Equal Risk, Unequal Size

Risk, not dollars

R5 answered the question for one position; a portfolio asks it several times over, and the answer is not "the same amount in each". Risk is position size multiplied by the stop distance, so a book where every holding is the same dollar amount is a book where each holding risks a different share of capital — and the most volatile one risks the most. On a set of stops placed at a constant multiple of ATR, the positions that fall furthest before the thesis breaks end up with the smallest notionals, which is exactly the behaviour that keeps one holding from deciding the month. Volatility-based sizing makes that mechanical rather than judgemental. Place each stop at **k × ATR** for the timeframe you trade — two is the customary starting point — and compute each position from the same risk budget. The count is then a function of how far this instrument travels, so a fast name gets fewer shares for the same risk. The method also makes the stops comparable across holdings: a stop 2 ATR away on one name and 8 ATR away on another is not one rule applied twice, it is two different rules, and the second one is risking four times as much capital per unit of the instrument’s own movement. There is a limitation worth stating in the same breath. ATR is estimated from a window of recent bars, so it is a description of the recent past rather than a property of the future: it rises when a name becomes volatile and falls in quiet periods, and it does so after the change rather than before. Position sizes therefore move around as the estimate moves, which is correct behaviour — a name that has become twice as volatile should be half the size — but it means the sizing rule is not a constant and should not be treated as a number you set once. Recomputing the ATR as part of the review cycle is how the rule stays honest. One $750 budget, three instruments — AAA: 2 × $1.00 stop, $2.00 a share: 375 shares, $18,750 · BBB: 2 × $3.60 stop, $7.20 a share: 104 shares, $12,500 · CCC: 2 × $0.56 stop, $1.12 a share: 670 shares, $18,750 · Risk if any one is stopped: $750 — identical ← 500 shares of BBB — a count that looks conservative next to CCC — would risk $3,600, nearly five times the budget. The share count is not a measure of risk; the count times the stop is.

What changes when the whole book is sized this way

The first effect is on the shape of the outcome distribution. When every position carries the same risk, no single holding can dominate the month, and the book is diversified in the dimension that actually matters — how much each idea can cost. Equal dollar weights leave the volatile holding carrying both the position and the risk, which is diversification that only appears to work: several names, one of them deciding everything. The second effect is on the review conversation. With a uniform risk rule, the question after a loss is not "how much did that position cost" but "was the stop in the right place", because the size is by construction not the variable. That is what makes the R4 discipline of placing stops at invalidation affordable: if a far-away stop simply produces a smaller position, there is no pressure to move the stop closer to keep the size, which is the adjustment that quietly converts a plan into a hope. The third effect is on what is left when several positions fail together. A book where every name risks 0.75% loses 0.75% per stopped position, so the maths of a bad day is addition rather than surprise — five stops is 3.75%, which the portfolio heat cap in R11 then limits directly. Without a uniform risk rule that number is not knowable in advance, and a risk limit that cannot be computed is not a limit. Equal dollars against equal risk — $12,500 in each of the three names: $1,500 risk on BBB, $250 on AAA · $750 risk in each of the three: notionals of $18,750, $12,500, $18,750 ← · What the second version buys: no position can decide the month ATR describes the recent past. A name that has just become volatile will size smaller only after the estimate has moved, which is why the rule is recomputed on a schedule rather than set once — and why a sudden regime change is a reason to reduce the whole book rather than to trust one window.

Where the ATR rule quietly breaks

Average true range is a measure of **range**, not of dispersion, and the difference matters when you use it as a stand-in for risk. It is computed from highs, lows and closing gaps over a chosen window, so it depends entirely on the timeframe you measure it on: a stock’s daily ATR and its weekly ATR describe different things, and a stop sized from the daily figure on a position you intend to hold for a month is comparing two different clocks. The practical discipline is that the ATR window should match the holding period — the volatility that matters is the volatility over the time you expect the position to live, not the volatility of a chart you happen to have open. Ranges also understate the risk that hurts most, because a gap is not a range. ATR is built from prices that traded, and an overnight gap from $60 to $48 never printed anything between the two, so the true range that day records the gap but the average is still anchored in ordinary days. When a position gaps through its stop, the realized loss is a multiple of the ATR-sized risk, and no amount of careful averaging changes the fact that the distribution has a fat tail the average does not describe. That is the reason this lesson’s sizing rule is a starting point and the gap lesson’s stress test is the check: size to the ATR stop, then ask what the position costs if it opens below it. The third break is the one that is invisible position by position. Sizing each position to the same risk produces a book whose total risk is **not** the sum of those risks, because the positions move together to some degree; five names sized to $750 of risk each can carry $3,750 of risk in a bad day for their shared sector, or as little as $1,500 if they are genuinely independent. Equal-risk sizing is a per-position rule, and a portfolio rule has to be layered on top of it. That layering — counting drivers rather than positions — is what the correlation lesson supplies, and the two rules only work as a pair. • ATR is timeframe-dependent: match the window to the expected holding period. • It measures range, not the size of a gap through the stop. • Equal risk per position does not mean equal risk for the book. • Layer a portfolio-level rule (drivers, caps, total heat) on top of per-position sizing.

Volatility targeting, and why it feels wrong

Sizing each position by its own volatility is the position-level version of an idea that professional funds apply to whole portfolios: choose a level of volatility to run, and scale exposure inversely to what the market is currently delivering. Both rest on the same fact — volatility clusters, so the recent past is a usable one-period forecast — and both trade the same thing away. The mechanics are simple to state. Estimate realised volatility over a window of a month or a quarter, compute the exposure that would bring the book’s expected volatility to the target, and rebalance on a schedule or when the deviation gets large enough to matter. When volatility rises, the exposure falls and the book de-risks on its own; when volatility falls, the book adds exposure. The result, documented across futures and equity indices, is a return stream with a more stable risk profile and a shallower maximum drawdown than the unscaled version of the same strategy. The reason it feels wrong is the timing of the trades, and it is worth being blunt about it. The rule sells into weakness and buys into calm. When volatility spikes, it cuts exposure — often immediately before a sharp reversion, so the insurance is paid in visible, badly timed trades rather than in a fee. A trader who cannot watch that happen without overriding the rule does not have a volatility target; they have a target they abandon on the day it is doing its job. Four trade-offs belong beside the idea. **Procyclicality**: if enough capital runs the same rule, the de-risking adds to a selloff, which is a genuine systemic concern rather than a private one. **The lag**: the window is backward-looking, so the scaling is always late to a change of regime — the first days of a shock are taken at full size. **Turnover**: frequent rescaling pays the spread repeatedly, which makes the window length and the rebalance band cost decisions as much as risk decisions. And **leverage**: hitting a fixed volatility target in a calm market can require borrowing, which introduces a funding risk — the possibility of a forced reduction — that the unlevered version never faces. The practical version is therefore modest. Use a wide estimation window, rebalance in bands rather than continuously, cap the exposure at one for an account that cannot be forced to sell, and judge the result on the drawdown rather than on the average return, because the average is not where the benefit lives. Volatility targeting does not make a strategy better; it makes its shape more survivable, which for an account that has to stay in the game is the more useful property. • Scale exposure inversely to recent realised volatility, and rebalance in bands. • The benefit shows up in the drawdown and the path, not in the average return. • The cost is badly timed trades: it cuts into spikes and adds into calm. • Lag, turnover, procyclicality and leverage are the four prices of the approach. A volatility target and a fixed fractional risk rule are not substitutes: the first controls the book’s day-to-day swing, the second controls the loss on any single idea. A serious account uses both, and needs to know which one is binding when they disagree.

Sources

• Average True Range and volatility-scaled stopsJ. Welles Wilder, "New Concepts in Technical Trading Systems" (1978)
• Equal-risk position sizing across a portfolioVan Tharp, "Trade Your Way to Financial Freedom"
• Why equal weights are not equal risk in a volatile bookStandard portfolio-construction literature; CFA Institute readings
• Volatility clustering and why ATR is estimated over a windowEngle, ARCH and volatility-clustering literature (1982)