Advanced Quantitative Analytics Platform
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Position sizing is arguably the single most important variable in portfolio management — and yet most retail investors handle it intuitively. "I'll put in 50,000 CZK" regardless of whether the stock is calm like ČEZ or wild like NVDA. This article shows how to connect volatility measurement (ATR), stop derivation, and the mathematics of the Kelly Criterion into a concrete, reproducible process.
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Average True Range (ATR) is an indicator developed by Welles Wilder that measures the average true daily volatility of an asset over a chosen period (typically 14 days).
"True Range" (TR) is the maximum of three values:
| Property | ATR | Std. Deviation of Returns |
|---|---|---|
| Unit | CZK / $ | % or decimal |
| Sensitivity to gaps | Yes (includes overnight) | Depends on calculation |
| Intuitive for stops | High — directly in price | Requires conversion |
| Use for stop placement | Direct (n × ATR) | Needs recalculation |
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The core idea: risk a fixed CZK amount (or % of portfolio) on every trade, and adjust position size to match the stop width.
Number of shares = Risk in CZK / Stop in CZK per share
where:
Stop in CZK per share = n × ATR(14)
Risk in CZK = Portfolio × % risk per trade
A common setting is n = 2 (stop is 2× ATR below entry) and % risk = 1–2% of portfolio per trade.
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Assume a portfolio of 1,000,000 CZK and a rule: risk max 1% of portfolio per trade = 10,000 CZK.
| Parameter | ČEZ (calm) | NVDA (volatile) |
|---|---|---|
| Current price | 850 CZK | 3,100 CZK* |
| ATR(14) | 18 CZK | 185 CZK |
| Stop (2× ATR) | 36 CZK | 370 CZK |
| Risk per trade | 10,000 CZK | 10,000 CZK |
| Number of shares | 10,000 / 36 ≈ 277 shares | 10,000 / 370 ≈ 27 shares |
| Total position value | ~235,450 CZK | ~83,700 CZK |
Result: Same CZK risk — completely different share counts and capital allocation. With the calm stock, the strategy naturally enters a larger position; with the volatile one, a smaller position. Without this approach, an investor buying 100,000 CZK in each would be risking ~5× more in NVDA than in ČEZ.
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The Kelly Criterion (John L. Kelly Jr., 1956) answers the question: what fraction of capital maximizes long-term geometric growth?
f* = (p × b − q) / b
where:
A strategy with a win rate of 55% and average R/R of 1.5:1:
f* = (0.55 × 1.5 − 0.45) / 1.5
f* = (0.825 − 0.45) / 1.5
f* = 0.375 / 1.5
f* = 0.25 → 25% of capital per trade
Full Kelly is mathematically optimal, but in the real world it is extremely aggressive and highly sensitive to the accuracy of input estimates:
| Approach | Risk per Trade | Drawdown | Psychological Sustainability |
|---|---|---|---|
| Full Kelly (25%) | Very high | ~50–60% | Low |
| ½ Kelly (12.5%) | High | ~30–40% | Medium |
| ¼ Kelly (6.25%) | Medium-low | ~15–20% | High |
| Fixed 1–2% | Conservative | <10% | Very high |
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A stop-loss is not an arbitrary number — it should respect the market's natural "noise." A stop placed too close to price will be triggered by normal intraday volatility. A stop placed too far creates an unacceptably large loss per trade.
Empirical guidelines:
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QMA provides several tools that directly support this approach:
/stocks/NVDA or /stocks/CEZ), technical indicators including ATR(14) are available. This is where the current ATR value can be monitored and compared to its historical average — a high ATR signals elevated volatility and the need to reduce position size.
/strategy section, it is possible to backtest rules including volatility-based sizing — the strategy tool evaluates historical results of different stop-loss and position-sizing approaches, enabling an empirical comparison of full Kelly vs. ¼ Kelly on historical data.
/smart-money section displays institutional flows and unusual volume. High institutional interest in a stock with a low ATR may indicate stable accumulation — contextual information relevant to sizing decisions.
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/stocks/[symbol]---
QMA is an analytical and educational tool, not investment advice. Past performance is not a guarantee of future results. All investment decisions are your own responsibility.
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