Dynamic Position Sizing: How ATR and the Kelly Criterion Protect Your Portfolio from Volatility

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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What Is ATR and Why Does It Matter

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:

• High − Low of the current day
• |High − previous Close|
• |Low − previous Close|

ATR then averages these values. Key property: ATR is expressed in absolute price units (CZK / $), not percentages — for a stock trading at 1,000 CZK with ATR = 30 CZK, we know it typically moves ±30 CZK per day.

ATR vs. Standard Deviation

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

For position sizing, ATR is more practical — stops are set as a multiple of ATR (e.g., 2× ATR below entry price).

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Volatility-Based Position Sizing: The Formula

The core idea: risk a fixed CZK amount (or % of portfolio) on every trade, and adjust position size to match the stop width.

Formula

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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Concrete Example: ČEZ vs. NVDA

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

\* Prices are illustrative for calculation purposes only, not a recommendation.

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: Optimal Bet Size

The Kelly Criterion (John L. Kelly Jr., 1956) answers the question: what fraction of capital maximizes long-term geometric growth?

Formula

f* = (p × b − q) / b

where:

• f* = optimal fraction of capital per trade
• p = probability of profit (win rate)
• q = probability of loss = 1 − p
• b = average gain / average loss (reward/risk ratio)

Example

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

Why Fractional Kelly (¼ Kelly) Is Used in Practice

Full Kelly is mathematically optimal, but in the real world it is extremely aggressive and highly sensitive to the accuracy of input estimates:

• Win rate and R/R are estimates — small errors significantly change the result
• Full Kelly produces enormous drawdowns (even 50%+) on the path to the optimum
• An investor using full Kelly will psychologically fail before the math "pays off"

¼ Kelly (f / 4) dramatically reduces drawdown while preserving most of the long-term return. In practice, the fractional Kelly result is used as an upper bound* on risk per trade, while ATR-based sizing provides the concrete share count.

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

Most professional systematic traders use either ¼ Kelly or fixed 1–2% as a practical compromise.

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The Relationship Between ATR and Stop Placement

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:

• 1.5–2× ATR below entry for swing trading (3–10 days)
• 2.5–3× ATR for positional trading (weeks to months)
• Never a stop tighter than 0.5× ATR — statistically very likely to be hit prematurely

When volatility changes (e.g., NVDA pre-earnings vs. post-earnings), position size should be recalculated — ATR changes significantly around such events.

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How to Do This in QMA

QMA provides several tools that directly support this approach:

/stocks/[symbol] — Stock Detail Page

On the detail page of a specific stock (e.g., /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.

/portfolio — Portfolio Management

The portfolio section displays total exposure and position breakdown. It allows a visual check of whether the portfolio is diversified not only by sector but also by volatility — a balance between high-volatility and low-volatility positions is important for overall risk management.

/screener — Stock Filtering

The screener allows filtering stocks by various parameters including volatility metrics. A strategy targeting low volatility for conservative sizing can screen for stocks with ATR% below a defined threshold.

/strategy — Rules Backtesting

In the /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 — Institutional Flow

The /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.

QMA Confidence Score

QMA assigns stocks a confidence score that aggregates fundamental, technical, and sentiment factors. This score does not constitute investment advice, but can serve as one input when deciding whether to open a position at all — historically, a higher score has correlated with a lower probability of adverse outcomes, which directly influences the win rate estimate used in the Kelly formula.

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Summary: Step-by-Step Process

1. Find ATR(14) for the stock at /stocks/[symbol]
2. Set the stop at 2× ATR below entry price
3. Determine risk in CZK = portfolio × % risk (typically 1–2%, or the ¼ Kelly result)
4. Divide risk in CZK / stop in CZK = number of shares
5. Check total position value relative to portfolio — it should not exceed a reasonable limit (e.g., 20–25% of the portfolio in a single position)
6. Recalculate whenever ATR changes significantly (earnings, macro events)

This process turns the decision of "how much to buy" into a mathematical result, not a guess.

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Disclaimer

Past performance is not a guarantee of future results. All investment decisions are your own responsibility.