Thorp Kelly Risk Engine [JOAT]Thorp Kelly Risk Engine
Introduction
Thorp Kelly Risk Engine is a risk-quality study that tracks virtual outcomes, Kelly estimates, Bayesian shrinkage, drawdown pressure, survival score, and deployment state.
This open-source indicator is designed as a context tool, not a standalone trading system. It focuses on explaining the current market state with restrained visuals and confirmed-bar logic where signals are used.
Core Concepts
1. Virtual Outcome Tracker
Trend setups create virtual reward/risk outcomes measured in ATR units.
2. Kelly Estimate
Win rate and payoff ratio produce full and fractional Kelly-style estimates.
3. Bayesian Shrinkage
A prior win rate reduces overconfidence when sample size is small.
4. Survival and Desk Score
Drawdown, volatility, signal density, convexity, and uncertainty combine into risk state.
kelly = (payoff * winRate - lossRate) / payoff
Features
Virtual outcome sampling
Fractional and Bayesian Kelly estimates
Drawdown throttle and volatility brake
Ruin-adjusted Kelly
Prime, defense, and lockdown states
Input Parameters
Trend, RSI, and ATR lengths
Reward and risk ATR
Kelly fraction and max allocation
Minimum sample and drawdown brake
Display toggles and HUD position
How to Use This Script
Use TKR as risk context. Prime states suggest healthier virtual samples; defensive and lockdown states warn that model risk is elevated.
Limitations
The script uses historical OHLCV data and cannot know future prices.
Signals and states can be late during fast reversals because confirmed-bar logic is used to reduce repainting.
Model outputs should be interpreted with market context, risk controls, and independent analysis.
No visual state should be treated as a certain trade outcome.
Originality Statement
TKR is original in combining Kelly math, Bayesian shrinkage, drawdown throttling, survival scoring, and uncertainty cones.
Disclaimer
This indicator is provided for educational and informational purposes only. It is not financial advice, investment advice, or a recommendation to buy or sell any financial instrument. All calculations are derived from historical market data and may produce inaccurate readings in some market conditions. No indicator can predict future market behavior. Use proper risk management and independent judgment.
-Made with passion by jackofalltrades
Indicator
Volatility Managed Kelly LeverageThe Volatility Managed Kelly Leverage (VMKL) indicator is a tool that dynamically adjusts position sizing based on forecasted market volatility. It helps you to optimize leverage exposure by systematically reducing risk during high volatility periods and increasing exposure when markets are calm.
VMKL adapts in real-time to changing market conditions, potentially generating alpha while smoothing volatility and reducing maximum drawdown.
This indicator implements the Optimal Volatility Plus Mean Strategy (OVPMS) from one of my favorite leverage papers:
" Alpha Generation and Risk Smoothing using Managed Volatility " by Tony Cooper (2010)
These are the key findings from the paper, which this indicator translates to real life:
Volatility is predictable while returns are not
Dynamic leverage based on volatility forecasts can generate significant excess returns
The strategy reduces volatility of volatility (vovo), kurtosis, and maximum drawdown
Tested on 125+ years of market data across multiple global indices
The OVPMS strategy (translated into this indicator) returned 12.6% annual return vs 7.0% for buy-and-hold, with the same volatility as the underlying index. Outstanding.
The indicator calculates optimal leverage using a three-step process
1. Volatility Forecasting
Uses Exponential Weighted Moving Average (EWMA):
σ²(t) = λ·σ²(t-1) + (1-λ)·r²(t-1)
This predicts next-day volatility from recent price movements
2. Return Prediction
Expected Return = a × σ^(b+1)
Where:
a = Power coefficient (baseline return, default: 0.10)
b = Power exponent (return-volatility relationship, default: -1.76 for SPY)
σ = Forecasted volatility
The negative exponent means returns decrease as volatility increases - a well-documented market behaviour.
3. Optimal Leverage Calculation
Full Kelly Leverage = μ / σ²
Actual Leverage = Full Kelly × Kelly Fraction × Caps × Smoothing
The Kelly Criterion provides the theoretically optimal leverage, which is then reduced via:
Kelly Fraction: Safety margin (default 75% = three-quarter Kelly)
Leverage Caps: Hard maximum and minimum limits
Smoothing: SMA to reduce rebalancing frequency
The Core Insight: Volatility varies over time (volatility of volatility), and this variation is costly. By targeting consistent volatility through dynamic leverage:
Reduces volatility drag - Compounding works better with stable volatility
Reduces drawdowns - Automatically deleverages before crashes
Reduces kurtosis - Fewer extreme return events
Generates alpha - Exploits the return-volatility relationship
The indicator calculates optimal leverage in real-time using EWMA volatility forecasting and Kelly Criterion mathematics, automatically detecting market regimes from CASH to VERY AGGRESSIVE and respective leverages. The statistics table shows Full Kelly leverage, Kelly Fraction leverage, forecasted volatility, predicted returns, and current regime.
Settings Guide
Please check the informational "i" in setting to get a lot more info.
You can also use preset configurations:
Conservative (Safe)
Kelly Fraction: 0.50
Max Leverage: 2.0x
Lambda: 0.97
Sensitivity: Enhanced
Moderate (Balanced) ⭐ DEFAULT
Kelly Fraction: 0.75
Max Leverage: 3.0x
Lambda: 0.94
Sensitivity: Enhanced
Aggressive (Maximum)
Kelly Fraction: 1.0
Max Leverage: 5.0x
Lambda: 0.90
Sensitivity: Standard
Paper Replication (Academic)
Kelly Fraction: 1.0
Max Leverage: 3.0x
Lambda: 0.94
Sensitivity: Standard
Adaptive: ON
Smoothing: 1
Remember: LEVERAGE MAGNIFIES BOTH GAINS AND LOSSES
Let me know if you have questions!
By Henrique Centieiro Indicator
Kelly Criterion CurveThe Kelly Criterion Curve indicator gives you the leverage/return tradeoff by displaying a bell curve with growth and leverage. This indicator shows where you are on the risk curve depending your allocation/leverage used and the optimal leverage to use in any asset.
What Does It Show?
The indicator plots the Kelly growth function:
g(f) = μ·f - 0.5·σ²·f²
Where:
g(f) = Expected growth rate at leverage f
μ = Annualized return
σ = Annualized volatility
f = Leverage multiplier
The curve peaks at the Optimal Kelly leverage (full Kelly) and then declines, showing that:
Too little leverage = underutilized capital
Too much leverage = volatility drag destroys returns
The curve is dynamically divided into zones based on your asset's return profile:
Underinvesting (Green) - Too conservative, underutilized capital
Optimal Sizing (Teal) - Sweet spot for position sizing
High Risk (Yellow) - Diminishing returns, high volatility drag
Never Logical (Red) - Risk outweighs reward
Suicidal (Black) - Negative expected returns
Position Markers
★ Kelly Optimal (Green/Red) - Maximum long-term log growth leverage
½ Kelly (Yellow) - Conservative sizing (recommended most times)
Settings for Kelly Calculation
Lookback Period - Historical data window for calculations (default: 252 = 1 year)
Annual Trading Days - For annualization (default: 252)
Use Log Returns - More accurate for compounding (recommended: ON)
Curve Smoothness (20-200) - Number of points on curve (default: 100)
Maximum Leverage Display (2-10x) - X-axis range
Show Short Positions - Display negative leverage for short strategies. Note the chart is not fully optimized for shorts.
Show Optimal Kelly Marker - Mark optimal leverage on curve
Show Half Kelly Marker - Mark conservative leverage
How to Use
Look at Optimal Kelly - This is the theoretical maximum for the period analyzed
Use Half Kelly for conservative sizing
Check which risk zone your position falls into
If your leverage is in the High Risk zone → Consider reducing
If you're in Never Logical or Suicidal → I wish you good luck because you will need a lot
If you're in Underinvesting → You may be too conservative
IMPORTANT
The indicator is based on past returns and volatility. It CANNOT predict:
Market crashes
Regime changes
Black swan events
If you use Optimal Kelly and suddenly there's a crash, you are toasted.
Full Kelly maximizes long-term growth but can experience large drawdowns
Most traders use ¼ to ½ Kelly for risk management
You should almost never use full Kelly, unless you are extremely confident
Remember leverage amplifies gains and losses
Notice how Max Growth isn't simply Ann. Return × Leverage
The formula accounts for volatility drag (the cost of using leverage)
Higher volatility = lower optimal leverage
The Kelly Criterion was developed by John L. Kelly Jr. in 1956 for information theory and later adapted for gambling (card counting for example, pioneered by Edward O. Thorp), and investing.
Optimal Leverage:
f* = μ / σ²
Expected Growth Function:
g(f) = μ·f - 0.5·σ²·f²
This is a quadratic function that forms the bell curve you see on the chart.
This indicator pairs perfectly with my other indicators:
Kelly Optimal Leverage Indicator
Jensen's Inequality + Kelly Leverage
Multi-Leverage VAR/VaG Indicator
For deeper insights on Kelly Criterion and optimal leverage:
Read my article: Unlock the Power of Monte Carlo
Read these papers:
Alpha Generation and Risk Smoothing using Managed
Volatility
Leverage for the Long Run - A Systematic Approach to Managing Risk and Magnifying Returns in Stocks
Trading with leverage involves substantial risk of loss.
The Kelly Criterion provides a theoretical framework - actual trading requires additional risk management, market analysis, and psychological discipline.
Some examples of using the Kelly Criterion Curve:
Russel 2000, last 500 days Kelly curve
Here's you can see that the optimal sizing over the last 500 days would have been around 1.7x leverage and that full Kelly is 3.4x leverage.
While Russel 2000 returned 16%, full Kelly would have returned 27.8%, and more that full Kelly (3.4x leverage) would lower the returns.
Berkshire Hathaway, last 1000 days Kelly curve
BRK stock optimal Kelly (full Kelly) is 2.5x for the last 1000 trading days. To reduce volatility, one could use 1/2 Kelly which is 1.25x leverage.
Bitcoin, last 2000 trading days Kelly curve
Very interestingly, the indicator tells us not to leverage Bitcoin. Even a 2x leverage can lead to ruin given its volatility, and in fact, in 2025 many traders got liquidated while leveraging Bitcoin by 2x.
Let me know if you have questions, suggestions and comments.
- Henrique Centieiro Indicator
Trade Strategy Calculator [WillyAlgoTrader]📊 Trade Strategy Calculator is the first comprehensive mathematical strategy calculator built entirely inside PulseWire — a 4-panel dashboard that computes position sizing, risk analysis, deposit growth projection, and Kelly Criterion optimization in real time, directly on your chart. No spreadsheets, no external tools, no switching tabs. Every number you need before entering a trade — position size, stop loss level, take-profit targets, commission impact, expected value, probability of ruin, compound growth forecast, and optimal bet sizing — calculated from your strategy parameters and displayed in a single organized view.
This tool is useful for every trader regardless of market, instrument, or timeframe — stocks, forex, crypto, futures, indices, commodities. Whether you trade scalping on 1-minute charts or swing on daily, whether you use 1x spot or 125x futures leverage — the mathematics of position sizing, risk management, and bankroll growth are universal. This calculator puts those mathematics at your fingertips.
🧩 WHY ALL FOUR PANELS WORK TOGETHER
Most traders calculate position size in isolation — they know how much to risk but don't connect it to their long-term growth trajectory. They know their win rate but don't know if it's mathematically profitable after commissions. They have a "feel" for their risk level but haven't computed what happens after 7 consecutive losses.
This calculator connects four mathematical dimensions into one coherent picture:
🎯 TRADE panel answers: "How large should this specific trade be, and what are the exact entry/SL/TP prices?"
⚠️ RISK panel answers: "What happens when things go wrong — how many losses until I hit my daily limit, my max drawdown, and what's my expected value per trade?"
📈 GROWTH panel answers: "If I trade consistently with these parameters, where will my deposit be in 30/90/365 days — and how long to reach my target?"
📐 KELLY panel answers: "Am I betting the mathematically optimal amount — or am I over-betting (risking ruin) or under-betting (leaving growth on the table)?"
A trader who only uses the TRADE panel knows their position size but not whether their strategy has positive expected value. A trader who only uses KELLY knows the optimal bet size but not the specific position for their current trade. A trader who only uses GROWTH knows the projection but not whether the underlying math is sound. All four together give you the complete picture: "Is my strategy profitable? Am I sizing correctly? What's the worst case? And where does this lead?"
🔍 WHAT MAKES IT ORIGINAL
There is no other indicator on PulseWire that combines all four of these mathematical models — position sizing, risk stress testing, compound growth simulation, and Kelly Criterion — into a single, real-time, interactive dashboard. Each panel alone would be a useful tool. Together, they create something that doesn't exist elsewhere on the platform.
🎯 PANEL 1 — TRADE (Position Sizing + Targets)
This panel calculates the exact position size for your trade based on your deposit, risk percentage, stop loss distance, leverage, and commissions.
Core formula:
positionSize = riskAmount / (slDistance% + commissionBothSides)
Where:
— riskAmount = deposit × riskPerTrade%
— slDistance% = slPercent × (1 + slippage%) — slippage is added to the stop distance for realistic sizing
— commissionBothSides = commission% × 2 (open + close)
This formula ensures that if your stop loss is hit, you lose exactly riskAmount — not more, not less — after accounting for both slippage and round-trip commission.
What you see:
— Direction (Long / Short)
— Entry Price (manual or auto from chart)
— Stop Loss price (calculated from entry ± SL%)
— 💰 Position Size in USD — the headline number
— Margin Required (if leverage > 1)
— Quantity (units/coins/shares)
— 🔴 Risk (loss) in USD and % of deposit
— 🟢 Profit at TP — in USD, % of deposit, and net R:R after commission
— TP Price level
— Commission cost in USD
— Liquidation price (for leveraged positions)
— ⚠️ Insufficient margin warning (if position exceeds deposit)
Multi Take-Profit mode:
When enabled, the position is split across 2 or 3 TP levels with configurable volume allocation:
— TP1 at R:R 1.0 with 50% of position → locks partial profit early
— TP2 at R:R 2.0 with 30% → captures the main move
— TP3 at R:R 3.0 with 20% (if 3 TPs) → runner for extended moves
Each TP shows: profit in USD, target price. The panel also computes:
— Total blended profit across all TPs
— Net R:R (blended, after commissions)
— Breakeven price after TP1 — the price where your remaining position becomes zero-loss after banking TP1 profit. This is critical: after TP1, you move your stop to this price — the trade can no longer lose money.
Example:
Deposit: $10,000. Risk: 1% ($100). SL: 2%. Commission: 0.04%.
Position = $100 / (0.02 + 0.0008) = $4,808.
If BTC at $100,000 → SL at $98,000, TP1 at $102,000.
If stopped out → you lose exactly $100 (1% of deposit).
If TP1 hit → you gain ~$96 (after commission).
⚠️ PANEL 2 — RISK (Stress Testing + Expected Value)
This panel answers: "What happens when I have a losing streak, and is my strategy mathematically profitable?"
Daily risk limit:
maxLosingDaily = floor(dailyRiskLimit% / riskPerTrade%)
Example: 3% daily limit, 1% per trade → you stop after 3 losses in a day.
Max drawdown limit:
maxLosingTotal = floor(maxDrawdown% / riskPerTrade%)
Example: 20% max DD, 1% per trade → 20 consecutive losses to hit max DD.
Stress test — losing streaks:
The panel computes what happens after 5, 7, and 10 consecutive losses:
— depositAfterN = deposit × (1 − riskPerTrade%)^N
— drawdownAfterN = (1 − (1 − riskPerTrade%)^N) × 100%
— probabilityOfN = (1 − winrate%)^N × 100%
Example: $10,000 deposit, 1% risk, 55% winrate:
— 5 losses: −4.9% DD ($9,510), probability 1.85%
— 7 losses: −6.8% DD ($9,321), probability 0.37%
— 10 losses: −9.6% DD ($9,044), probability 0.03%
This tells you: a 5-loss streak WILL happen (1.85% probability over hundreds of trades). A 10-loss streak is extremely rare (0.03%). Your risk% must be sized so that even the realistic worst case doesn't blow your account.
Expected Value (EV):
EV per trade = winrate × riskAmount × avgR:R − (1 − winrate) × riskAmount − commission
This is the single most important number in trading. If EV > 0, your strategy makes money over time. If EV < 0, no amount of position sizing saves you.
The panel shows:
— 📈 EV per trade in USD (highlighted — this is the headline metric)
— EV per 100 trades
— Break-even winrate WITH commission — the minimum winrate needed to be profitable at your R:R, accounting for commission drag
— Your actual WR and R:R for comparison
Break-even winrate formula (with commission):
beWinrate = (1 + commissionCost / riskAmount) / (avgR:R + 1)
This is more accurate than the standard 1/(R:R+1) because it accounts for commission reducing your net edge.
📈 PANEL 3 — GROWTH (Deposit Projection + Scenarios)
This is the unique deposit growth simulator — it projects where your deposit will be after N days of consistent trading, using either compound (reinvest profits) or simple (fixed risk from initial deposit) growth.
Compound growth formula:
EV per trade as % = winrate × (risk% × R:R) − (1 − winrate) × risk%
totalTrades = tradesPerDay × projectionDays
finalDeposit = deposit × (1 + evPerTrade%)^totalTrades
Simple growth formula:
finalDeposit = deposit + deposit × evPerTrade% × totalTrades
The difference is massive. Compound growth reinvests profits — each winning trade increases the base for the next trade. Simple growth always risks a fixed amount from the initial deposit.
Example — compound vs simple:
$1,000 deposit, 55% WR, 1:2 R:R, 1% risk, 3 trades/day, 30 days:
— Simple: $1,000 + $1,000 × 0.65% × 90 = $1,585
— Compound: $1,000 × (1.0065)^90 = $1,795
Over 90 days: $1,585 vs $1,795. Over 365 days the gap becomes enormous. This is why compound growth (reinvesting profits) is the key to deposit acceleration.
Three scenarios:
— 🟢 Optimistic: your winrate + 10% (what happens if you're having a great month)
— 🟡 Realistic: your actual parameters
— 🔴 Pessimistic: your winrate − 10% (what happens during a drawdown period)
This gives you a range, not a single number. If even the pessimistic scenario is positive, your strategy is robust.
Goal milestones:
— Days to 2× deposit (double your money)
— Days to 3× deposit
— Days to custom target ($5,000, $10,000, etc.)
Formula: daysToTarget = log(target / deposit) / (log(1 + evPerTrade%) × tradesPerDay)
Risk metrics:
— Max estimated drawdown: based on expected worst losing streak × risk%
— Ruin probability: the probability of losing your entire bankroll at your current risk level
Ruin probability formula:
edge = winrate × R:R − (1 − winrate)
bankrollUnits = floor(100 / risk%)
ruinProb = ((1 − winrate) / (winrate × R:R))^bankrollUnits
If edge ≤ 0, ruin probability is effectively 100%. If edge > 0, ruin probability decreases exponentially with more bankroll units (lower risk%).
Presets for quick scenarios:
— Beginner: 45% WR, 1:2 R:R, 1% risk — conservative starting point
— Moderate: 55% WR, 1:2 R:R, 2% risk — typical intermediate trader
— Aggressive: 50% WR, 1:3 R:R, 3% risk — higher risk, needs discipline
— Custom: uses your exact My Strategy values
📐 PANEL 4 — KELLY CRITERION (Optimal Bet Sizing)
The Kelly Criterion is the mathematically optimal percentage of your bankroll to risk on each bet, given your edge. It maximizes the long-term growth rate of your account.
Kelly formula:
edge = winrate × avgR:R − (1 − winrate)
kellyPercent = edge / avgR:R
If edge ≤ 0 → Kelly = 0% (no edge, don't trade). If edge > 0 → Kelly tells you the maximum you should risk.
What the panel shows:
— Your winrate and avg R:R
— Break-even winrate (with commission)
— 📐 Edge per $1 risked — your mathematical advantage. If +$0.15, every $1 risked returns $1.15 on average.
— Full Kelly % — the theoretical maximum. Most traders should NOT use this — it's too aggressive.
— Half Kelly ✦ — the recommended practical value. Reduces variance by ~75% while giving up only ~25% of growth.
— Quarter Kelly — ultra-conservative, minimal variance.
— Your current risk % — so you can compare
— Status: 🟢 Optimal (between half and full Kelly), 🟡 Conservative (below half), 🔴 Over-bet (above full Kelly), 🚨 >2× Kelly (danger zone)
Growth rate comparison:
— Growth rate at Kelly %: the compound growth rate per trade at the optimal bet size
— Growth rate at your %: your actual compound growth rate per trade
Formula: growthRate = winrate × log(1 + risk% × R:R) + (1 − winrate) × log(1 − risk%)
If your rate is close to the Kelly rate, you're near-optimal. If it's much lower, you're leaving growth on the table. If it's negative (possible when over-betting!), you're actually losing money despite having a positive edge — the over-betting destroys the compounding.
Why this matters:
A trader with a 55% WR and 1:2 R:R has an edge. Kelly says risk ~4.6%. But if that trader risks 10% per trade (2× Kelly), their actual growth rate can become negative — they go broke despite having a winning strategy. This is the most counterintuitive result in trading mathematics: over-betting a winning system turns it into a losing system . The Kelly panel prevents this.
📖 HOW TO USE — STEP BY STEP
Step 1 — Enter your strategy parameters (My Strategy section):
— Deposit: your actual account balance in USD
— Risk per Trade: how much you risk per trade (start with 1% if unsure)
— Winrate: your historical win rate (be honest — check your journal)
— Average R:R: your average reward-to-risk on winning trades
— Trades per Day: how many trades you typically take
— Leverage: 1 for spot, or your futures leverage
— Commission: your exchange fee per side (Binance Futures taker: 0.04%)
Step 2 — Set up your current trade (Trade Setup section):
— Direction: Long or Short
— Stop Loss %: how far your SL is from entry
— Risk:Reward: your target R:R for this trade
— Entry Price: manual or auto from chart
Step 3 — Read the TRADE panel:
— The 💰 Position Size number is your order size in USD
— If using leverage, check Margin Required doesn't exceed your deposit
— Note the SL and TP prices — set these in your exchange
Step 4 — Check the RISK panel:
— Is your EV per trade positive? If not, your strategy loses money long-term
— Is your winrate above the break-even? If not, improve your R:R
— Check the stress test: can your deposit survive 7 losses in a row?
— If the risk badge shows 🚨 DANGER, reduce your risk% or leverage
Step 5 — Review the GROWTH panel:
— The projected deposit shows where you'll be in 30 days
— Check the pessimistic scenario — is it still above your starting deposit?
— Note the days to 2× — this is your compound growth timeline
— If ruin probability > 5%, your risk is too high
Step 6 — Optimize with KELLY panel:
— Compare your risk% to Half Kelly — this is the recommended level
— If Status shows 🔴 Over-bet, reduce your risk%
— If Status shows 🟡 Conservative, you could increase (but don't have to)
— Check Growth Rate at Your % — is it positive? Is it close to Kelly's rate?
🎯 PRACTICAL EXAMPLES
Example 1 — Conservative Spot Trader:
Deposit $5,000, Risk 1%, WR 55%, R:R 1:2, 2 trades/day, No leverage, Commission 0.1%
— Position: ~$2,500 per trade. Risk: $50.
— EV: +$5.60 per trade. Positive — strategy is profitable.
— 30-day projection (compound): $5,000 → $5,705 (+14.1%)
— Days to double: ~98 days
— Kelly: 4.6%. Your 1% = conservative. Status: 🟡
Example 2 — Crypto Futures Scalper:
Deposit $1,000, Risk 2%, WR 50%, R:R 1:3, 5 trades/day, Leverage 10x, Commission 0.04%
— Position: ~$10,000 per trade. Margin: $1,000. Risk: $20.
— EV: +$10.40 per trade. Strong positive edge.
— 30-day projection (compound): $1,000 → $4,680 (+368%)
— Days to double: ~14 days
— Kelly: 8.3%. Your 2% = well below Kelly. Room to grow.
— ⚠️ But 7-loss streak probability: 0.78%. DD: −13.2%. Manageable.
Example 3 — Why Over-Betting Kills:
Same as Example 2, but Risk 15% (almost 2× Kelly):
— EV per trade still positive (+$78)
— BUT growth rate per trade: NEGATIVE (−0.3%)
— 30-day projection: $1,000 → $620 (−38%)
— Kelly Status: 🚨 >2× Kelly
— Despite winning 50% with 1:3 R:R, you LOSE money because over-betting destroys compounding.
⚙️ KEY SETTINGS REFERENCE
⚙️ My Strategy:
— Deposit : account balance in USD
— Risk per Trade (default 1%): % of deposit risked per trade
— Winrate (default 55%): historical win rate
— Average R:R (default 2.0): average reward-to-risk on wins
— Trades per Day (default 3): daily trade count
— Leverage (default 1): 1 = spot, >1 = futures
— Commission (default 0.04%): exchange fee per side
🎯 Trade Setup:
— Direction : Long / Short
— Stop Loss % (default 1%): SL distance from entry
— Risk:Reward (default 2.0): target R:R
— Slippage (default 0.05%): expected execution slippage
— Entry Price : Manual or Auto (chart price)
🎯 Multi Take-Profit:
— Enable Multi TP (default Off): split into 2–3 targets
— R:R for TP1/TP2/TP3 (default 1.0/2.0/3.0)
— Volume allocation (default 50%/30%/20%)
📈 Growth Projection:
— Preset : Beginner / Moderate / Aggressive / Custom
— Projection Period (default 30 days)
— Compound (default On): reinvest profits
— Target Deposit (default 0 = off): goal amount
— Max Daily Risk (default 3%): daily loss limit
— Max Drawdown (default 20%): total DD limit
🎨 Visual:
— Font Size: Tiny / Small / Normal / Large
— Auto / Dark / Light theme
⚠️ IMPORTANT NOTES
— 📊 This is a calculator, not a signal generator. It does not produce buy/sell signals. It computes the mathematical framework for your trading decisions — position sizing, risk limits, growth projections, and optimal bet sizing. The math is universal and applies to any strategy.
— 📐 All calculations are deterministic — they depend only on your input parameters, not on price data. The dashboard updates in real-time when you change any input.
— ⚖️ The growth projection assumes consistent strategy parameters over the projection period. Real trading involves varying win rates, R:R ratios, and market conditions. The three scenarios (optimistic/realistic/pessimistic) partially address this by showing a range.
— 📏 The Kelly Criterion assumes known, fixed probabilities . In practice, your winrate and R:R fluctuate. This is why Half Kelly (not Full Kelly) is recommended — it accounts for parameter uncertainty.
— 💰 Commission is calculated as round-trip (both sides) and deducted from both profit calculations and expected value. This provides realistic net returns.
— 📊 The break-even winrate calculation includes commission drag — it's higher than the simplified 1/(R:R+1) formula because commission erodes your edge.
— 🔄 The compound growth formula uses logarithmic overflow protection — if the projected growth exceeds exp(23) ≈ 10 billion ×, it displays "∞" instead of crashing.
— 🛠️ Works on any chart, any instrument, any timeframe . The calculator is price-independent — it uses your manual inputs. "Auto" entry price mode uses the current chart close for convenience.
— 🌐 Useful for all markets : stocks (set leverage = 1, commission = 0.1%), forex (adjust for pip-based SL), crypto spot (leverage = 1), crypto futures (set your leverage), indices, commodities. Indicator
Jensen's Inequality + Kelly LeverageThis indicator reveals how volatility drag erodes returns through Jensen's Inequality and calculates scientifically optimal leverage levels using the Kelly Criterion. It answers the question: "At what leverage does volatility drag destroy more returns than leverage creates?"
I have created other indicators related to optimal leverage, Kelly Criterion and Jensen's inequality which you can fin in the comments.
Understand Jensen's Inequality
Jensen's Inequality is a theorem stating that for concave functions (like logarithms or sad face), the expected value of the function is less than the function of the expected value:
E ≤ log(1+E )
What this means for investors is that your realized geometric return (what you actually earn through compounding) is always less than your arithmetic average return. This gap is called volatility drag.
The drag formula: Drag = L² × σ² / 2
The quadratic term (L²) is crucial because if you double your leverage, quadruple your drag. This helps us to understand how much leverage we can take during volatile times (for example leveraged ETFs).
Understand Kelly Criterion
The Kelly Criterion, developed by John Kelly at Bell Labs in 1956, calculates the optimal bet size (or leverage) that maximizes long-term logarithmic growth of wealth:
Kelly = (μ - r_f) / σ²
Where:
μ = arithmetic return (expected return)
r_f = risk-free rate
σ² = variance (volatility squared)
Kelly tells you the exact leverage that balances return amplification against volatility drag to maximize your long-term compound growth rate.
Why I Combine Both?
Jensen's Inequality explains why leverage has, after a certain point, diminishing returns and eventually becomes destructive. Volatility drag grows faster than return amplification. The Kelly Criterion tells you exactly where the optimal point is before drag overwhelms your gains.
Together, they provide:
Jensen: How much drag you're experiencing
Kelly: What leverage maximizes your growth
Both: Where leverage becomes dangerous
The Math Behind It
Geometric return formula:
r_geometric = L × r_arithmetic - (L² × σ²) / 2
This shows the tug-of-war between leverage amplification (L × r_arithmetic) and drag (L² × σ²/2).
Maximum survivable leverage:
L_max = 2 × r_arithmetic / σ²
At this point, drag completely cancels out returns (geometric return = 0). Beyond this, you're guaranteed to lose money over time.
How To Read The Chart
Y-axis: Geometric returns (%) - what you actually earn after accounting for drag
Colored lines: Expected returns at different leverage levels over time
Green line (1.0x): Unleveraged baseline
Orange/Red lines (2x/3x): Higher leverage scenarios
Blue circles: Kelly optimal leverage level
Red label at zero: Max survivable leverage (breakeven point)
The Table Breakdown
Jensen's Inequality (1x & 2x): Side-by-side comparison demonstrating:
How drag scales quadratically (1.99% → 7.96% when leverage doubles)
The verification that L×E - Drag = Realized Return
Optimal Leverage: Kelly calculations with fractional variants
Full Kelly: Theoretically optimal but aggressive
0.75x, 0.5x, 0.25x Kelly: Conservative risk management
Sharpe Optimal: Maximizes risk-adjusted returns
Max Leverage: Your "game over" threshold
Leverage Scenarios: Detailed comparison of 1x, 2x, 3x positions showing geometric returns, drag costs, and Sharpe ratios
Practical Insights
Low volatility assets: Higher Kelly → can handle more leverage safely
High volatility assets (crypto for example): Lower Kelly → even 2x can be destructive
Current market regime matters: The indicator adapts to changing volatility conditions
Fractional Kelly is wisdom: Full Kelly assumes perfect parameter estimates (which we never have)
Settings
Risk-free rate: Auto-fetches FRED:DGS3MO (3-month T-Bills) or manual override
Log returns: Enabled by default for mathematically accurate compounding
Display options: Toggle curve/table, adjust positioning and font sizes
Lookback period: Adjustable from 50 to 1500 bars
As you should know by now, leverage is a double-edged sword. This indicator shows you exactly where the edge cuts both ways, helping you find the sweet spot between aggressive growth and mathematical ruin.
Let me know if you have any suggestions.
- Henrique Centieiro Indicator
Kelly Optimal Leverage IndicatorThe Kelly Optimal Leverage Indicator mathematically applies Kelly Criterion to determine optimal position sizing based on market conditions.
This indicator helps traders answer the critical question: "How much capital should I allocate to this trade?"
Note that "optimal position sizing" does not equal the position sizing that you should have. The Optima position sizing given by the indicator is based on historical data and cannot predict a crash, in which case, high leverage could be devastating.
Originally developed for gambling scenarios with known probabilities, the Kelly formula has been adapted here for financial markets to dynamically calculate the optimal leverage ratio that maximizes long-term capital growth while managing risk.
Key Features
Kelly Position Sizing: Uses historical returns and volatility to calculate mathematically optimal position sizes
Multiple Risk Profiles: Displays Full Kelly (aggressive), 3/4 Kelly (moderate), 1/2 Kelly (conservative), and 1/4 Kelly (very conservative) leverage levels
Volatility Adjustment: Automatically recommends appropriate Kelly fraction based on current market volatility
Return Smoothing: Option to use log returns and smoothed calculations for more stable signals
Comprehensive Table: Displays key metrics including annualized return, volatility, and recommended exposure levels
How to Use
Interpret the Lines: Each colored line represents a different Kelly fraction (risk tolerance level). When above zero, positive exposure is suggested; when below zero, reduce exposure. Note that this is based on historical returns. I personally like to increase my exposure during market downturns, but this is hard to illustrate in the indicator.
Monitor the Table: The information panel provides precise leverage recommendations and exposure guidance based on current market conditions.
Follow Recommended Position: Use the "Recommended Position" guidance in the table to determine appropriate exposure level.
Select Your Risk Profile: Conservative traders should follow the Half Kelly or Quarter Kelly lines, while more aggressive traders might consider the Three-Quarter or Full Kelly lines.
Adjust with Volatility: During high volatility periods, consider using more conservative Kelly fractions as recommended by the indicator.
Mathematical Foundation
The indicator calculates the optimal leverage (f*) using the formula:
f* = μ/σ²
Where:
μ is the annualized expected return
σ² is the annualized variance of returns
This approach balances potential gains against risk of ruin, offering a scientific framework for position sizing that maximizes long-term growth rate.
Notes
The Full Kelly is theoretically optimal for maximizing long-term growth but can experience significant drawdowns. You should almost never use full kelly.
Most practitioners use fractional Kelly strategies (1/2 or 1/4 Kelly) to reduce volatility while capturing most of the growth benefits
This indicator works best on daily timeframes but can be applied to any timeframe
Negative Kelly values suggest reducing or eliminating market exposure
The indicator should be used as part of a complete trading system, not in isolation
Enjoy the indicator! :)
P.S. If you are really geeky about the Kelly Criterion, I recommend the book The Kelly Capital Growth Investment Criterion by Edward O. Thorp and others.
Indicator
FunctionKellyCriterionLibrary "FunctionKellyCriterion"
Kelly criterion methods.
the kelly criterion helps with the decision of how much one should invest in
a asset as long as you know the odds and expected return of said asset.
simplified(win_p, rr)
simplified version of the kelly criterion formula.
Parameters:
win_p : float, probability of winning.
rr : float, reward to risk rate.
Returns: float, optimal fraction to risk.
usage:
simplified(0.55, 1.0)
partial(win_p, loss_p, win_rr, loss_rr)
general form of the kelly criterion formula.
Parameters:
win_p : float, probability of the investment returns a positive outcome.
loss_p : float, probability of the investment returns a negative outcome.
win_rr : float, reward on a positive outcome.
loss_rr : float, reward on a negative outcome.
Returns: float, optimal fraction to risk.
usage:
partial(0.6, 0.4, 0.6, 0.1)
from_returns(returns)
Calculate the fraction to invest from a array of returns.
Parameters:
returns : array trade/asset/strategy returns.
Returns: float, optimal fraction to risk.
usage:
from_returns(array.from(0.1,0.2,0.1,-0.1,-0.05,0.05))
final_f(fraction, max_expected_loss)
Final fraction, eg. if fraction is 0.2 and expected max loss is 10%
then you should size your position as 0.2/0.1=2 (leverage, 200% position size).
Parameters:
fraction : float, aproximate percent fraction invested.
max_expected_loss : float, maximum expected percent on a loss (ex 10% = 0.1).
Returns: float, final fraction to invest.
usage:
final_f(0.2, 0.5)
hpr(fraction, trade, biggest_loss)
Holding Period Return function
Parameters:
fraction : float, aproximate percent fraction invested.
trade : float, profit or loss in a trade.
biggest_loss : float, value of the biggest loss on record.
Returns: float, multiplier of effect on equity so that a win of 5% is 1.05 and loss of 5% is 0.95.
usage:
hpr(fraction=0.05, trade=0.1, biggest_loss=-0.2)
twr(returns, rr, eps)
Terminal Wealth Relative, returns a multiplier that can be applied
to the initial capital that leadds to the final balance.
Parameters:
returns : array, list of trade returns.
rr : float , reward to risk rate.
eps : float , minimum resolution to void zero division.
Returns: float, optimal fraction to invest.
usage:
twr(returns=array.from(0.1,-0.2,0.3), rr=0.6)
ghpr(returns, rr, eps)
Geometric mean Holding Period Return, represents the average multiple made on the stake.
Parameters:
returns : array, list of trade returns.
rr : float , reward to risk rate.
eps : float , minimum resolution to void zero division.
Returns: float, multiplier of effect on equity so that a win of 5% is 1.05 and loss of 5% is 0.95.
usage:
ghpr(returns=array.from(0.1,-0.2,0.3), rr=0.6)
run_coin_simulation(fraction, initial_capital, n_series, n_periods)
run multiple coin flipping (binary outcome) simulations.
Parameters:
fraction : float, fraction of capital to bet.
initial_capital : float, capital at the start of simulation.
n_series : int , number of simulation series.
n_periods : int , number of periods in each simulation series.
Returns: matrix(n_series, n_periods), matrix with simulation results per row.
usage:
run_coin_simulation(fraction=0.1)
run_asset_simulation(returns, fraction, initial_capital)
run a simulation over provided returns.
Parameters:
returns : array, trade, asset or strategy percent returns.
fraction : float , fraction of capital to bet.
initial_capital : float , capital at the start of simulation.
Returns: array, array with simulation results.
usage:
run_asset_simulation(returns=array.from(0.1,-0.2,0.-3,0.4), fraction=0.1)
strategy_win_probability()
calculate strategy() current probability of positive outcome in a trade.
strategy_avg_won()
calculate strategy() current average won on a trade with positive outcome.
strategy_avg_loss()
calculate strategy() current average lost on a trade with negative outcome. Library
