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Deterministic Runtime
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Trading Formulas Directory

The canonical repository of verified quantitative equations, Greek derivations, and clearing friction algorithms across CalcTrading computational tools. Every formula operates deterministically on the client device with zero telemetry.

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Summary • Institutional Verification Standard

All 41 trading formulas across our equity, options, futures, and crypto tools are documented below with complete variable definitions and worked numerical proofs. Each model connects directly to its live client-side calculator.

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41 Formulas
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Risk Management & Expectancy

10 Models

Deterministic algorithms for calculating exact equity risk, stop distances, capital preservation, and probability of ruin.

#1

Core Position Sizing Formula

Open Calculator open_in_new
functions Mathematical Expression
Position Size (Units) = floor( (Account Capital × Risk %) / |Entry Price - Stop Loss Price| )

Determines the exact unit position size based strictly on total equity risk parameters. Eliminates emotional bias by making unit allocation an inverse function of price risk distance.

Parameter Operational Definition & Clearing Mechanics
Account Capital × Risk% Absolute dollar capital at risk ($R). Typically capped at 0.5% - 2.0% for institutional capital preservation.
|Entry - Stop Loss| Risk per share ($/Delta P$). Defines the exact adverse price excursion prior to trade invalidation.
Floor Function [•] Truncates fractional units downward to ensure defined risk cannot be breached by fractional round-up.
verified Worked Numerical Proof

$100,000 Capital • 1.0% Risk ($1,000) • Entry $150.00 • Stop $146.00 ($4.00 Risk/Share)

arrow_forward Result = 250 Shares ($1,000.00 Exact Risk)
#2

Stop Loss Price Calculation

Open Calculator open_in_new
functions Mathematical Expression
Stop Loss (Long) = Entry Price - ( Max Dollar Risk / Position Quantity ) Stop Loss (Short) = Entry Price + ( Max Dollar Risk / Position Quantity ) // Percent Model: Stop Price = Entry Price × ( 1 ± Stop Loss % )

Calculates the exact execution price where a trade must be liquidated to limit total loss to an exact predetermined dollar amount or risk percentage.

Parameter Operational Definition & Clearing Mechanics
Entry Price Executed average cost basis per share.
Max Dollar Risk Total acceptable loss budget for the trade.
Position Quantity Number of shares, units, or contracts held.
verified Worked Numerical Proof

Long 500 shares at $45.00 • Max Tolerated Loss = $750.00 ($1.50/share)

arrow_forward Stop Loss = $43.50 (-3.33%)
#3

Take Profit Target Formula

Open Calculator open_in_new
functions Mathematical Expression
Take Profit (Long) = Entry Price + [ R:R Ratio × ( Entry - Stop Loss ) ] Take Profit (Short) = Entry Price - [ R:R Ratio × ( Stop Loss - Entry ) ]

Projects the theoretical exit price required to fulfill a desired Risk/Reward multiple based on underlying entry and protective stop levels.

Parameter Operational Definition & Clearing Mechanics
R:R Ratio Desired payout multiple relative to unit risk (e.g. 2.5R).
Risk Distance |Entry - Stop Loss| defining baseline 1R denomination.
Take Profit Price Automated limit target satisfying asymmetric edge criteria.
verified Worked Numerical Proof

Entry $200.00 • Stop Loss $192.00 ($8.00 Risk) • Target R:R = 2.5:1

arrow_forward Target Price = $220.00 (+10.0%, +$16.00/Share)
#4

Risk/Reward Ratio (R:R)

Open Calculator open_in_new
functions Mathematical Expression
Risk/Reward Ratio (R) = |Target Price - Entry Price| / |Entry Price - Stop Loss Price|

Quantifies the asymmetric payoff ratio between upside potential and defined risk exposure. Asymmetric setups (> 2.0R) allow trading systems to remain profitable even with win rates below 40%.

Parameter Operational Definition & Clearing Mechanics
Target - Entry Expected upside profit per unit if thesis succeeds.
Entry - Stop Loss Maximum potential downside loss per unit if invalidated.
Payoff Ratio Multiples of risk rewarded upon target fulfillment.
verified Worked Numerical Proof

Entry $100.00 • Stop $95.00 ($5.00 Risk) • Target $115.00 ($15.00 Gain)

arrow_forward R:R = 3.00:1 (3.0R Asymmetric Edge)
#5

Risk of Ruin (Perry Absorbing Barrier)

Open Calculator open_in_new
functions Mathematical Expression
Risk of Ruin (RoR) = ( ( 1 - W ) / W ) ^ Units To Ruin where: W = Probability of Winning (Win Rate > 0.50) Units = Maximum Drawdown Tolerated (%) / Risk Per Trade (%)

Calculates the mathematical probability of a trading account hitting zero (or catastrophic drawdown threshold) before realizing the long-term expected edge.

Parameter Operational Definition & Clearing Mechanics
Win Rate (W) Statistical historical win rate expressed as a decimal > 0.50.
Units to Ruin Buffer of consecutive maximum-loss risk units until bankruptcy.
RoR Probability Terminal probability of absorbing barrier ruin.
verified Worked Numerical Proof

Win Rate = 55% • Max Drawdown = 25% • Risk Per Trade = 1.0% (25 Units)

arrow_forward Risk of Ruin = 0.68% (Statistically Safe)
#6

The Kelly Criterion (Optimal Growth Sizing)

Open Calculator open_in_new
functions Mathematical Expression
Kelly % (f*) = W - ( ( 1 - W ) / R ) Institutional Half-Kelly: f*_half = f* × 0.50 // Retains 75% growth with 50% less drawdown volatility

Derived by Bell Labs scientist John L. Kelly Jr., this model calculates the exact capital fraction ($f^*$) that maximizes logarithmic wealth growth across an infinite series of independent trials.

Parameter Operational Definition & Clearing Mechanics
Win Probability (W) Frequency of winning trades expressed as a decimal (e.g. 0.60).
Payoff Ratio (R) Average dollar win divided by average dollar loss.
Full Kelly (f*) Theoretical optimum; institutional desks deploy Half-Kelly (0.5 f*).
verified Worked Numerical Proof

Win Rate = 60% • Payoff Ratio (Avg Win / Avg Loss) = 1.50

arrow_forward Full Kelly = 33.3% • Recommended Half-Kelly = 16.7%
#7

Breakeven Win Rate Formula

Open Calculator open_in_new
functions Mathematical Expression
Required Breakeven Win Rate (W_be) = 1 / ( 1 + Risk/Reward Ratio )

Identifies the exact minimum trading accuracy required to generate zero net loss for any specified Risk/Reward ratio before fees.

Parameter Operational Definition & Clearing Mechanics
Risk/Reward Ratio (R) Average win unit size relative to fixed 1R loss.
W_be Threshold Minimum win rate boundary for positive mathematical expectancy.
verified Worked Numerical Proof

Target Risk:Reward = 1 : 2.00 (Risk $100 to gain $200)

arrow_forward Breakeven Win Rate = 33.33% (Win 1 out of 3 trades)
#8

R-Multiple Realization (Van Tharp Metric)

Open Calculator open_in_new
functions Mathematical Expression
Realized R-Multiple = ( Exit Price - Entry Price ) / |Entry Price - Stop Loss Price|

Normalizes trade outcome returns relative to initial capital risked ($1R$). Standardizes performance metrics across different trade sizes, timeframes, and asset classes.

Parameter Operational Definition & Clearing Mechanics
Dollar Profit ($P) (Exit Price - Entry Price) × Position Size.
Initial Risk (1R) |Entry Price - Stop Price| × Position Size.
R Multiple Unitless standardized score of trade execution performance.
verified Worked Numerical Proof

Bought @ $50.00 • Initial Stop @ $48.00 ($1R = $2.00) • Sold @ $56.00

arrow_forward Return = +$6.00 / share = +3.00R
#9

Portfolio Heat & Aggregate Risk Exposure

Open Calculator open_in_new
functions Mathematical Expression
Total Portfolio Heat (%) = Σ [ Position Risk ($)_i / Total Account Equity ($) ] × 100%

Measures the total combined percentage of account equity at risk across all simultaneously open active trades if every protective stop is triggered.

Parameter Operational Definition & Clearing Mechanics
Position Risk ($)_i Quantity × |Entry - Stop| for each individual open asset position.
Total Account Equity Current cash plus net liquidation value of portfolio.
Safe Heat Range Institutional systematic desks limit aggregate heat between 6% - 10%.
verified Worked Numerical Proof

$100,000 Equity • 4 Open Positions with defined risks ($1.2k, $800, $1.5k, $500)

arrow_forward Total Heat = 4.00% ($4,000 Total Capital At Risk)
#10

Maximum Drawdown (MDD)

Open Calculator open_in_new
functions Mathematical Expression
Drawdown (%) = [ ( Peak Equity - Current Trough Equity ) / Peak Equity ] × 100% Max Drawdown (MDD) = max [ Drawdown(t) ] across all t in evaluation window

Measures the largest peak-to-trough percentage decline in portfolio equity before a new all-time high is established.

Parameter Operational Definition & Clearing Mechanics
High-Water Mark (Peak) The highest historical account balance recorded prior to drawdown.
Trough Equity Lowest interim balance reached before surpassing previous high.
Calmar Ratio Ratio Annualized Compound Return divided by absolute Max Drawdown.
verified Worked Numerical Proof

Peak Equity = $125,000 • Trough Decline = $95,000 ($30,000 drop)

arrow_forward Max Drawdown = -24.00%
trending_up

Capital Growth & Compounding

5 Models

Non-linear drawdown recovery curves, compound interest models, dividend yield reinvestment, and Monte Carlo trade sequence simulation.

#11

Drawdown Recovery (Asymmetric Gain Model)

Open Calculator open_in_new
functions Mathematical Expression
Required Gain (%) = [ 1 / ( 1 - Drawdown % ) - 1 ] × 100%

Demonstrates the exponential asymmetry of capital destruction: as drawdown depth linearly increases, the gain required to break even accelerates quadratically.

Parameter Operational Definition & Clearing Mechanics
Drawdown % (D) Percentage decline from highest capital high-water mark.
Required Gain % Geometric growth rate required purely to restore original capital balance.
verified Worked Numerical Proof

Experienced a 30% drawdown ($100k -> $70k)

arrow_forward Required Recovery Gain = +42.86% ($70k × 1.4286 = $100k)
#12

Compound Interest & Exponential Capital Growth

Open Calculator open_in_new
functions Mathematical Expression
Future Value (A) = P × ( 1 + r / n )^(n × t) + PMT × [ ( ( 1 + r / n )^(n × t) - 1 ) / ( r / n ) ]

Calculates multi-year future asset value combining initial principal compounding and periodic recurring cash inflows (PMT).

Parameter Operational Definition & Clearing Mechanics
Principal (P) Initial trading account capital balance.
Annual Rate (r) & Frequency (n) Nominal rate of return; n = 12 for monthly compounding, n = 365 for daily.
Periodic Contribution (PMT) Monthly deposits added directly to compounding capital base.
verified Worked Numerical Proof

$25,000 Initial • 15% Annualized Return • Compounded Monthly • 5 Years • $500/mo deposit

arrow_forward Future Balance = $97,839.24 (+$72,839 Total Growth)
#13

Dividend Yield & Total Cash Return

Open Calculator open_in_new
functions Mathematical Expression
Dividend Yield (%) = ( Annual Dividends Paid Per Share / Current Market Share Price ) × 100% Total Return = Capital Gains ($) + Cumulative Dividends Received ($)

Quantifies the direct cash flow yield generated by an equity position independently of market price fluctuation.

Parameter Operational Definition & Clearing Mechanics
DPS (Dividend Per Share) Gross annualized cash distributions declared per share.
Ex-Dividend Date Cut-off eligibility date required to receive the upcoming dividend.
DRIP Compounding Dividend Reinvestment Plan purchasing additional fractional shares.
verified Worked Numerical Proof

500 shares of stock @ $85.00 ($42,500 value) • Pays $3.40 DPS annually

arrow_forward Dividend Yield = 4.00% ($1,700.00 Annual Passive Cash Flow)
#14

Average Down & Tranche Cost Basis

Open Calculator open_in_new
functions Mathematical Expression
Weighted Average Price = Σ ( Quantity_i × Price_i ) / Σ Quantity_i

Calculates the volume-weighted average price (VWAP) across multiple entry tranches to determine the true breakeven exit cost basis.

Parameter Operational Definition & Clearing Mechanics
Tranche 1 (Base Entry) Initial purchase price and volume quantity.
Tranche 2 (Averaging Add) Lower/higher secondary fill price and volume quantity.
Effective Breakeven Price New aggregate baseline price required to exit at net zero.
verified Worked Numerical Proof

Tranche 1: 100 @ $120.00 ($12k) • Tranche 2: 200 @ $90.00 ($18k)

arrow_forward New Average Cost = $100.00 / share (300 Total Shares, $30,000 Invested)
#15

Monte Carlo Trade Sequence Simulation

Open Calculator open_in_new
functions Mathematical Expression
Equity(t) = Equity(t-1) × [ 1 + ( R_i × Risk_Fraction ) ] Geometric Growth Rate = ( Terminal Equity / Starting Capital )^(1/N) - 1

Simulates thousands of randomized trade sequence permutations via Monte Carlo bootstrapping to evaluate strategy robustness against streak clustering.

Parameter Operational Definition & Clearing Mechanics
R-Distribution Array of historical or probabilistic trade outcomes in R units.
Bootstrap Resampling Draws trade outcomes with replacement to simulate non-linear equity paths.
Confidence Interval 95th and 99th percentile boundaries of simulated terminal equity.
verified Worked Numerical Proof

100 Trades • 50% Win Rate • 2.0R Payoff • 10,000 Monte Carlo Paths

arrow_forward Median Expectancy = +142.5% Growth • 95% Worst-Case Drawdown = 18.4%
rule

Trade Planning & Execution

2 Models

Multi-tranche execution plans, risk/reward validation, scale-outs, and comparative strategy performance metrics.

#16

Integrated Trade Execution Planner

Open Calculator open_in_new
functions Mathematical Expression
Required Capital = Position Size × Entry Price Max Loss ($) = Position Size × |Entry - Stop| Net Target Return ($) = Position Size × |Target - Entry| - Estimated Clearing Costs

Synthesizes position sizing, multi-tranche take-profit scaling, and exchange clearing overhead into a single deterministic trade execution framework.

Parameter Operational Definition & Clearing Mechanics
Staged Scale-Outs Target 1 (1.5R, 50% exit) + Target 2 (3.0R, 50% exit).
Friction Adjustment Deducts broker commissions, statutory taxes, and bid-ask spread.
Net Expectancy True take-home realized return after all counterparty frictions.
verified Worked Numerical Proof

Long 200 shares @ $150.00 • Stop $145.00 ($1,000 Risk) • TP1 $157.50, TP2 $165.00

arrow_forward Weighted Return = +$2,250.00 (+2.25R Net Payoff)
#17

Comparative Strategy Performance Metrics

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functions Mathematical Expression
Sharpe Ratio = ( Strategy Return % - Risk Free Rate % ) / Standard Deviation of Returns % Profit Factor = Total Gross Profits ($) / Total Gross Losses ($)

Compares two competing trading strategies to evaluate which generates superior risk-adjusted alpha per unit of portfolio volatility.

Parameter Operational Definition & Clearing Mechanics
Sharpe Ratio Measures excess return per unit of total return volatility (> 1.5 is strong).
Profit Factor Ratio of winning dollars to losing dollars (> 1.75 is institutional grade).
Win-Loss Payoff Average win dollar size relative to average loss dollar size.
verified Worked Numerical Proof

Strategy A (Sharpe 1.85, PF 2.10) vs Strategy B (Sharpe 1.20, PF 1.45)

arrow_forward Strategy A delivers 54% higher risk-adjusted excess returns
account_balance

Indian Stock & Derivatives Markets (NSE/BSE)

7 Models

Full statutory friction models, SEBI peak margin frameworks, STT schedules (post-Oct 2024 hikes), and contract multiplier calculators.

#18

Indian Brokerage & Statutory Taxes (NSE/BSE)

Open Calculator open_in_new
functions Mathematical Expression
Total Friction = Brokerage + STT + Exchange Txn Charges + GST (18%) + SEBI Charges + Stamp Duty

Computes the complete, verified 6-component statutory friction schedule across Indian cash equity and derivatives transactions.

Parameter Operational Definition & Clearing Mechanics
Discount Brokerage Min(0.03%, £20) per executed order on intraday/F&O.
GST (18%) 18% applied strictly on [Brokerage + Exchange Txn Charges + SEBI Fees].
Stamp Duty State levy on buy-side turnover (0.015% delivery, 0.003% intraday).
verified Worked Numerical Proof

Intraday Buy 1,000 shares @ £500, Sell @ £505 (£1,005,000 Turnover)

arrow_forward Net Profit = £4,772.40 (Gross £5,000.00 - £227.60 Statutory Deductions)
#19

NSE/BSE Delivery (CNC) Profit Schedule

Open Calculator open_in_new
functions Mathematical Expression
Delivery STT = 0.1% on Both Buy & Sell Turnover DP Charges = £13.50 + 18% GST = £15.93 per stock sold (CDSL/NSDL debit)

Calculates cash-and-carry delivery profit accounting for CDSL/NSDL depository participant charges and both-side STT levies.

Parameter Operational Definition & Clearing Mechanics
Delivery STT 0.1% assessed on both entry value and exit value.
Depository Debit Fixed flat fee levied on sell date regardless of volume sold.
verified Worked Numerical Proof

Bought 200 shares @ £1,000, Sold @ £1,100 after 6 months

arrow_forward Net Realized Profit = £19,534.00 (Gross £20,000.00 - £466.00 Deductions)
#20

NSE Intraday (MIS) Profit & Auto-Square-off

Open Calculator open_in_new
functions Mathematical Expression
Intraday STT = 0.025% on Sell Side Only Brokerage = Min( 0.03%, £20 ) on Buy + Min( 0.03%, £20 ) on Sell

Computes same-session Margin Intraday Square-off (MIS) net returns factoring in favorable one-sided sell STT tax treatment.

Parameter Operational Definition & Clearing Mechanics
Sell-Side STT 0.025% on exit turnover only (Buy side is exempt from STT).
Exchange ETC NSE cash charge 0.00297% on roundtrip turnover.
verified Worked Numerical Proof

MIS 500 shares @ £800 Buy, £806 Sell (£803,000 Turnover)

arrow_forward Net Profit = £2,818.20 (Gross £3,000.00 - £181.80 Deductions)
#21

NSE Futures & Options (F&O) Profit Matrix

Open Calculator open_in_new
functions Mathematical Expression
Futures PnL = ( Sell Price - Buy Price ) × Lot Size × Number of Lots Options PnL = ( Exit Premium - Entry Premium ) × Lot Multiplier × Lots

Calculates leveraged derivatives gains across standardized NSE index contracts (Nifty, BankNifty, FinNifty, MidcapNifty).

Parameter Operational Definition & Clearing Mechanics
Futures STT (Oct 2024) 0.02% on sell turnover (hiked from 0.0125%).
Options STT (Oct 2024) 0.10% on option premium sell turnover (hiked from 0.0625%).
verified Worked Numerical Proof

Long 4 Lots Nifty Futures (100 Qty) @ 25,000, Sold @ 25,120 (+120 pts)

arrow_forward Net Profit = £11,392.50 (Gross £12,000.00 - £607.50 F&O Friction)
#22

Statutory Securities Transaction Tax (STT) Schedule

Open Calculator open_in_new
functions Mathematical Expression
Delivery: 0.1% Buy + 0.1% Sell Intraday: 0.025% Sell Equity Futures: 0.02% Sell (Post Oct 1, 2024) Equity Options: 0.1% on Premium Sell (Post Oct 1, 2024)

Standardized statutory tax tables issued by the Ministry of Finance, Government of India, reflecting the revised Union Budget rate hikes.

Parameter Operational Definition & Clearing Mechanics
Futures STT 0.02% applied to total nominal contract value on sell side.
Options Premium STT 0.10% applied strictly to premium turnover on sell side.
verified Worked Numerical Proof

Sold 500 Nifty Option Premiums @ £150 (£75,000 Turnover)

arrow_forward STT Due = £75.00 (0.10% of Premium Value)
#23

Nifty & BankNifty Option Lot Sizing

Open Calculator open_in_new
functions Mathematical Expression
Maximum Lots = floor( ( Capital × Risk % ) / ( Invalidation Points × Lot Multiplier ) )

Computes safe, non-fractional lot quantity sizing for Indian index derivatives to prevent over-allocation during volatility spikes.

Parameter Operational Definition & Clearing Mechanics
Nifty 50 Lot Size 25 shares per standardized contract.
BankNifty Lot Size 15 shares per standardized contract.
Points Risk Stop-loss distance measured in index premium points.
verified Worked Numerical Proof

£500,000 Capital • 1% Risk (£5,000) • Stop Distance = 20 pts Nifty (25 Lot Size)

arrow_forward Safe Size = 10 Lots (250 Units • £5,000 Exact Defined Risk)
#24

NSE Derivatives Margin Requirement (SPAN + Exposure)

Open Calculator open_in_new
functions Mathematical Expression
Total Margin Requirement = SPAN Margin (99% VaR) + Exposure Margin Exposure Margin = Contract Value × Exposure % (typically 3% index, 5% stock)

Computes clearinghouse initial margin requirements for writing options and holding futures under SEBI Peak Margin guidelines.

Parameter Operational Definition & Clearing Mechanics
SPAN Margin Standard Portfolio Analysis of Risk evaluating worst-case loss across 16 scenarios.
Exposure Margin Fixed percentage buffer against intra-day tail price shocks.
Hedging Benefit Up to 70% margin reduction when legs are paired into defined-risk spreads.
verified Worked Numerical Proof

Nifty Short Call 25,000: SPAN £85,000 + Exposure £18,750

arrow_forward Total Upfront Margin Required = £103,750.00 / lot
receipt_long

US Equities & Options (NYSE/NASDAQ)

6 Models

SEC Section 31 fees, FINRA TAF, short vs. long term capital gains tax brackets, and Black-Scholes Greeks sensitivities.

#25

US Stock Profit with SEC & FINRA Statutory Fees

Open Calculator open_in_new
functions Mathematical Expression
Net Profit = Gross Capital Gain - Commission - SEC Section 31 Fee - FINRA TAF SEC Fee = Sell Turnover × $27.80 / $1,000,000 FINRA TAF = min( $8.30, Shares Sold × $0.000166 )

Models the complete US equity transaction fee schedule governing NYSE, NASDAQ, and OTC executions.

Parameter Operational Definition & Clearing Mechanics
SEC Section 31 Statutory transaction fee assessed on all equity sell executions.
FINRA TAF Trading Activity Fee levied by FINRA to fund market surveillance.
verified Worked Numerical Proof

Sell 2,000 shares @ $150.00 ($300,000 Proceeds)

arrow_forward SEC Fee = $8.34 • FINRA TAF = $0.33 • Total Fees = $8.67
#26

US Capital Gains Tax (STCG vs LTCG + NIIT)

Open Calculator open_in_new
functions Mathematical Expression
Short-Term (< 1 Year) = Net Gain × Ordinary Federal Income Tax Bracket (up to 37%) Long-Term (≥ 1 Year) = Net Gain × Preferential Rate (0%, 15%, or 20%) + NIIT (3.8% if applicable)

Computes federal tax liabilities comparing short-term trading against long-term holding brackets under IRS rules.

Parameter Operational Definition & Clearing Mechanics
Net Investment Income Tax (NIIT) 3.8% surtax on investment income above $200k (Single) / $250k (Married).
Wash-Sale Rule Losses disallowed if substantially identical security repurchased within 30 days.
verified Worked Numerical Proof

$50,000 Capital Gain (High Income Bracket): Short-Term @ 37% vs Long-Term @ 20% + 3.8%

arrow_forward Short-Term Tax = $18,500.00 vs Long-Term Tax = $11,900.00 (Savings = $6,600.00)
#27

US Equity Position Size with Fractional Shares

Open Calculator open_in_new
functions Mathematical Expression
Fractional Shares = ( Account Balance × Risk % ) / |Entry Price - Stop Loss Price|

Computes decimal share allocations supported by modern US brokers, ensuring exact dollar-risk parity on high-priced equities.

Parameter Operational Definition & Clearing Mechanics
Fractional Accuracy Sizes positions down to 0.0001 shares.
Buying Power Check Verifies position nominal value does not breach Regulation T margin limits.
verified Worked Numerical Proof

$10,000 Account • 1.5% Risk ($150) • Entry $480.00 • Stop $465.00 ($15.00 Risk)

arrow_forward Order Size = 10.0000 Shares ($4,800.00 Position Notional)
#28

US Options Profit & Expiration Settlement

Open Calculator open_in_new
functions Mathematical Expression
Call Net PnL = [ max( 0, Stock Price - Strike Price ) - Premium Paid ] × 100 × Contracts Put Net PnL = [ max( 0, Strike Price - Stock Price ) - Premium Paid ] × 100 × Contracts

Evaluates long and short option contract payoffs incorporating standard US 100-share multipliers and OCC clearing exercises.

Parameter Operational Definition & Clearing Mechanics
100-Share Multiplier Each standard US option controls exactly 100 shares of underlying equity.
Intrinsic Value Realizable value if exercised immediately at market price.
verified Worked Numerical Proof

Long 5 Call Contracts @ $4.50 Premium ($2,250 Paid) • Strike $150.00 • Stock reaches $162.00

arrow_forward Net Profit = +$3,750.00 (+166.7% Return On Capital)
#29

US Options Breakeven Price Matrix

Open Calculator open_in_new
functions Mathematical Expression
Long Call Breakeven = Strike Price + Net Premium Paid Long Put Breakeven = Strike Price - Net Premium Paid Covered Call Breakeven = Stock Purchase Price - Premium Received

Identifies the terminal stock prices at expiration required for an option structure to break even after paying contract premiums.

Parameter Operational Definition & Clearing Mechanics
Premium Drag Underlying must move sufficiently beyond strike to offset upfront debit paid.
Extrinsic Value Zero At expiration, extrinsic time value decays to zero; only intrinsic remains.
verified Worked Numerical Proof

Buy $180 Call @ $6.20 Premium

arrow_forward Breakeven Stock Price = $186.20 at Expiration
#30

US Options Greeks Sensitivity Engine

Open Calculator open_in_new
functions Mathematical Expression
d1 = [ ln(S / K) + ( r + &sigma;^2 / 2 ) × T ] / ( &sigma; × &radic;T ) d2 = d1 - &sigma; × &radic;T Delta = N(d1) | Gamma = N'(d1) / ( S × &sigma; × &radic;T ) | Vega = S × &radic;T × N'(d1)

Closed-form Black-Scholes equations estimating option price changes relative to stock moves, volatility shifts, and time decay.

Parameter Operational Definition & Clearing Mechanics
Delta (&Delta;) Price change per $1.00 move in underlying.
Theta (&Theta;) Theoretical points lost per calendar day of time decay.
Vega (&nu;) Price change per 1.0% shift in Implied Volatility.
verified Worked Numerical Proof

Stock $100 • Strike $100 • 30 DTE • IV 25% • Risk-Free 5.0%

arrow_forward Delta = 0.536 • Gamma = 0.055 • Theta = -$0.048/day • Vega = $0.114
currency_bitcoin

Crypto Perpetual Futures & Leverage

9 Models

Cross vs. isolated margin mechanics, 8-hour funding rates, grid trading arbitrage, and automated liquidation price triggers.

#31

Crypto Breakeven with Maker/Taker Fees

Open Calculator open_in_new
functions Mathematical Expression
Breakeven Price (Long) = Entry Price × [ ( 1 + Fee_Entry ) / ( 1 - Fee_Exit ) ] Breakeven Price (Short) = Entry Price × [ ( 1 - Fee_Entry ) / ( 1 + Fee_Exit ) ]

Calculates exact price movement required to cover exchange trading fees across maker limit orders and taker market fills.

Parameter Operational Definition & Clearing Mechanics
Taker Fee Typical 0.05% - 0.06% charged on aggressive market orders.
Maker Fee Discounted 0.02% charged on passive limit orders providing book liquidity.
verified Worked Numerical Proof

Bitcoin Long @ $60,000 • Taker Open (0.05%) • Maker Close (0.02%)

arrow_forward Breakeven Exit = $60,042.01 (+$42.01 needed to cover fees)
#32

Crypto Dollar-Cost Averaging (DCA)

Open Calculator open_in_new
functions Mathematical Expression
Average Cost Per Coin = Total Fiat Invested ($) / Total Coins Accumulated Harmonic Mean = N / &Sigma; ( 1 / Price_i )

Models scheduled recurring crypto purchases, mathematically demonstrating how fixed-fiat DCA lowers effective purchase cost below arithmetic mean.

Parameter Operational Definition & Clearing Mechanics
Total Invested Cumulative currency deployed across all scheduled DCA intervals.
Harmonic Advantage Buys more units when price dips and fewer units when price rallies.
verified Worked Numerical Proof

4 weekly buys of $250 BTC @ $65k, $58k, $52k, $60k ($1,000 total)

arrow_forward Average Cost = $58,074.88 (0.017219 BTC Accumulated)
#33

Crypto Perpetual Funding Fee & Basis Arbitrage

Open Calculator open_in_new
functions Mathematical Expression
Funding Payment ($) = Position Notional Value ($) × Funding Rate % Annualized Yield (APR) = Funding Rate % × 3 cycles/day × 365 days

Calculates 8-hour cash transfers exchanged between long and short contract holders to anchor perpetual prices to spot indices.

Parameter Operational Definition & Clearing Mechanics
Positive Funding Rate Longs pay shorts (market is bullish/leveraged long).
Negative Funding Rate Shorts pay longs (market is bearish/leveraged short).
Cash & Carry Arbitrage Long spot + short perps to harvest risk-free funding yield.
verified Worked Numerical Proof

$100,000 Notional Short Perps • Funding Rate = +0.03% per 8hr cycle

arrow_forward Earns $30.00 / 8 hours ($90.00 / day • 32.85% Annualized APR)
#34

Crypto Grid Trading Bot Profit Matrix

Open Calculator open_in_new
functions Mathematical Expression
Arithmetic Grid Spacing = ( Price_Upper - Price_Lower ) / Grid_Count Profit Per Grid = ( Grid Spacing / Current Price - 2 × Fee ) × Quantity Per Grid

Simulates automated quantitative market-making bots placing laddered limit orders within a defined horizontal consolidation channel.

Parameter Operational Definition & Clearing Mechanics
Grid Density Number of buy/sell order rungs spaced across boundary channel.
Roundtrip Harvest Captures spread each time price oscillates across neighboring rungs.
verified Worked Numerical Proof

ETH Range $2,800 to $3,600 • 40 Grids ($20 Spacing) • $10,000 Capital

arrow_forward Expected Profit = 0.58% net per matched roundtrip execution
#35

Crypto Initial & Maintenance Margin

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functions Mathematical Expression
Initial Margin Requirement (IMR) = Position Notional Value / Leverage Maintenance Margin Requirement (MMR) = Position Notional Value × MMR Tier %

Computes capital collateral necessary to initiate and sustain leveraged crypto derivatives positions across exchange tier brackets.

Parameter Operational Definition & Clearing Mechanics
Initial Margin Upfront collateral locked upon order placement (e.g. 10% on 10x).
Maintenance Margin Minimum equity buffer required before liquidation engine triggers (e.g. 0.5%).
verified Worked Numerical Proof

$50,000 Notional Position • 20x Leverage • 0.5% MMR

arrow_forward Initial Margin = $2,500.00 • Maintenance Margin Threshold = $250.00
#36

Crypto Futures PnL & Return on Equity (ROE)

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functions Mathematical Expression
Unrealized PnL (Long) = Quantity × ( Mark Price - Entry Price ) ROE (%) = ( PnL / Initial Margin ) × 100% = Price Change % × Leverage

Calculates leveraged percentage return on collateral equity versus absolute dollar profit on contracts.

Parameter Operational Definition & Clearing Mechanics
Mark Price Fair index price preventing market manipulation liquidations.
ROE Multiplier A 2% price move with 25x leverage generates +50% ROE.
verified Worked Numerical Proof

Entry $3,000 ETH • Exit $3,150 (+5%) • 10x Leverage ($1,000 Margin)

arrow_forward Net PnL = +$500.00 • ROE = +50.00%
#37

Crypto Contract Position Sizing

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functions Mathematical Expression
Position Quantity = ( Account Capital × Risk % ) / |Entry Price - Stop Loss Price| Required Collateral Margin = ( Position Quantity × Entry Price ) / Leverage

Sizes leveraged crypto contracts so that stopping out loses strictly the intended dollar risk budget regardless of leverage magnitude.

Parameter Operational Definition & Clearing Mechanics
Leverage Decoupling Leverage controls capital efficiency; Stop distance controls true risk.
Liquidation Safety Buffer Ensures liquidation price sits safely beyond stop loss.
verified Worked Numerical Proof

$20,000 Equity • 2% Risk ($400) • SOL Entry $150.00 • Stop $145.00 ($5 Risk) • 10x Leverage

arrow_forward Position = 80 SOL ($12,000 Notional) • Margin Allocated = $1,200
#38

Crypto Liquidation Price (Isolated & Cross)

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functions Mathematical Expression
Isolated Long Liq = Entry Price × [ 1 - ( 1 / Leverage ) + MMR ] Isolated Short Liq = Entry Price × [ 1 + ( 1 / Leverage ) - MMR ]

Determines the catastrophic price boundary where collateral is completely depleted, triggering automated exchange liquidation.

Parameter Operational Definition & Clearing Mechanics
Isolated Mode Loss strictly limited to allocated position margin.
Cross Mode Liquidation threshold floats dynamically based on total free wallet equity.
verified Worked Numerical Proof

Long BTC @ $60,000 • 20x Leverage • 0.5% Maintenance Margin

arrow_forward Liquidation Price = $57,300.00 (-4.50% from entry)
#39

Effective Leverage vs Nominal Exposure

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functions Mathematical Expression
Effective Leverage = Total Open Notional Exposure ($) / Total Net Account Equity ($) Margin Ratio (%) = ( Total Maintenance Margin / Equity ) × 100%

Differentiates exchange account leverage setting from true operational portfolio leverage.

Parameter Operational Definition & Clearing Mechanics
Effective Leverage True portfolio risk exposure ratio (> 5x carries extreme ruin vulnerability).
Margin Call Threshold Point where exchange prohibits opening new positions.
verified Worked Numerical Proof

$10,000 Equity holding $45,000 total notional positions

arrow_forward Effective Leverage = 4.50x
show_chart

Options Strategies & Complex Greeks

2 Models

Multi-leg synthetic payoff envelopes (Iron Condors, Straddles) and Black-Scholes Greeks adjusted for continuous index dividend yield.

#40

Multi-Leg Synthetic Strategy Payoff

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functions Mathematical Expression
Net Terminal Payoff = &Sigma; [ Quantity_j × ( Payoff_j(S_T, K_j) - Net_Debit_or_Credit_j ) ]

Computes net expiration payoffs for complex multi-leg options combinations including Straddles, Strangles, Iron Condors, and Butterflies.

Parameter Operational Definition & Clearing Mechanics
Breakeven Envelope Lower and upper underlying price bounds yielding zero net profit.
Capped Risk Defined maximum loss on vertical debit or credit spreads.
verified Worked Numerical Proof

Iron Condor: Sell 100P/110C, Buy 95P/115C • Net Credit Received = $2.20

arrow_forward Max Profit = +$220.00 • Max Loss = -$280.00 • Breakevens = $97.80 & $112.20
#41

NSE Options Greeks with Continuous Dividend Yield

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functions Mathematical Expression
Delta (Call) = e^(-qT) × N(d1) Delta (Put) = e^(-qT) × [ N(d1) - 1 ] where q = Continuous dividend yield percentage (e.g. 1.2% for Nifty 50)

Merton extended Black-Scholes framework tailored for index options where the underlying index pays continuous dividends.

Parameter Operational Definition & Clearing Mechanics
Dividend Yield Adjustment (q) Accounts for dividend leakage dampening long call theoretical pricing.
Early Exercise Boundary Identifies optimal early exercise conditions for American options.
verified Worked Numerical Proof

Nifty 50 Index 25,000 • Strike 25,000 • 15 DTE • IV 14% • r = 6.5% • q = 1.2%

arrow_forward Adjusted Call Delta = 0.518 • Put Delta = -0.481
verified

Audited Mathematical Rigor & Statutory Accuracy

Every formula on CalcTrading adheres strictly to the regulatory clearing handbooks of the CME Group, Chicago Board Options Exchange (CBOE), Securities and Exchange Board of India (SEBI), and the Financial Industry Regulatory Authority (FINRA).

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