assumed_gross_monthly_pnl": 40.0, "assumed_variable_monthly_friction": 30.0, "linear_monthly_pnl_before_fixed_cost": 10.0, "linear_monthly_pnl_after_fixed_cost": -40.0, "linear_monthly_return_after_fixed_cost": -0.02, "fixed_monthly_cost_over_equity": 0.025, "required_gross_notional_return_per_round_trip_for_break_even": 0.008 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 0.0, "status": "NO_FIXED_COST_THRESHOLD_TRADING_CONSTRAINTS_REMAIN", "equity": 10000.0, "round_trip_reference_notional_sum": 50000.0, "assumed_gross_monthly_pnl": 200.0, "assumed_variable_monthly_friction": 150.0, "linear_monthly_pnl_before_fixed_cost": 50.0, "linear_monthly_pnl_after_fixed_cost": 50.0, "linear_monthly_return_after_fixed_cost": 0.005, "fixed_monthly_cost_over_equity": 0.0, "required_gross_notional_return_per_round_trip_for_break_even": 0.003 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 3000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 10000.0, "round_trip_reference_notional_sum": 50000.0, "assumed_gross_monthly_pnl": 200.0, "assumed_variable_monthly_friction": 150.0, "linear_monthly_pnl_before_fixed_cost": 50.0, "linear_monthly_pnl_after_fixed_cost": 35.0, "linear_monthly_return_after_fixed_cost": 0.0035, "fixed_monthly_cost_over_equity": 0.0015, "required_gross_notional_return_per_round_trip_for_break_even": 0.0033 }, { "scenario_family": "capital_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 50.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 10000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD", "equity": 10000.0, "round_trip_reference_notional_sum": 50000.0, "assumed_gross_monthly_pnl": 200.0, "assumed_variable_monthly_friction": 150.0, "linear_monthly_pnl_before_fixed_cost": 50.0, "linear_monthly_pnl_after_fixed_cost": 0.0, "linear_monthly_return_after_fixed_cost": 0.0, "fixed_monthly_cost_over_equity": 0.005, "required_gross_notional_return_per_round_trip_for_break_even": 0.004 } ], "gross_return_sensitivity": [ { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.001, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": -0.01, "break_even_equity": null, "status": "NO_POSITIVE_EQUITY_BREAK_EVEN" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.001, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": -0.01, "break_even_equity": null, "status": "NO_POSITIVE_EQUITY_BREAK_EVEN" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.001, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 50.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": -0.01, "break_even_equity": null, "status": "NO_POSITIVE_EQUITY_BREAK_EVEN" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.003, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.0, "break_even_equity": null, "status": "ALL_POSITIVE_EQUITIES_BREAK_EVEN_NO_OPERATING_SURPLUS" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.003, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.0, "break_even_equity": null, "status": "NO_POSITIVE_EQUITY_BREAK_EVEN" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.003, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 50.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.0, "break_even_equity": null, "status": "NO_POSITIVE_EQUITY_BREAK_EVEN" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 0.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 0.0, "status": "NO_FIXED_COST_THRESHOLD_TRADING_CONSTRAINTS_REMAIN" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, "round_trips_per_month": 20, "assumed_gross_notional_return_per_round_trip": 0.004, "assumed_linear_round_trip_friction": 0.003, "fixed_monthly_cost": 15.0, "round_trip_reference_notional_sum_over_equity": 5.0, "linear_monthly_surplus_rate_before_fixed_cost": 0.005, "break_even_equity": 3000.0, "status": "POSITIVE_SURPLUS_FIXED_COST_THRESHOLD" }, { "scenario_family": "gross_return_and_fixed_cost", "deployed_fraction": 0.25, 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