Strategy Calculation Formulas

Mathematical reference for funding rate arbitrage calculations, position sizing, and profitability analysis

Table of Contents

• Funding Rate Arbitrage
• Expected Value (EV) Calculation
• Position Sizing
• Fee Calculations
• Profit & Loss
• Risk Metrics
• Configuration Reference

Funding Rate Arbitrage

Core Concept

Funding rate arbitrage exploits differences in funding rates across exchanges while maintaining delta-neutral positions.

Funding Rate Spread

$$\text{spread}=|{\text{rate}}_{\text{short}}-{\text{rate}}_{\text{long}}|$$

Where:

• rate_short = funding rate on high-rate exchange (short position)
• rate_long = funding rate on low-rate exchange (long position)

Example:

Binance BTCUSDT: +0.0001 (1 basis point)
HyperLiquid BTCUSDT: +0.0006 (6 basis points)

spread = |0.0006 - 0.0001| = 0.0005 = 5 basis points = 0.05%

Annual Percentage Yield (APY)

$$\text{APY}=\text{spread}\times \text{funding\_intervals\_per\_year}$$

Where:

• funding_intervals_per_year depends on exchange funding frequency
• Spread is expressed as a decimal (e.g., 0.0005)

APY by Exchange Interval:

Example (8-hour interval):

spread = 0.0005 (5 basis points)
APY = 0.0005 × 1,095 = 0.5475 = 54.75%

Example (1-hour interval - HyperLiquid):

spread = 0.0001 (1 basis point per hour)
APY = 0.0001 × 8,760 = 0.876 = 87.6%

Expected Value (EV) Calculation

The bot uses risk-adjusted expected value to filter opportunities and ensure trades are profitable after all costs.

Funding Intervals by Exchange

*Bybit and Aster funding intervals vary by symbol. The bot automatically fetches per-symbol intervals via REST API at startup (refreshed every 4h) and from WebSocket streams in real-time.

Cross-Exchange Yield Normalization

When trading across exchanges with different funding intervals (e.g., HyperLiquid + Binance), the bot normalizes yields to a common 8-hour reference period. This is important because HyperLiquid pays funding 8x more frequently than Binance/Bybit.

How It Works:

Key Benefit: A 9 bps simple spread becomes 79 bps normalized yield when HyperLiquid's 8x payment frequency is properly accounted for.

Time Weighting

$$\text{time\_weight}=\min \left(\frac{\text{minutes\_to\_funding}}{\text{min\_interval}},1\right)$$

Where:

• min_interval = minimum of both exchange intervals (determines next funding)
• Weight approaches 1 as funding time approaches
• Weight approaches 0 immediately after funding

Gross Expected Value

$$\text{gross\_ev}=\text{normalized\_spread}\times \text{time\_weight}$$

Transaction Costs

$$\text{costs}={\text{fee}}_{\text{long\_entry}}+{\text{fee}}_{\text{long\_exit}}+{\text{fee}}_{\text{short\_entry}}+{\text{fee}}_{\text{short\_exit}}+\text{slippage}$$

For limit orders (maker fees): $$\text{costs}=2\times ({\text{maker}}_{\text{long}}+{\text{maker}}_{\text{short}})$$

For market orders (taker fees + slippage): $$\text{costs}=2\times ({\text{taker}}_{\text{long}}+{\text{taker}}_{\text{short}})+\text{slippage\_estimate}$$

Staleness Haircut

$$\text{staleness}=\{\begin{array}{ll}\text{haircut}& \text{if data age}>4\text{ minutes}\\ 0& \text{otherwise}\end{array}$$

Default: haircut = 0.03 (3 basis points = 0.03%)

Adjusted Expected Value

$$\text{adjusted\_ev}=\text{gross\_ev}-\text{costs}-\text{staleness}$$

Qualification Criteria

An opportunity qualifies if:

$$\text{adjusted\_ev}\ge \text{min\_ev\_bps}\text{AND}\text{spread}\ge \text{min\_spread\_threshold}$$

Default thresholds (percentage form):

• min_ev_bps = 0.05 (5 basis points = 0.05%)
• min_spread_threshold = 0.04 (4 basis points = 0.04%)

Complete EV Example

Scenario:

• Binance BTCUSDT: +0.01% (long position, 8h interval)
• HyperLiquid BTCUSDT: +0.10% (short position, 1h interval)
• Time to funding: 60 minutes (HyperLiquid's next funding)
• Order type: Limit (maker fees)

Step 1: Calculate normalized spread

Long Binance: -0.01% × (480/480) = -0.01% (pay 1 payment)
Short HyperLiquid: +0.10% × (480/60) = +0.80% (receive 8 payments)
Normalized spread = -0.01% + 0.80% = +0.79% (79 bps)

Step 2: Time weighting (using minimum interval = 60 min) $$\text{time\_weight}=\frac{60}{60}=1.0$$

Step 3: Gross EV $$\text{gross\_ev}=0.79\%\times 1.0=0.79\%=79\text{ bps}$$

Step 4: Calculate costs

Binance fees: 0.02% maker (entry) + 0.02% maker (exit) = 0.04%
HyperLiquid fees: 0.0144% maker (entry) + 0.0144% maker (exit) = 0.0288%
Total costs: ~7 bps

Step 5: Staleness haircut

Data age: < 4 minutes
Staleness: 0

Step 6: Adjusted EV $$\text{adjusted\_ev}=79-7-0=72\text{ bps}$$

Step 7: Qualification check

adjusted_ev (72 bps) >= min_ev (5 bps) ✅
raw_spread (9 bps) >= min_spread (4 bps) ✅

Result: QUALIFIES

Expected profit per $10,000 position (over 8h reference): $$\text{profit}=\$10,000\times 0.0072=\$72$$

Note: The normalized EV (72 bps after costs) is much higher than what you'd calculate from the simple 9 bps spread because HyperLiquid pays funding 8 times per Binance cycle.

Position Sizing

Conservative Sizing Formula

The bot reserves margin for both opening AND closing positions:

$$\text{position\_size}=\left(\frac{\text{balance}\times \text{percentage}}{2}\right)\times \text{leverage}$$

Where:

• balance = available balance on exchange (USDT)
• percentage = position size percentage (default: 0.30 = 30%)
• leverage = configured leverage (default: 10x)
• Division by 2 reserves margin for closing

Example:

balance = $1,000 USDT
percentage = 0.30 (30%)
leverage = 10x

position_size = (1,000 × 0.30 / 2) × 10
              = (300 / 2) × 10
              = 150 × 10
              = $1,500 USD notional

Quantity Calculation

$$\text{quantity}=\frac{\text{position\_size}}{\text{price}}$$

Must be rounded to exchange precision:

$$\text{quantity\_rounded}=\lfloor \frac{\text{quantity}}{10^{-\text{precision}}}\rfloor \times 10^{-\text{precision}}$$

Example:

position_size = $1,500
BTC price = $50,000
precision = 3 decimals (0.001 BTC minimum)

quantity = 1,500 / 50,000 = 0.030 BTC
quantity_rounded = floor(0.030 / 0.001) × 0.001 = 0.030 BTC ✅

Kelly Criterion Sizing

The bot supports two position sizing modes:

Mode 1: Kelly Criterion (Dynamic)

Enabled when use_kelly_criterion = true (default). Sizes positions based on expected value and variance:

$$\text{kelly\_fraction}=\frac{\text{EV}}{\text{variance}}$$

$$\text{raw\_kelly\_size}=\text{kelly\_fraction}\times \text{reference\_capital}\times \text{leverage}$$

With safety caps:

$$\text{final\_size}=\min \left(\text{raw\_kelly\_size}\times \text{kelly\_cap},\text{max\_notional},\text{balance}\times \text{max\_utilization}\right)$$

Where:

• kelly_cap = 0.25 (quarter-Kelly, default)
• max_notional = $10,000 (per-symbol cap, default)
• max_utilization = 0.50 (50% of balance, default)

Use when: You want dynamic sizing that increases with edge quality and decreases with variance.

Mode 2: Fixed Percentage (Simple)

Enabled when use_kelly_criterion = false. Uses fixed percentage of available capital:

$$\text{reference\_capital}=\min (\text{long\_balance},\text{short\_balance})$$

$$\text{fixed\_size}=\text{reference\_capital}\times \text{max\_utilization}\times \text{leverage}$$

With safety cap:

$$\text{final\_size}=\min (\text{fixed\_size},\text{max\_notional})$$

Use when: You want predictable, consistent position sizing regardless of opportunity quality.

Configuration:

[trading]
use_kelly_criterion = true    # Toggle between Kelly and fixed modes
kelly_fraction = 0.25          # Only used in Kelly mode
max_exchange_utilization = 0.5 # Used in both modes
max_notional_per_symbol = 10000 # Hard cap for both modes

Fee Calculations

Exchange Fee Structure

*Bybit and Aster funding intervals vary per symbol (4h or 8h), fetched dynamically via API and WebSocket **HyperLiquid has 24 funding payments per day (hourly)

Order Fee Calculation

$$\text{fee}=\text{notional\_value}\times \text{fee\_rate}$$

$$\text{notional\_value}=\text{quantity}\times \text{price}$$

Example:

quantity = 0.1 BTC
price = $50,000
fee_rate = 0.0004 (0.04% taker)

notional = 0.1 × 50,000 = $5,000
fee = 5,000 × 0.0004 = $2.00

Round-Trip Cost

For entering and exiting a position:

$$\text{round\_trip\_cost}=2\times ({\text{fee}}_{\text{long}}+{\text{fee}}_{\text{short}})+\text{slippage}$$

Example (limit orders):

Binance maker: 0.02%
HyperLiquid maker: 0.00%

Entry cost: (0.0002 + 0.0000) = 0.0002 = 0.02%
Exit cost: (0.0002 + 0.0000) = 0.0002 = 0.02%
Total: 0.0004 = 0.04% = 4 basis points

On $10,000 position: $10,000 × 0.0004 = $4.00

Breakeven Spread

Minimum spread needed to be profitable:

$$\text{breakeven\_spread}=\frac{\text{round\_trip\_cost}}{\text{holding\_periods}}$$

Example (3 funding periods = 24 hours):

round_trip_cost = 0.0004 (4 bps)
holding_periods = 3

breakeven = 0.0004 / 3 = 0.000133 = 1.33 bps per period

Profit & Loss

Funding Payment Calculation

$$\text{funding\_payment}=\text{position\_size}\times \text{funding\_rate}$$

For long position:

• Positive rate: pay funding
• Negative rate: receive funding

For short position:

• Positive rate: receive funding
• Negative rate: pay funding

Arbitrage Profit Per Period

$$\text{profit}=\text{position\_size}\times ({\text{rate}}_{\text{short}}-{\text{rate}}_{\text{long}})$$

Example:

position_size = $10,000
Binance rate (long): +0.0001
HyperLiquid rate (short): +0.0006

profit = 10,000 × (0.0006 - 0.0001)
       = 10,000 × 0.0005
       = $5.00 per funding period

Net Profit After Fees

$$\text{net\_profit}=\text{gross\_profit}-\text{entry\_fees}-\text{exit\_fees}$$

Example:

gross_profit = $5.00 per period × 3 periods = $15.00
entry_fees = $4.00
exit_fees = $4.00

net_profit = 15.00 - 4.00 - 4.00 = $7.00 per day
monthly = $7.00 × 30 = $210.00

Return on Capital

$$\text{ROC}=\frac{\text{net\_profit}}{\text{margin\_used}}$$

$$\text{margin\_used}=\frac{\text{position\_size}}{\text{leverage}}$$

Example:

position_size = $10,000
leverage = 10x
margin_used = 10,000 / 10 = $1,000

daily_profit = $7.00
daily_ROC = 7.00 / 1,000 = 0.007 = 0.7%
annual_ROC = 0.007 × 365 = 2.555 = 255.5%

ROI (Return on Investment)

The ROI displayed in the TUI is calculated as:

$$\text{ROI}=\frac{\text{funding\_collected}-\text{trading\_fees}}{\text{position\_size}}\times 100\%$$

Where:

• funding_collected = total funding payments received since position opened
• trading_fees = trading fees for both legs (entry + exit). Note: as of now, the fee tracker only captures entry fees; exit fees are included in the formula but are effectively $0 until exit-fee tracking is implemented.
• position_size = notional value of the position

ROI Display States:

Fee Estimation Fallback:

When exchange API calls fail or timeout (2 minutes), fees are estimated: $$\text{estimated\_fees}=\text{position\_size}\times 0.0005\times 2$$

This uses a default taker fee rate of 0.05% (5 basis points) per leg.

Example:

position_size = $1,000
funding_collected = $5.00
entry_fee_long = $0.50
entry_fee_short = $0.35

ROI = (5.00 - 0.50 - 0.35) / 1,000 × 100%
    = 4.15 / 1,000 × 100%
    = 0.415%

Unrealized P&L (Price Spread)

Added in v0.58: The TUI and metrics now display unrealized P&L from price spread movements, not just funding collected.

While funding rate arbitrage is theoretically delta-neutral, price divergence between exchanges creates real P&L that must be tracked. This is especially important when exchanges have different liquidity or when prices move during entry/exit.

Formula:

$$\text{unrealized\_price\_pnl}=\text{long\_leg\_pnl}+\text{short\_leg\_pnl}$$

Where:

$$\text{long\_leg\_pnl}=(\text{current\_price}-\text{long\_entry\_price})\times \text{quantity}$$

$$\text{short\_leg\_pnl}=(\text{short\_entry\_price}-\text{current\_price})\times \text{quantity}$$

Example (Spread Reversal - Loss):

# Position entered with 0.1 BTC
long_entry_price = $40,000 (Binance)
short_entry_price = $40,000 (Aster)
current_price = $40,100 (price moved up)

long_leg_pnl  = (40,100 - 40,000) × 0.1 = +$10.00 (profit)
short_leg_pnl = (40,000 - 40,100) × 0.1 = -$10.00 (loss)

# In theory, should net to $0 if hedged properly
# But with slippage or different prices on each exchange:

long_entry_price = $40,000 (Binance)
short_entry_price = $39,950 (Aster - worse fill)
current_price = $40,100

long_leg_pnl  = (40,100 - 40,000) × 0.1 = +$10.00
short_leg_pnl = (39,950 - 40,100) × 0.1 = -$15.00
total_price_pnl = 10.00 - 15.00 = -$5.00 (loss from spread)

Total Unrealized P&L:

$$\text{total\_unrealized\_pnl}=\text{funding\_collected}+\text{price\_spread\_pnl}$$

Important: A position can show positive funding collected but still be losing money overall if the price spread moved against you.

Risk Metrics

Maximum Position Size

$$\text{max\_size}=\min \left(\text{config\_max},\frac{\text{balance}\times \text{utilization}}{\text{margin\_rate}}\right)$$

Where:

• config_max = $10,000 (default per-symbol cap)
• utilization = 0.50 (50% of balance usage)
• margin_rate = 1 / leverage

Example:

balance = $5,000
utilization = 0.50
leverage = 10x
margin_rate = 0.1

balance_limit = (5,000 × 0.50) / 0.1 = 25,000
max_size = min(10,000, 25,000) = $10,000

Margin Requirement

$$\text{margin\_required}=\frac{\text{position\_size}}{\text{leverage}}\times 1.2$$

The 1.2 factor provides a 20% safety buffer.

Example:

position_size = $10,000
leverage = 10x

margin = (10,000 / 10) × 1.2 = 1,000 × 1.2 = $1,200

Liquidation Distance

$$\text{liq\_distance}=\frac{\text{margin}-\text{maintenance\_margin}}{\text{position\_size}}$$

Example:

margin = $1,000
maintenance = $100 (10% of margin)
position_size = $10,000

liq_distance = (1,000 - 100) / 10,000 = 0.09 = 9%

Position liquidates at 9% adverse price move

Sharpe Ratio

$$\text{Sharpe}=\frac{\text{mean\_return}-\text{risk\_free\_rate}}{\text{std\_deviation}}$$

Calculated over historical trades for strategy performance evaluation.

Maximum Drawdown

$$\text{max\_drawdown}=\max \left(\frac{\text{peak\_equity}-\text{current\_equity}}{\text{peak\_equity}}\right)$$

Tracks the largest peak-to-trough decline in account equity.

Configuration Reference

Default Values

Exchange Fee Rates

Example Configuration

[trading]
# Spread thresholds
min_funding_spread = 0.04        # 4 basis points
min_ev_bps = 0.05                # 5 basis points

# Position sizing
position_size_percent = 0.30       # 30% of balance
max_position_usd = 10000           # $10,000 cap
leverage = 10                      # 10x leverage

# Kelly criterion settings
use_kelly_criterion = true
kelly_fraction = 0.25              # Quarter-Kelly
max_exchange_utilization = 0.50    # 50% max usage

[risk]
# Slippage
max_slippage_bps = 50              # 0.5% maximum
estimated_slippage = 0.001         # 0.1% estimate

Quick Reference Card

Profit Estimation

APY by Spread

Minimum Capital Requirements

See Also

• Trading Strategy - Strategy overview and concepts
• Configuration Guide - Detailed parameter reference
• Getting Started - Initial setup
• Monitoring Guide - Track your positions

Note: All formulas use decimal representation (e.g., 0.0005 = 5 basis points = 0.05%). The bot maintains high precision using Rust's Decimal type (96-bit precision) for all calculations.