From instrument loss to portfolio loss
If a hypothetical position is 12% of initial portfolio value and loses half its value while other holdings stay unchanged, portfolio result is minus 6%. At 3%, the same position loss gives minus 1.5%. This limits one event’s influence; it does not improve the instrument.
The calculation does not set the probability of loss or prove other holdings remain still. If all positions share demand or financing, common stress is stronger. Position analysis must include joint events; counting names does not measure them.
A loss budget is not a rule
If a model limits contribution to two percentage points and position stress is 40%, 0.02/0.40 gives 5%. This follows from the chosen model and is not a recommended reader limit.
If the actual loss is 100%, the result changes. If the asset rises and its weight grows, initial arithmetic no longer describes current risk. A “limit” without scenario and date creates false confidence; a weight cap cannot guarantee a capped loss in every event.
Look through wrappers
Direct shares and fund units may contain the same economic exposure. Separate lines tied to one corporate group are not necessarily independent. FINRA warns that holding only funds does not eliminate concentration; inspect overlapping holdings.[103](#source-cv-concentration) If disclosure is incomplete, mark the unknown share instead of assuming diversification.
Build a map: position, issuer, group, sector, revenue currency and financing source. It need not turn every dependency into a precise coefficient; it should find a scenario affecting several lines at once.
Volatility sizing has limits
Mechanically reducing a more volatile asset can lower one statistic while missing other risks. A rarely revalued asset may look calm although exit is difficult. Joint dispersion depends on covariances, not only individual volatility; Sharpe’s portfolio formula illustrates this.[104](#source-cv-covariance)
Do not enlarge a position merely because recent history is calm or the analyst feels confident. Confidence is not a measured probability. Record information that could disprove the thesis and how wrong the stress scenario could be.
The practical output is a table of current weights, individual and common stresses, access conditions and unknowns. Position size does not repair a bad asset, prevent a joint crisis or replace maturity analysis. It makes consequences of assumptions visible.
Control weight changes without a trade
A position can become larger relative to the portfolio after a strong rise or withdrawals elsewhere. Record the calculation date and recompute stress contribution on the actual base, showing external cash flows separately.
Check exit capacity. The same portfolio percentage may require very different sale times in markets of different depth. A loss-based size limit does not guarantee bids at the needed time. Mark this as a condition without inventing an execution price.
A scenario loss is not a maximum. Beyond it may lie a larger loss, simultaneous declines and changed access. Label the result so one calculated weight does not masquerade as the whole risk analysis.
Related foundations: [Diversification: independent causes, not name counting](/guides/diversification/); [Portfolio risk: losses, timing and joint movement](/guides/portfolio-risk/).
Optimal is optimal for a criterion
“Optimal weight” is not synonymous with safe. For a historical sequence, maximise Π(1 + f × xₜ), where xₜ is the result in chosen loss units and f the fraction. Every multiplier must be positive. Scaling by the worst historical loss does not ensure the next loss is smaller; historical fitting and a known probability are different bases.
In a binary exercise, each trial returns plus or minus f of current capital, with constant known win probability p. Expected log growth is g(f)=p ln(1+f)+(1−p)ln(1−f). The derivative is zero at f=2p−1; with no negative stake and p≤0.5, the maximum is zero. This is the special Kelly case discussed by Ben Lynn.[1](#source-cp-kelly), not an estimate of a real trade’s success.
At p=0.55, formal maximum is f=0.10. Replacing p with 0.70 after seven wins in ten gives f=0.40. After six consecutive losses, balances are 0.9⁶=53.1441% and 0.6⁶=4.6656% of starting capital. Estimation error can matter more than optimisation precision; seven wins do not prove stable probability or independent future outcomes.
Safe requires a defined tolerable loss
Define “safe” with a scenario. To retain at least 80% after six consecutive losses, with exact loss f of current capital each time, (1−f)⁶≥0.8 and f≤1−0.8^(1/6), about 3.6508%. This is stricter than the previous growth maximum, is not a historical method with that name and does not guarantee a 20% real drawdown limit.
Seven losses, a different loss size, debt, fees or an unfilled order can breach it. If historical drawdown reduces a fitted size, state the original scale, recalculation order and new stresses. Do not divide incomparable amounts or call the result a guarantee.
Finite ruin risk is not infinite expectation
Define ruin as at least one of ten trials leaving no more than 6,000 from a 10,000 start. This is a model stop threshold, not literal zero. Keep independent outcomes with p=0.55 and exact multipliers 1±f, no costs. Enumerate all 1,024 sequences, check the path, then sum paths crossing the threshold. A path with k wins has probability 0.55^k×0.45^(10−k).
Full enumeration gives about 6.3895% at f=10% and 74.7441% at f=40%. This is not merely the final balance below the boundary: a path can cross it and recover, but stopping has already occurred. These results apply only to this finite game, not an exchange.
With a constant fraction below one, ideal capital does not reach exact zero in finitely many trials. Practical ruin, minimum trade size and obligations remain. “Probability of zero is zero” is not evidence of safety.
Fixed proportion creates a ladder
For a fictional rule, starting capital E₀=10,000, one initial contract and Δ=2,000, define threshold for n contracts as Eₙ=E₀+Δ×n(n−1)/2. Thresholds for one through four contracts are 10,000, 12,000, 16,000 and 22,000. The move from two to three needs 4,000; three to four needs 6,000. A reduction rule must be stated separately.
If loss per contract is 600, one contract at 10,000 risks 6%; three contracts at the 16,000 threshold risk 1,800, or 11.25%. Fixed proportion does not mean a constant 6% and is not automatically safer than fixed-fraction sizing. Capital, criterion and stop condition come first; no method creates an advantage from none.