“Two investors can run the same trades. Only one of them had to be right about anything.”
Compounding is one of those ideas in finance that sounds simple until you actually live through it. A return is not earned in isolation. It lands on whatever capital survived the returns that came before it.
That makes the path important.
Suppose you lose 50 per cent. You now need 100 per cent on what remains just to get back to where you started. Nothing about the average return captures that asymmetry. Wealth compounds through a sequence, and the sequence determines how much capital is still available for the next return to act upon.
This is the companion piece to Two Roads to a High Sharpe. It also sits naturally beside the Risk Is Not Variance series, because I need to make an important distinction before we go any further.
I do not regard volatility as risk.
Nor do I regard the Sharpe ratio as a complete measure of risk-adjusted performance. Volatility tells us something about the dispersion of returns. Sharpe tells us how much return was earned relative to that volatility. Both can be useful. Neither tells us the path an investor actually had to survive.
I use them here for a narrower purpose.
If two sizing methods are run at very different levels of volatility, comparing their terminal wealth tells us little about the sizing method itself. One may simply be taking a bigger ride. Matching realised volatility allows us to remove that obvious scaling difference.
It does not make the two portfolios equally risky.
That distinction matters.
The question I want to answer is a different one:
How much do we need to know in order to size the journey?
The Kelly criterion gives us a useful place to start. In its classical form, Kelly chooses the fraction of capital that maximises expected logarithmic growth. If the probabilities and payoffs are known, the mathematics is elegant.
Markets give us a harder problem.
The edge is not handed to us. We have to estimate it from a finite sample drawn from a world that keeps changing.
A classic trend follower can take a very different route. Rather than deciding that one market or one recent estimate deserves more capital, each position is given the same small loss budget.
Throughout this article, that loss budget means the fraction of capital exposed if price moves from entry to the initial stop. I am not using the word “risk” as a synonym for volatility.
The loss budget is known.
The future edge is not.
So I wanted to test a simple question on the actual trade history:
After all the estimation required by Kelly, what did it buy?
Figure 1.The same 6,321 Donchian breakout trades across 68 futures markets from September 1984 to July 2026, sized three different ways. The top panel shows the aggregate capital-at-stop exposure created by each sizing method through time. The second panel shows compounded equity, and the third shows drawdowns. The lower-left panel shows how the realised edge changed by decade. The lower-right panel shows 4,000 six-month block-bootstrap comparisons of the Sharpe difference between Kelly and the fixed-loss-budget approach after their realised volatility has been matched. Volatility is matched here as a scaling control, not as a definition of risk.
The first number fools you
Begin with the result that is easiest to sell.
Apply the re-estimated Kelly rule to these trades and one unit of starting capital becomes 137.3.
Run exactly the same trades with a fixed loss budget of 0.25 per cent of capital per position and it becomes 7.7.
At first glance that looks devastating. Kelly finishes with roughly seventeen times as much terminal wealth, using real market prices over more than four decades.
But it is the wrong comparison.
Kelly ran at 19.2 per cent annualised volatility. The 0.25 per cent fixed-loss-budget book ran at only 6.9 per cent.
We have changed two things at once: the sizing rule and the scale of the ride.
If one portfolio is allowed to run at almost three times the volatility of the other, terminal wealth cannot tell us how much of the difference came from the sizing intelligence and how much simply came from taking more exposure.
So we need to remove that difference first.
Match the volatility, not the risk
This distinction is important enough to put in the heading.
I am not going to “match the risk”, because volatility is not risk.
I am going to match the realised volatility.
Increase the fixed loss budget until the resulting portfolio carries approximately the same realised volatility as Kelly. In this sample that occurs at 0.72 per cent of capital per position.
The trades themselves do not change.
Only their size changes.
Now the apparent Kelly advantage disappears.
At virtually the same realised volatility, the fixed-loss-budget book finishes at 176.2 times starting capital versus 137.3 for Kelly. Its CAGR is 13.2 per cent versus 12.5 per cent. Its Sharpe is 0.72 versus 0.69. Its worst drawdown is 57 per cent versus 60 per cent.
That does not prove that fixed sizing is intrinsically superior. The differences are too small for that claim.
What it does show is something more useful.
The spectacular terminal-wealth advantage in the first comparison disappears once we control for the scale of the ride.
And notice what I am not saying.
I am not saying the two portfolios now carry the same risk because they have the same volatility. They do not necessarily have the same risk at all. They have simply been placed on a comparable volatility footing so that scale is no longer an obvious explanation for the difference in terminal wealth.
That leaves us with the sizing decision itself.
And there is no visible reward for having estimated a supposedly optimal fraction at every entry.
What does Sharpe tell us here?
The Sharpe ratios are also worth looking at, but for a very specific reason.
The fixed-loss-budget approach produces a Sharpe of 0.72 at both the lower and higher sizing levels. Kelly produces 0.69.
I have spent considerable time elsewhere explaining why Sharpe should not be mistaken for a complete measure of risk-adjusted performance. It divides return by volatility, and volatility is not the same thing as the risk an investor actually experiences.
But that does not make Sharpe useless.
Here it gives us a conventional return-to-volatility scoreboard. Nothing more.
That is useful because Kelly is supposed to improve the way capital is allocated. If all that estimation is adding something valuable, we might reasonably expect some trace of it to appear even on this conventional measure once the portfolios are being compared at similar volatility.
The observed Sharpe difference is only 0.031 in favour of the fixed-loss-budget book.
Can we distinguish even that?
Can we tell the rules apart?
To get some sense of the uncertainty, I resampled the daily return record 4,000 times in six-month blocks.
I used blocks rather than individual days because market returns do not arrive as completely independent observations. Keeping chunks of the original record together preserves more of the structure of the path.
The 95 per cent bootstrap interval for the Sharpe difference runs from about -0.27 to +0.35. The fixed-loss-budget approach finishes ahead in 58 per cent of those resamples.
Put simply, even on the conventional Sharpe measure, the evidence is nowhere near strong enough to say that either sizing rule produced a reliably better return per unit of volatility.
After 42 years, 68 markets and 6,321 trades, I cannot distinguish the two sizing methods on conventional return-to-volatility performance with any confidence.
That is not evidence that Kelly is bad.
It is evidence that, in this test, all of the additional estimation failed to produce a measurable improvement even on the conventional scoreboard.
For me, that is the more interesting result.
Complexity has to earn its place.
If I add an estimate, I want evidence that the dependency it creates is buying me something.
The data problem is structural
You might think 42 years of futures history should settle a question like this.
It does not.
The problem is not simply the length of the calendar. It is the number of independent opportunities a medium-term trend system actually produces.
Trend following is deliberately patient. That patience is part of the problem for anyone trying to estimate an edge precisely.
The system tested here enters on a 120-day Donchian breakout, exits on a 60-day reverse breakout and uses a trailing stop five times the 20-day Average True Range.
Positions are therefore given room to move.
The median holding period is 42 days.
Across all 68 markets, the entire 1984 to 2026 record produces 6,321 trades, or about 94 trades per market on average.
Forty-nine of the 68 markets do not even reach 100 trades in their full available history.
That makes a sensible per-market Kelly estimate extremely difficult to test. If I use enough past trades to estimate the edge, very little independent history remains to judge the estimate.
The version used here is therefore struck at the book level from the trailing 50 closed trades across all markets. It gives Kelly considerably more data to work with than a market-by-market implementation would have.
There is a deeper tension here.
Trend following earns its living from a relatively small number of unusually large trends. Wide exits and loose stops are intended to keep us aboard those moves.
But the same design produces fewer observations.
The more the strategy depends on rare outliers, the less precisely its payoff distribution can be estimated from recent history.
There is something wonderfully awkward about that.
The observations that matter most are precisely the observations we have least of.
That is not a flaw in the database.
It is a consequence of the strategy we chose to trade.
The edge would not sit still
The lower-left panel makes the estimation problem visible. It shows the mean R-multiple per trade by decade.
One R is the initial loss budget assigned to a trade, so a result of +0.20R means the average trade earned one fifth of the amount initially exposed to the stop.
The decade ending in 1995 averaged +0.2898R per trade. By the decade ending in 2025 it was +0.0211R.
More importantly, the recent annual readings move around zero rather than tracing a smooth decline: +0.45R in 2021, -0.16R in 2023, -0.09R in 2024 and -0.13R in 2025.
This matters because Kelly is only as good as the inputs it receives.
In the test, the fraction is recalculated from the most recent 50 closed trades. Across the full record that estimate ranged from 0.000 to 1.086.
A number can be calculated to several decimal places and still describe a moving target.
Precision in the calculation is not the same thing as certainty about the world that generated the data.
The fixed-loss-budget rule avoids that particular problem.
It does not assume the edge is constant, nor does it pretend to know its current value.
It simply decides in advance how much capital a single trade is allowed to lose before the initial stop says the trade is wrong.
What does the extra dependency cost?
There is no catastrophe to report for Kelly in the main specification.
It survives the full sample and compounds strongly.
On the conventional return-to-volatility measures used above, it is statistically indistinguishable from the volatility-matched fixed-loss-budget approach.
Again, that is not a statement that their risks are identical.
The paths are not identical. Their drawdowns are not identical. Their sequences of gains and losses are not identical. Matching volatility cannot make those differences disappear.
It merely removes one scaling difference so that we can ask whether all the extra estimation improved the sizing decision.
The issue is not that Kelly blew up.
The issue is what we had to assume in order to use it.
Every new trade requires an estimate of the recent payoff distribution, and the position size then depends on that estimate being useful.
The fixed-loss-budget rule has no equivalent dependency.
More importantly, the result is sensitive to nearby system specifications.
Tightening the stop from 5 ATR to 4 widens the Sharpe difference from 0.031 to 0.127 in favour of fixed sizing.
Changing the breakout windows from 120/60 days to 100/50 widens it to 0.253. On that neighbouring specification Kelly finishes at 14.3 times starting capital while the volatility-matched fixed-loss-budget approach finishes at 118.3 times.
Those neighbouring tests do not prove that fixed sizing will always win.
They do tell us that the apparent optimality becomes fragile once the inputs have to be estimated from real, finite and changing data.
That distinction matters.
Kelly’s theoretical attraction comes from maximising long-run logarithmic growth under a specified return distribution.
The market implementation has an extra layer.
First estimate the distribution.
Then decide how much real capital to expose on the assumption that the estimate tells you something useful about what comes next.
Once the inputs have to be estimated rather than known, estimation error becomes part of the position.
For a systematic trader, that leaves a practical hurdle.
If an added estimate cannot be shown to improve the outcome, can hurt materially under nearby assumptions, and introduces another quantity that can drift, I need a very good reason to make the portfolio depend on it.
Why I call this the compounder's delight
The attraction of classic trend-following position sizing is not that it has discovered the true edge.
It is that it can function without pretending the true edge is knowable in advance.
Each market receives the same small loss budget.
I do not need to decide that gold currently deserves twice the conviction of copper, or that a recent run of profitable trades means the next signal deserves more capital.
I can be wrong about which market trends next and still have the position on.
I can be wrong about the size of the future edge and still control how much capital I initially expose if the trade fails.
And if I want a more aggressive return target, I do not need a new forecasting engine.
I can increase the common loss budget knowingly.
In this test, moving from 0.25 per cent to 0.72 per cent per position lifts the fixed-loss-budget book to roughly Kelly’s realised volatility.
That does not make the two portfolios equally risky.
It simply gives us a cleaner comparison.
At that comparable level of volatility, the fixed approach compounds at least as well in the historical sample without making position size a function of a freshly estimated edge.
That, to me, is the delight.
Compounding does not reward intellectual decoration. It rewards capital that survives long enough to remain available when the large payoff finally arrives.
And this is where the argument reconnects with Risk Is Not Variance.
Volatility describes dispersion.
Sharpe describes return relative to that dispersion.
Neither tells me whether I can survive the path.
The path is where drawdowns happen. It is where losses arrive in sequence. It is where estimates fail, positions are sized, capital disappears and future opportunities either remain available to me or they do not.
A simple sizing rule cannot remove that uncertainty.
But it can reduce the number of uncertain things upon which my survival depends.
Perhaps that is the more useful form of optimisation.
Not extracting the theoretical maximum from a future I cannot know.
Remaining exposed to the future long enough for the outlier I cannot predict to matter.
The next question follows naturally.
If estimating the edge adds so little here, where in a systematic process does estimation genuinely earn its keep?
Why I rebuilt the article
A note on this revision, 11 August 2026.
This article was previously published on the ATS website using a simulated return stream. I no longer think that was good enough for the point I was trying to make, so I have rebuilt the analysis from the ground up using real futures data.
The simulation reproduced the broad shape I wanted: a low hit rate, a long positive tail and changing regimes.
But the edge itself was still a parameter I had chosen.
That created a circularity. Leveraged terminal wealth is highly sensitive to the assumed edge, so some of the most impressive results were simply the simulation returning my own assumption to me rather than telling me anything new about markets.
The simulation also imposed a correlation structure rather than allowing cross-market relationships to behave as they actually did through time.
The replacement uses Donchian breakout trades across the same 68-market futures universe used in Risk Is Not Variance. Whatever edge appears is the edge the historical breakout system actually delivered, including its deterioration and its bad periods. The cross-market behaviour is whatever occurred in the data.
I also corrected two errors in the original.
The figure caption gave the diversified book an average pairwise correlation of 0.32 when the correct number was 0.21.
More importantly, the diversified book had been run at roughly half the per-trade loss budget of the concentrated positions used for comparison. That was not like-for-like.
Matching realised volatility is therefore not a footnote in this version.
It is the central control.
And to be clear one final time: I match volatility because I need to control for scale, not because I believe volatility is risk.
The original also suggested that one figure had isolated the effect of sizing from the effect of diversification. It had not, because one of the lines changed both at once. That claim has been removed.
The replication code published with this revision supersedes the original analysis.
This analysis is illustrative and provided for information only. It is not investment advice and it is not a claim about the expected returns of any particular trading program. Results are gross of commission, slippage, financing and roll costs, so absolute historical returns would be lower after implementation costs. Because the same underlying trades are used in the sizing comparison, common trading costs do not explain the relative result. Past performance is not indicative of future results.
Richard Brennan writes on systematic trading, complex adaptive markets, and the philosophical foundations of trend following at atstradingsolutions.com. His books include The Fractals of Finance, Complex Adaptive Markets, Carved by Impossibility and The Aussie Turtles Trend Following Guide.
Want to explore why structure exists at all?
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Want the theoretical foundation for why trend following works?
The Fractals of Finance: Determinism, Adaptation and the Geometry of Markets bridges complexity science with practical trading implementation. With a foreword by Jerry Parker, original Turtle Trader.
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