The 1% Rule, Computed

One division, and the fraction is the whole system

The formula is short enough to do in your head, and the reason it needs restating is that its inputs are routinely swapped. The risk budget is the account multiplied by the risk fraction — $100,000 at 1% is $1,000. The risk per share is the entry price minus the stop, which is a measurement of the chart rather than a preference. The number of shares is the budget divided by the risk per share, and everything else — notional, position as a percentage of capital — falls out of that. Work an example both ways to see what the fraction controls. With a $10,000 account, 1% risk and a stop 5% below the entry, risk per share is $2.40, so the budget of $100 buys 41.7 shares and a $2,000 position: 20% of the account carrying a hundredth of its risk. Halve the stop distance and the same budget buys twice the shares; double the account and it buys twice the shares; raise the fraction to 2% and every number doubles. Only the fraction changes what is at stake — the rest change how it is expressed. The classic alternative, a fixed number of shares or a fixed dollar amount per trade, fails for the same reason a fixed percentage stop fails: it says nothing about where the invalidation is. On a name with a 15% structural stop, a fixed 500 shares might risk 7% of the account; on a name with a 3% stop the same 500 shares might risk 1.5%. The rule cannot be evaluated without the chart, which is why the fraction is the input and the count is the output. The same budget, three stops — Stop 2.5% away — $1.20 a share: 83 shares, a $4,000 position · Stop 5% away — $2.40 a share: 41.7 shares, a $2,000 position · Stop 10% away — $4.80 a share: 20.8 shares, a $1,000 position ← · What stays fixed through all three: the $100 at risk Notice the inverse relationship: wider stops shrink the position automatically. That is how the chart, and not the trader, ends up deciding how much is owned.

Why 1% rather than 10%

The argument for a small fraction is not caution, it is the streak arithmetic. Even a good system loses several trades in a row regularly — at a 45% win rate, eight losses in a row turns up in about 85% of five-hundred-trade samples — and the same streak leaves wildly different accounts depending on the fraction. Eight losses at 1% a trade leave 92.3% of capital, which is an uncomfortable week. At 5% they leave 66.3%. At 10% they leave 43.1%, and recovering that needs 132% — you have to more than double what is left, on a system whose edge is a tenth of an R. The simulation in this lesson puts the two halves together on one set of trades. Expectancy stays at +0.125R at 0.5%, 2%, 10% and 20%, because expectancy is a property of the strategy and not of the size. Meanwhile the median account at 1% finishes at 1.26 times its starting capital, and at 20% it finishes at 0.19 times, with 65% of the accounts ruined along the way. A larger size raises the median for a while — there is more capital working — and then destroys it, because the drawdowns compound against a shrinking base. That is the shape to carry into the rest of the subject. There is a range of sensible fractions rather than a magic number: some households run 0.5% in a volatile book, some 2% in a diversified one, and the honest test is whether the sizes you would have to use in a bad month leave you able to trade the next month. The rule to write down is not "1%" but "risk a fixed small fraction, computed from the stop, and never let conviction change it". Eight losses in a row, from the streak arithmetic — 1% risk per trade: 92.27% of capital left · 5% risk per trade: 66.34% left · 10% risk per trade: 43.05% left, needing +132% to recover ← · What did not change: the edge, the trades, the sequence Sizing by conviction has no units. "I am very confident" cannot be divided into a risk budget, and every version of this mistake — a bigger position because the setup looks perfect, a smaller one because it feels uncertain — reintroduces the guess the fraction was there to remove.

The other half of the fraction: how many at once

The risk fraction decides what one position can lose. It says nothing about what the book can lose, and a book of small positions taken together can carry more risk than a single large one. The bridge between the two is the number of simultaneous positions: if each is sized to risk one percent and the book holds six, the total open risk is six percent, and that is the number that decides how bad a genuinely bad day is. The one-percent rule is a per-trade rule and it is only safe in combination with a portfolio-level cap on the sum — the subject of the heat lesson. The second thing the fraction interacts with is the **stop distance**, and the interaction is the reason the rule is expressed in risk rather than in shares. A wider stop on the same account means fewer shares for the same risk, so the position shrinks as the stop moves away; the dollar risk stays fixed and the exposure varies. This is why equal-dollar positions are a different strategy from equal-risk positions, and why the same view on the same stock can be held at very different sizes by two people who agree about everything except where the idea would be wrong. The third is that the fraction has a **lower bound set by costs and an upper bound set by ruin**. Size too small and the fixed costs of trading eat the edge, since the spread is paid in percentage terms regardless of the size. Size too large and the arithmetic of streaks does the work the strategy was supposed to do: at a given win rate, a run of losses that is not unusual in a hundred trades will remove a fixed fraction of the account, and the fraction compounds downward in a way that gains do not. The correct fraction is therefore found by asking what the worst plausible run costs, not what the best plausible run earns — which is exactly the calculation in the streak lesson, and the reason this lesson’s workbench has a size slider rather than a formula. • Risk per trade times number of positions is the book’s open risk — cap the sum, not just the trade. • A wider stop means fewer shares for the same dollar risk; the risk stays fixed, the exposure changes. • Too small and fixed costs eat the edge; too large and a normal losing run decides the outcome. • Choose the fraction from the worst plausible run, not from the best plausible one.

What a smaller fraction actually buys, and what a larger one costs

The ruin rates in this lesson come from a simulation, and the same relationship has a closed form that makes the trade-off legible without a workbench. For a fixed-fraction bet with a known edge, the probability of eventual ruin is approximately a function of how far the chosen fraction sits from the growth-optimal one: as the fraction approaches the **Kelly** optimum from below, the expected growth rate rises and the time-average wealth path improves, and as it passes the optimum the growth rate falls and the ruin probability rises until, at a large enough fraction, ruin becomes certain even with a positive edge. The intuitive version is the one worth carrying: the fraction controls how much of the edge you harvest, and past the peak it controls how quickly the streak that ends the account arrives. There is no fraction at which a positive edge is guaranteed to pay, because the path is what the holder experiences and the path includes streaks. What a smaller fraction buys is not safety in the sense of avoiding loss — it buys **time**, and time is the input that expectancy needs. The lesson’s own numbers show the exchange rate: moving from 1% to 0.5% per trade halves the arithmetic return that the same edge produces in a perfect sequence, and it roughly halves the depth of the worst drawdown the account has to survive, which is the variable that decides whether the strategy is still running when the edge expresses itself. Two consequences follow that the simulation does not show. The first is that the *expected maximum drawdown* of a strategy scales roughly with the fraction: a system with a 10% expected drawdown at 1% risk will show something near 5% at half a percent and near 20% at two percent, so the fraction should be chosen by asking what drawdown can be held without abandoning the process — and then converting that into a fraction, rather than choosing a fraction and discovering the drawdown. The second is that the fraction has a **floor**: the fixed costs of trading, the spread and the commission, are paid in proportion to the notional traded, so a fraction small enough to make each trade economically meaningless turns a positive edge into a flat line after costs. The final piece is the reason 1% is a convention rather than an optimum. The growth-optimal fraction from R9 is the size that maximises the long-run growth rate of a *known* edge, and the edge is not known — it is estimated from a sample with an error, as the expectancy lesson showed. When you optimise against an estimate rather than a parameter, the optimum you compute is systematically too large, because the estimate’s error is highest in the strategies that looked best. That is why every practical sizing rule is a **fraction of the theoretical maximum**, and why the fraction is chosen to survive the error in the estimate rather than to maximise growth against it. The 1% rule is not a law of markets; it is a widely used number because it keeps the expected drawdown of a modest-edge strategy within the range a person can actually hold, which is the same reason the whole subject prefers it to a formula. The same edge, three fractions — 0.5% per trade: Half the arithmetic return and roughly half the expected drawdown of the 1% case · 1% per trade: The convention: a drawdown shallow enough to hold through a normal streak ← · 2% per trade: Double the return, roughly double the drawdown — and the point where behaviour starts to break · Past the growth-optimal fraction: Growth falls and ruin probability rises, with the edge unchanged ← The pair of questions that produce a fraction without a formula: what is the deepest drawdown I will hold through without changing the process, and what fraction of a modest edge produces that drawdown? The first question is psychological, the second is arithmetic, and the order matters — sizing from the arithmetic upward produces a number the holder cannot live with.

Sources

• Fixed-fractional risk and the arithmetic of survivalVan Tharp, "Trade Your Way to Financial Freedom"
• Risk of ruin and why oversized bets end accountsRalph Vince, "The Mathematics of Money Management"
• Why the share count is an output of the risk budgetElder, "Come Into My Trading Room"
• The cost of overconfidence in position sizeBarber & Odean, "Trading Is Hazardous to Your Wealth" (2000)