Introduction to Position Sizing for Quantitative Traders

Yep, Size Matters

This interview with Michael Wallace (who was inspired by Larry Williams and Ralph Vince) brings a few things to mind. First is the absolute centrality of the role of position sizing in trading, second is the nature of ‘probabilities’ in trading. They are highly related obviously. Sizing is not an afterthought; it can change everything. Presuming an ‘average win rate’ is going to apply to your next 10 trades is not a wise way to proceed either. You want to be more ‘statistically minded’ than that – just toss a coin 10 times, and do that 10 times, the number of heads you get in each group of 10 is going to vary wildly no doubt. Toss it 10,000 times and ‘averages will tend to show up, this is the law of large numbers, but accounts can blow up a long time before averages play out. Sequencing risk is real. Let’s dig into this stuff a little.

We don’t want you picking up pennies in front of steam rollers.

First, Algo Collective (our members area) and Algo Academy (our course platform hosting courses from market wizards) are now OPEN! Check it out on the website. I’m pretty excited about this step: the Collective is already buzzing and courses from Tom Starke (Python for Quants) and David Bush (Crypto Trader’s Edge) are ready to go. The Founding Member discounted deal is only THREE spots away from being full (only took a day!), and you can jump in for a free two-week trial. See you inside my friends (over 30 mins of extra deep dive with Michael).

If you’ve ever blown up a trading account or sat through a gut‑churning drawdown, you already know why position sizing isn’t just an academic exercise. It’s the lever that controls how much capital is exposed on every trade, and therefore how likely you are to survive long enough to let your edge play out. Good sizing techniques limit losses to a tolerable fraction of your capital and can reduce the stress of trading. Good traders often risk no more than 1–2 % of their account on any single trade; this modest risk per trade means even a string of ten losses only knocks the account down by ~20 %, leaving plenty of room to recover.

But there’s a paradox. The math tells us we could stake more when the edge is good – the Kelly criterion, for example, may suggest risking 20 % when win–loss ratios are favourable. Real markets, however, rarely deliver independent outcomes with fixed win rates or identical loss sizes. Slippage, gap risk and regime changes can turn theoretical optimums into account killers. Survival trumps theory.

In this primer we’ll lay out the common position sizing methods, comment on how different types of traders (futures vs. stock, short‑term vs. long‑term) use them, and share a simple mental framework for thinking about sizing from a risk and statistical perspective. Throughout we’ll lean on the mathematics of the Kelly criterion and its cousins – but we’ll also recognise the messy reality of actual trading which can only be seen by careful back-testing or live trading experience. My conclusion is that the goal is necessarily to optimise every cent of expected return but to stay in the game long enough to compound whatever edge you have. Survivors can compound wealth, the other 90% become cautionary tales that don’t get told.

Let’s start with the basics.

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Overview of Position Sizing Methods

I’m going to break the concept of position sizing into two groups and present them in two tables (non-exhaustive). These tables separate initial trade‑sizing techniques—methods that determine how much to risk on the first entry—from dynamic scaling rules, which adjust position sizes as trades evolve, account equity changes or market regimes shift.

I’m not smart enough to work out how to insert a table into Substack, so the following is a list of sizing techniques with their Method, Key Idea & Usage / Implementation:

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Fixed percentage risk (Fixed fractional)

Risk a constant percentage of account equity on each trade; size = (account × risk %) ÷ (stop-loss distance).

Typical example is to risk 1-2% of your account on each and every trade.

Can be implemented on stocks or futures. Generally, requires measuring the volatility (usually an ATR) of the contract, and setting a stop based on that volatility. A highly volatile stock will need to be given more room to move, and thus a smaller percentage of the account can be allocated to the trade so that the total loss on this trade is the equivalent to the loss on any other trade.

Very much the focus for trend followers who want to be as ‘non-predictive’ about the future as possible. Since the future is unknown, assign the same odds to every trade and wait for the outliers to carry you home. Already we can see that the emphasis is on managing your capital to survive, rather than trying to ‘read the market’ and ‘predict the odds on this trade’.

Suitable for stocks, forex and futures. This method normalises risk across instruments and market regimes by adjusting the position when ATR changes.

On the downside, you may have a data-driven reason that you feels provides compelling evidence that ‘some trades are better than others’ and are worth putting the pedal to the metal on.

Fixed fractional/Equity-based

Allocate a fixed fraction of total capital to each position (e.g., 5 % of account) regardless of stop distance.

Suitable for portfolios of stocks or ETFs. Amount invested per position remains constant as capital changes. Stops are secondary and would add an additional layer of thought.

The advantage of simplicity, and if it tests out that simple is as good as complex, go with simple.

Fixed contract size

Trade a predetermined number of shares/contracts; risk varies with price and stop distance.

Common in futures or when trading lots. A trader might always buy 1 contract or 100 shares; the monetary risk changes with stop-loss size and volatility.

Frequently an artifact of the fact that smaller account holders can’t trade less than 1 futures contract, since the contract values are so large. This generally means it’s a sub-optimal approach, but you have to work with what you have.

Common in prop shops and very short-term trading where other risk controls dominate.

Leverage-based

Size positions to maintain a target leverage ratio (e.g., 5:1).

Used in margin trading or leveraged futures; position size = (account × target leverage) ÷ price.

Just a variant of equity based really, beefing it up.

Kelly criterion / Optimal f

Use win rate and average win/loss to calculate the “optimal” fraction of capital to risk using the precisely optimised formula.

Academic method; maximises expected growth but can produce high drawdowns. Many traders use a fraction (e.g., half-Kelly) to reduce volatility.

Produces outstanding returns in theory (because it’s literally the mathematical optimum), opens up risks if reality doesn’t line up with the textbook.

Risk parity / Equal risk contribution

Allocate capital based on risk, not dollar amounts; each asset contributes equally to portfolio volatility.

Used by portfolio managers across asset classes. Weights are inversely proportional to each asset’s volatility and rebalanced periodically to maintain equal risk.

Usually, the idea is to maintain a certain overall volatility for the portfolio, and that (rather than strict profitability), becomes the focus. Think institutional fund manager.

Equal dollar weighting

Invest identical dollar amounts in each instrument.

Simple to implement for stock portfolios; makes rebalancing mechanical but may overweight smaller, more volatile names.

Sort of the stock equivalent of ‘fixed contract size’ for futures. Stocks don’t have the same limitation of futures however (since they are quite divisible) so, I’m not sure why you’d bother with this. Nevertheless, you often hear about it on the web.

Value-at-Risk (VaR) sizing

Limit positions so that the calculated VaR per trade or portfolio stays under a specified threshold. Used by institutional funds. Requires models of historical or parametric Value at Risk (think, ‘how much could I lose under a worst-case scenario); translates allowed loss into number of shares / contracts.

CPPI (Constant-Proportion Portfolio Insurance)

Maintain a floor (safe asset) and invest a multiple of the cushion (equity above the floor) in risky assets. Popular in asset-allocation strategies. When equity rises, the risky allocation increases; when markets fall, exposure shrinks to protect the floor.

Maximum drawdown control

Cap position size so that a worst-case losing streak cannot exceed a predetermined drawdown threshold.

Translate the allowable drawdown into a per-trade or per-day size cap; popular among hedge-fund managers and systematic traders to avoid “risk of ruin”.

Now we are thinking ‘real world’ rather than ‘expected probability’.

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This is definitely not an exact science, but now I’ll try and define position sizing concepts that pertain more to “how position sizing might change over time” (dynamic) as opposed to how to set “initial size”.

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Again, the below covers Method / Key idea / Usage / Implementation

Martingale

Double position size after each loss to recover previous losses.

High-risk approach sometimes used in gambling or small-stake strategies; increases tail-risk dramatically and can lead to catastrophic drawdowns. Most professional traders avoid it.

Anti-martingale (reverse martingale)

Increase size after a winning trade and reduce it after a loss.

Emphasises capital preservation. The trader uses profits to fund larger positions and resets to baseline risk after any loss. Suitable for trend-following strategies where long winning streaks can be exploited.

Pyramiding

Add to winning positions in increments; never add to losers. Start small (e.g., 1–2 % of capital) and add only when the trade moves in your favour, moving the stop to lock in gains.

Used by swing and futures traders. Helps compound gains in strong trends while keeping initial risk small. Requires clear rules for profit milestones and stop adjustments.

Equity-curve scaling

Adjust position size according to your trading equity curve: increase size when the equity curve shows statistically significant improvement and cut size when the curve weakens.

Turns the equity curve into a “governor” for sizing. Useful for systematic traders to capitalise on hot streaks and reduce risk during drawdowns.

Generally, every trader wants to scale as their account size scales in one form or another to maximise compounding. This can be more or less aggressive (e.g. you could measure your account size daily and change sizes accordingly, or you could size every trade the same for the whole year, see where you’re at come year end, and decide how much to increase your sizing then).

Dynamic volatility / edge / risk-adjusted sizing

Dynamically shrink positions when market volatility rises and expand when it falls; size trades based on setup quality (edge) and portfolio correlation.

Institutional desks might adjust position size according to ATR or VIX thresholds and stop distance. They might also cut size after equity drawdowns or sequences of losses, and cap exposures when correlations cluster.

Drawdown-based scaling

Reduce position size after a series of losses or when account equity drops by a set percentage; resume normal sizing only after equity recovers.

Helps traders survive losing streaks by preserving capital; widely used by discretionary and algorithmic traders to maintain psychological stability.

Equity-adjusted percentage risk

Recompute position size daily or after each trade based on current account equity; positions naturally grow or shrink as the account grows or declines.

Common for stocks and futures; automatically scales risk without changing the percentage; sometimes combined with pyramiding to increase size after winners.

A method of equity-curve scaling if you like.

Constant leverage rebalancing

Maintain a fixed leverage ratio by periodically rebalancing exposure; when equity grows, borrow more to maintain the ratio; when equity falls, reduce borrowed exposure.

Used by leveraged ETFs and futures funds; ensures constant volatility but requires strict margin monitoring to avoid forced liquidation.

Equal-risk contribution rebalancing (ERC)

Continuously rebalance so each asset’s marginal risk contribution stays equal.

In multi-asset portfolios, position sizes adjust as volatilities and correlations change. Similar to risk parity but applied dynamically to maintain equal risk contributions over time.

As an example, a winning trade which is becoming a massive outlier in your portfolio (perhaps making your whole year), will have its size reduced (reducing your profit if it continues its run) for fear of increasing the volatility of your portfolio.

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Lessons from the Academics: Martingale and Kelly Math

There’s a seductive appeal and yet hidden dangers of Martingale and Kelly sizing. In a toy example with a $100,000 account risking $1,000 per trade and a 60% win-rate, a pure Martingale strategy (doubling after each loss) can absorb at most six consecutive losses before the required next bet exceeds the remaining capital (the drawdown would be $63,000, leaving only $37,000 to attempt a $64,000 bet). The probability of six losses in a row in a 60/40 game is 0.4096 %, but over hundreds of trades the chance of encountering such a streak approaches certainty (ask GPT for the math). The P&L distribution becomes highly negatively skewed: many small gains and an occasional blow‑up.

So, even if your strategy is genuinely 60% winners, the probability you avoid a 6-loss streak over many cycles goes to zero. If you trade enough, you will eventually experience the exact loss pattern the Martingale cannot fund. Basically, you can only keep doubling while you can still fund the next bet. This is the market’s ‘table limit’.

To make it concrete, the expected number of 6-loss streaks:

For 100 trades:

• N=100: (95)(0.004096) ≈ 0.39 expected streaks

For 1000 trades:

• N=1000: (995)(0.004096) ≈ 4.07 expected streaks

So in 1,000 trades, you shouldn’t be asking “will it happen?” but “how many times?”

Let’s ask it this way, what’s the probability of at least one 6-loss streak?

A decent back-of-the-envelope is Poisson: P(≥1)≈1-e^(-(N-5)q^6 )

• N=100: 1-e^(-0.389) ≈ 32%

• N=1000: 1-e^(-4.07) ≈ 98%

Different approximations vary a bit, but the conclusion is stable:

Over a long enough sequence, the catastrophic streak is not a “risk.” It’s an appointment.

Looking at Kelly, in an even‑money 60% win‑rate scenario, full Kelly suggests risking 20% of the account per trade. A single loss drops equity by 20%, five losses by roughly 67%. Under realistic conditions – slippage, gaps, non‑stationary edges and clustered losses – such aggressive sizing is suicidal. Fractional Kelly (half, quarter or even one‑tenth) is more prudent.

Alternatively, you can pick a fixed risk per trade (1–2 %) and ask, “how many consecutive losses can I survive before my account hits my maximum drawdown?”. With a 2.5 % risk per trade, 20 losses reduce the account by about 40%. If you can handle that psychologically and financially, that risk level is acceptable; if not, size down.

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Enter Real Life – Markets are Full of Noise

Secondary risks (the stuff that kills real traders, not textbook traders)

Martingale math assumes a toy world. Trading is not a toy world.

1) Win rate is not constant

Your 60% is an estimate or an average over time. It says nothing about the path of those statistics in the short term. Regimes change. Execution changes. Slippage changes.

If the true win rate drops even a bit, the tail risk spikes.

Example: if win rate is 55% ⇒ q=0.45

0.45^6=0.0083

That’s about double the blow-up probability per cycle, from ~1/244 to ~1/120.

2) Loss sizes aren’t identical

Martingale assumes each loss is exactly “-$risk.”
Real trades have:

• gaps

• partial fills

• slippage

• volatility clustering

So the “6 losses = $63k” can become “6 losses = $80k” faster than you can say “liquidity”.

3) Risk-of-ruin is replaced by “risk of irrecoverable drawdown”

Even if you “survive” at $37k, you’re in a crater:

• You cannot continue the Martingale.

• Your required return to get back to $100k is: 100k/37k-1 ≈ 170%

That’s not “a setback.” That’s a new career.

4) Psychological liquidation

A 63% drawdown is where humans start inventing new religions.

Most traders:

• shut it down,

• change rules mid-stream,

• or revenge trade.

So the effective risk is worse than the math.

The core takeaway

A Martingale paired with a positive edge does not eliminate risk—it concentrates it into rare, catastrophic outcomes.

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But… Surely We Can We Capitalize on Probabilities?

Sure, people do it.

First, you have to have a very strong risk framework. You had better know when it’s time to pick up your chips and walk away.

Second, you have to have a data-driven reason for assigning different probabilities to different trades. Now, I don’t think this is unreasonable at all. Most traders would agree long trades are less profitable in bear markets than in bull markets. Listening to Michael in this interview tells me he’s done an extraordinary amount of work on these two points. Prop traders and many discretionary traders also behave exactly the same way. They press hard into ‘A-grade’ trades, and fall back after a series of losses, or happily stand aside when conditions are not suited to their trading style.

In order to keep it short, I’ll reserve for members inside the Algo Collective the 30-minute deep-dive I did with Michael to really get into the rules of his strategies. I’m also happy to chat about the differences for futures versus stock traders, longer-term versus shorter-term, etc.

So, what’s my perspective?

Forget the academics, forge a path for survival, bring risk of ruin to zero, build additional skills over time. Stay in the game to compound your edge.

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A Practical Framework for Sizing

Thinking about position sizing requires balancing three competing forces:

1. Mathematical optimality (Kelly) – The Kelly criterion maximises the expected rate of growth but is highly sensitive to estimation errors and assumes independent, identically distributed outcomes. Use it as an upper bound for how aggressive you can be. For example, if your backtest suggests a Kelly fraction of 20%, you might cap your risk at one‑eighth of that (~2.5%) to allow for estimation error and regime changes.

2. Drawdown survival (streak‑based) – Decide how big a drawdown you can stomach. If a 40% drawdown would force you to quit or drastically change your strategy, calculate the position size that makes a 20‑loss streak produce no more than 40% damage. This implicitly sets your risk per trade and provides a psychological anchor. In futures, you can translate a 1% risk into a number of contracts; in stocks, you can determine how many shares that risk represents given your stop distance.

3. Take a portfolio-based approach – the more strategies across the more markets you trade, naturally reduces bet sizes on each contract and on each strategy. You maximise your real-world capability of survival by diversification and trading an ensemble of strategies.

4. Real‑world noise – Win rates and payoffs drift, trades are correlated, and losses cluster. Add a safety factor by sizing for the worst plausible regime, not the average one. That might mean using fractional Kelly on pessimistic estimates of win rate and payoff, or sticking to a fixed percentage regardless of perceived edge. Keep an eye on volatility – if the market becomes wild, reduce size even further.

Survive First, Thrive Later

Position sizing is not about finding the magic number that maximises every theoretical dollar. It’s about staying alive. If you blow up your account, no future edge can save you. When evaluating any sizing rule:

• Run back‑tests or Monte Carlo simulations on your strategy, focusing on worst‑case losing streaks and drawdown depth, not just average returns.

• Account for slippage, gaps, changing win rates and fat tails. Rus stress tests and you’ll see how small deviations in win rate can dramatically increase blow‑up risk for both Martingale and Kelly strategies.

• Choose a sizing rule appropriate for your instrument. Futures traders should consider contract specifications and margin; stock traders should consider gap risk and diversification; long‑term investors might emphasise risk parity or equal weight; high‑frequency traders might lean towards very small fixed percentages.

• Be consistent. Constantly switching sizing methods because of emotions or recent results undermines the statistical edge of any strategy.

Above all, remember: your trading career is a marathon, not a sprint. Reality rarely matches the neat curves of a spreadsheet. “Optimal” f derived from a formula means nothing if you’re forced out of the game by a nasty losing streak or a market regime change. Know the math – it will inform your intuition and give you upper bounds. But then size so that you can survive the worst‑case scenarios, because only those who stay in the game long enough can compound their gains and eventually thrive.

Here’s to thriving!

Simon

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