What is risk of ruin?

It is the chance that a run of trades takes an account down to a level from which the trader cannot or will not carry on. In a simple model it depends on three things: how often trades win, how large a gain is against a loss, and how much of the account is risked on each trade. The machine on this page counts how many simulated runs reach the level you choose.

Why does a 50% loss need a 100% gain to recover?

Because the gain is earned on what is left, not on what there was. After a 50% loss, 100 has become 50, and 50 must double to be 100 again. In general a loss of x needs a gain of x ÷ (1 − x): 10% needs about 11.1%, 20% needs 25%, 50% needs 100% and 90% needs 900%.

How likely is a long losing streak?

More likely than most people expect, and more likely the more trades are taken. For independent trades the chance can be worked out exactly. Three fair coin flips give three tails one time in eight, yet across a hundred trades with a 45% win rate, six losses in a row somewhere is more likely than not. The machine works out the figure for the numbers you choose.

What does rebalancing a portfolio do, and what does it cost?

Rebalancing sells some of what has grown and buys some of what has shrunk, so that each holding is back at its chosen share of the whole. It keeps the mix from drifting towards whichever holding has risen most. Every such trade has a cost, so rebalancing more often costs more. The sixth machine on this page runs the same invented paths with and without rebalancing, with a cost you set, and shows the end value, the deepest fall and the total cost side by side. It also shows the same exposure held with borrowed money, which can be wiped out by a fall the unleveraged portfolio survives.

Can this page tell me my own risk of ruin?

No. It models independent trades with fixed odds and losses that are never larger than planned. Real trading has none of those properties, and a person’s true win rate is not known. The page shows how the arithmetic behaves, which is worth understanding, but its figures are not a measurement of any real account or method.

GIO4X Labs · Simulation

The Risk Room

Six machines about how an account is lost and how slowly it comes back, the last about how a portfolio is put together. Each is a simulation on invented figures, or arithmetic you can check, and each says what it leaves out.

On a keyboard: with the pointer over a machine, the left and right arrows move its slider and Enter presses its main button.

Risk of ruin

A few hundred futures at the same odds.

Set a win rate, the size of a gain against a loss, the share risked on each trade and the fall that counts as ruin. The fan shows where 240 simulated runs went, and how many hit the level.

Tool: Position Size

Of 240 simulated runs of 150 trades, 74 (30.8%) fell 50% below where they began and stopped there, drawn in red. The other 166 did not, within these trades.

Runs that hit ruin: 74 of 240
Share: 30.8%
Average trade: +0.04 × risk
Middle ending, per 100: 96

Win rate: 45%

Average gain ÷ average loss: 1.3 to 1

Risked per trade: 5.0% of the account

The fall that counts as ruin: 50% below the start

Average trade = win rate × gain − loss rate × 1, in units of the amount risked: here 0.45 × 1.3 − 0.55 = +0.04. Each trade risks the same share of the account as it then stands. The picture’s scale is proportional, and the luckiest runs go off the top.

A simulation on invented odds. Every trade is independent and the odds never change; real trades are neither, and nobody knows their own win rate this exactly.

The sizing ladder

The same trades at five sizes.

One invented run of wins and losses, replayed at 0.5%, 1%, 2%, 5% and 10% risk per trade. The larger sizes fall further and take longer to get back.

Tool: Drawdown

One invented run of 150 trades (75 wins, 75 losses, each gain the size of each loss) replayed at five sizes. At 0.5% risk the deepest fall was 6.3%; at 10% it was 76.1%, and the account spent 91 trades below an earlier peak.

Each size on the same run of trades
Risk per trade	Deepest fall	Gain needed to undo it	Longest time below a peak	Ended on, per 100
0.5%	6.3%	6.7%	75 trades	100
1%	12.3%	14.0%	75 trades	99
2%	23.3%	30.3%	75 trades	97
5%	49.4%	97.7%	76 trades	83
10%	76.1%	317.9%	91 trades	47

The dot on each curve is the bottom of its deepest fall. The wins and losses are the same for all five; only the share of the account risked on each trade differs. The scale is proportional: equal distances are equal percentages.

A run with more wins than losses ends higher at the larger sizes, and one with more losses ends lower. With equal numbers of each, every size ends below where it began and the larger sizes end lowest, because each loss takes a larger gain to undo.

A simulation on invented trades with fixed, even odds. It shows what size does to a given run. It does not say what size to use.

Losing streaks

A long run of losses is ordinary.

For a win rate and a number of trades, the exact chance of at least so many losses in a row, and one simulated run with its longest streak marked.

The Mind Room

With a win rate of 45%, the chance of at least 6 losses in a row somewhere in 100 trades is 72.9%. In the simulated run below the bars, the longest losing streak was 6.

At least 6 in a row: 72.9%
Longest in this run: 6

Win rate: 45%

Number of trades: 100

Losses in a row: at least 6

The method: keep the chance of each possible length of the losing run a sequence currently ends on (0 up to 5), and one more for “the streak has happened”. Each trade, a win sends every length back to 0 and a loss moves it one along; a loss from 5 lands in “happened”, which nothing leaves. After 100 trades that number is the answer. It is exact, not an estimate.

It assumes each trade is independent with the same odds. Real losses tend to cluster more than this, because the conditions that cause one often cause the next.

Correlation of a portfolio

Several holdings, or one in disguise?

Two to four invented holdings in equal shares. Move the slider to set how closely they move together, and compare the combined swing with the average of the parts.

The Engine Room

2 invented holdings in equal shares with a correlation of 0.30: the combined swing is 9.7 points a step against 12.0 for the average of the parts, 81% of it. The less they move together, the more their swings cancel.

Combined swing: 9.7
Average of the parts: 12.0
Combined ÷ average: 81%
Correlation: 0.30

Holdings (each one invented)

How closely they move together: correlation 0.30

For two holdings: σ = √(w₁²σ₁² + w₂²σ₂² + 2·w₁·w₂·ρ·σ₁·σ₂). With A and B alone, half each: √(0.25 × 10² + 0.25 × 14² + 2 × 0.25 × 0.30 × 10 × 14) = 9.7.

Swings (standard deviations) of one step, in invented points: A 10, B 14. σ is a swing, w a share of the whole and ρ the correlation. With more than two holdings the same sum runs over every pair. The slider stops at −0.30 because four holdings cannot all move against one another by more than −0.33.

The combined swing is arithmetic; the paths are one simulated draw with that correlation. Real correlations are not fixed: holdings that moved apart in calm periods have often fallen together under stress.

Recovery arithmetic

The way back is longer than the way down.

A loss of x needs a gain of x ÷ (1 − x) to undo it. The bar falls and must climb back; the curve shows how fast the climb grows.

Tool: Compound Growth

A loss of 50% leaves 50 of every 100. To be back at 100, what is left must gain 100%: 50 ÷ (100 − 50) = 1.00.

Loss: 50%
Gain needed: 100%

The loss: 50%

Gain needed = loss ÷ (1 − loss), with the loss as a fraction. The dotted line is where a gain equal to the loss would sit; the solid curve leaves it further behind the deeper the loss.

Arithmetic, not a forecast. It says how far there is to climb, not whether or how soon a climb comes.

Building a portfolio

Weights, rebalancing, and what borrowing changes.

Three invented holdings at weights you set, money paid in or taken out each month, and rebalancing that costs something. Switch on a stress stretch, an exchange rate, or the same exposure with borrowed money, and compare the result with never rebalancing and with equal weights on the same paths.

Investing explained

Over 120 invented months, 10,000 units held as 40% Steady, 40% Lively, 20% Abroad, with 50 paid in each month and rebalanced every 12 months, ended on 19,565 against 16,000 paid in; it was rebalanced 10 times at a cost of 50, and its deepest fall was 34.1%.

The same invented paths under these settings, never rebalanced, and at equal weights
	These settings	Never rebalanced	Equal weights
End value	19,565	19,009	19,743
Deepest fall	34.1%	34.6%	34.6%
Total contributed	16,000	16,000	16,000
Total cost paid	50	0	56
Times rebalanced	10	0	10

End value:: what the whole portfolio is worth after month 120, in invented units, after every cost and every payment in or out.
Deepest fall:: the largest drop from an earlier peak in the value of one unit held throughout. Money paid in or taken out is left out of it, so a payment does not count as a rise or a fall.
Total contributed:: the starting 10,000, plus everything paid in, less everything taken out.
Total cost paid:: every rebalancing cost added up. Each is the cost rate × the value bought plus the value sold.
The columns:: “Never rebalanced” keeps these weights at the start and then lets them drift. “Equal weights” gives each holding a third and keeps this rebalancing rule and cost. All three use the same paths.

End, exchange rate counted: 19,565
End, exchange rate left out: 21,880
Swing of this mix, calm: 2.46% a month
In the stress stretch: 6.41% a month

Weights (they always total 100%)

Steady: 40%

Lively: 40%

Abroad: 20%

Drag one weight and the other two share what is left, in the proportions they already had (equally, if both were at nothing).

Each month: 50 paid in

Cost of a rebalancing trade: 0.50% of its value

Rebalance

Count the exchange rate: Abroad is priced in another currency, and its value in the home unit moves with an invented rate as well.Stress stretch (an assumption built into the model): from month 19 to month 42 every correlation is 0.9 instead of 0.2 and every swing is doubled.

The same exposure with borrowed money

A separate comparison. Investing with only your own money and holding a leveraged exposure are different things, even on the same paths: a fall that the first survives can leave the second with nothing.

Show the same exposure with borrowed money. The upper picture then follows the starting amount alone, per 100, with nothing paid in or taken out.

What this machine assumes

Three invented holdings and 120 monthly steps. Each month a holding returns its average plus a bell-curve step: Steady 0.3% on average with a swing of 1.5%; Lively 0.6% on average with a swing of 5.0%; Abroad 0.4% on average with a swing of 3.5%. These figures are made up and describe no real asset.
Every pair of holdings shares a correlation of 0.2, fixed, outside the stress stretch. Inside it the correlation is 0.9 and each swing is doubled. The stretch widens the swings in both directions: on some paths it is a sharp rise, not a fall.
The exchange rate starts at 1 and takes its own bell-curve step with a swing of 2.5% a month, independent of the holdings and unchanged by the stress stretch. With it counted, Abroad’s monthly return is (1 + its own return) × (rate now ÷ rate before) − 1.
The portfolio starts with 10,000 units bought at the target weights at no cost. Each month the holdings move first; then money paid in is split at the target weights, or money taken out is taken from each holding in proportion to its value; then the rebalancing rule is checked.
Rebalancing puts every holding back to its target weight. Its cost is the rate you set × the value bought plus the value sold, taken from the whole. Paying in and taking out cost nothing here. Taxes, spreads and any other cost are left out.
“Swing of this mix” is √(Σ wᵢ²σᵢ² + 2 Σ wᵢwⱼρσᵢσⱼ) on the holdings’ own swings at the target weights, before the exchange rate.
No holding can fall by more than 99% in a month, and no value goes below zero. If withdrawals empty the portfolio, the run ends there.

A simulation on invented paths. It shows what each choice did on one run; another run can favour a different column. It is not a forecast and does not say what to hold or how often to rebalance.

The model

What the machines assume.

Ordinary arithmetic and a seeded random number generator, run in your browser: no data feed, nothing sent anywhere and nothing stored. The sizing sum that turns a risk per trade into a position is in the Position Size tool.

SimulationInvented odds, invented holdings, an invented exchange rate and example accounts. Educational information, not investment advice or a recommendation to trade.

01
Every trade is independent.
The result of one trade tells the next one nothing. In the simulations a win or a loss is one draw from a seeded generator, so the same run number always gives the same run.
02
The odds never change.
The win rate and the size of a gain against a loss are whatever the sliders say, for every trade. A gain is always the same multiple of the amount risked, and a loss is always exactly the amount risked.
03
The risk is a share of the account as it stands.
Each trade risks the same percentage of the current balance, so the amount shrinks after a loss and grows after a gain. Ruin is counted the first time a run is the chosen percentage below where it began, and the run stops there.
04
The streak figure is exact; the fan is a count.
The chance of a losing streak is computed in full by dynamic programming, with the method stated beside it. The risk of ruin is the share of 240 simulated runs that hit the level: another 240 would give a slightly different share.
05
The holdings are bell-curve steps.
Each invented holding moves by a random step with a fixed swing, and every pair shares one correlation. The combined swing is the standard formula for the standard deviation of a weighted sum.
06
The portfolio is three invented holdings over 120 months.
In the sixth machine each holding has a made-up average return and swing that never change, and every pair shares one correlation. Money paid in is split at the target weights, money taken out comes from each holding in proportion, and rebalancing costs the rate you set on the value bought and sold. Nothing else is charged.
07
The stress stretch and the exchange rate are assumptions.
For a marked run of months the model raises every correlation to 0.9 and doubles every swing, because it was told to, not because anything was measured. The exchange rate is one more invented path, independent of the holdings.
08
Borrowed money is a fixed loan that ends at zero.
The leveraged comparison borrows once at the start, lets the loan grow by the financing cost, and stops for good the first month the exposure is worth no more than the loan. A real lender would usually act before that point; that is not modelled.

What it is not

Real trading is not a row of fixed bets.

The model is simple on purpose, so the arithmetic can be seen. Each simplification makes the picture tidier than the thing it describes, and none of the figures here measures a real account or method.

Real trades are not independent.
Losses tend to arrive together, because the conditions that cause one often cause the next, and because people trade differently after a loss. Streaks in practice can be longer than the independent figure suggests.
Nobody knows their odds.
A win rate measured over past trades is an estimate with a wide margin, and it shifts as markets change. The sliders ask for numbers that in practice cannot be known this exactly.
A loss is not always the amount risked.
A price can pass through a stop in a gap or a fast market, so a real loss can be larger than planned. Costs such as spread, commission and financing are not modelled here at all.
Correlations move.
The correlation between two holdings is not a fixed property. Holdings that moved apart in calm periods have often fallen together under stress, which is when the relief was wanted.

Questions people ask

Ruin, streaks and the way back.

What is risk of ruin?: It is the chance that a run of trades takes an account down to a level from which the trader cannot or will not carry on. In a simple model it depends on three things: how often trades win, how large a gain is against a loss, and how much of the account is risked on each trade. The machine on this page counts how many simulated runs reach the level you choose.
Why does a 50% loss need a 100% gain to recover?: Because the gain is earned on what is left, not on what there was. After a 50% loss, 100 has become 50, and 50 must double to be 100 again. In general a loss of x needs a gain of x ÷ (1 − x): 10% needs about 11.1%, 20% needs 25%, 50% needs 100% and 90% needs 900%.
How likely is a long losing streak?: More likely than most people expect, and more likely the more trades are taken. For independent trades the chance can be worked out exactly. Three fair coin flips give three tails one time in eight, yet across a hundred trades with a 45% win rate, six losses in a row somewhere is more likely than not. The machine works out the figure for the numbers you choose.
What does rebalancing a portfolio do, and what does it cost?: Rebalancing sells some of what has grown and buys some of what has shrunk, so that each holding is back at its chosen share of the whole. It keeps the mix from drifting towards whichever holding has risen most. Every such trade has a cost, so rebalancing more often costs more. The sixth machine on this page runs the same invented paths with and without rebalancing, with a cost you set, and shows the end value, the deepest fall and the total cost side by side. It also shows the same exposure held with borrowed money, which can be wiped out by a fall the unleveraged portfolio survives.
Can this page tell me my own risk of ruin?: No. It models independent trades with fixed odds and losses that are never larger than planned. Real trading has none of those properties, and a person’s true win rate is not known. The page shows how the arithmetic behaves, which is worth understanding, but its figures are not a measurement of any real account or method.

Trading foreign exchange on margin carries a high level of risk, and may not be suitable for all investors. The high degree of leverage can work against you as well as for you. Before deciding to trade foreign exchange you should carefully consider your investment objectives, level of experience, and risk appetite. The possibility exists that you could sustain a loss of some or all of your initial investment and therefore you should not invest money that you cannot afford to lose.

Continue

Fetching the page

Risk per trade

Deepest fall

Gain needed to undo it

Longest time below a peak

Ended on, per 100

0.5%

6.3%

6.7%

75 trades

100

12.3%

14.0%

75 trades

23.3%

30.3%

75 trades

49.4%

97.7%

76 trades

10%

76.1%

317.9%

91 trades

Weights, rebalancing, and what borrowing changes.

Investing explained

The same invented paths under these settings, never rebalanced, and at equal weights
	These settings	Never rebalanced	Equal weights
End value	19,565	19,009	19,743
Deepest fall	34.1%	34.6%	34.6%
Total contributed	16,000	16,000	16,000
Total cost paid	50	0	56
Times rebalanced	10	0	10

These settings

Never rebalanced

Equal weights

End value

19,565

19,009

19,743

Deepest fall

34.1%

34.6%

Total contributed

16,000

Total cost paid

Times rebalanced

What the machines assume.

SimulationInvented odds, invented holdings, an invented exchange rate and example accounts. Educational information, not investment advice or a recommendation to trade.

A few hundred futures at the same odds.

The same trades at five sizes.

A long run of losses is ordinary.

Several holdings, or one in disguise?

The way back is longer than the way down.

Weights, rebalancing, and what borrowing changes.

The same exposure with borrowed money

What this machine assumes

What the machines assume.

Every trade is independent.

The odds never change.

The risk is a share of the account as it stands.

The streak figure is exact; the fan is a count.

The holdings are bell-curve steps.

The portfolio is three invented holdings over 120 months.

The stress stretch and the exchange rate are assumptions.

Borrowed money is a fixed loan that ends at zero.

Real trading is not a row of fixed bets.

Real trades are not independent.

Nobody knows their odds.

A loss is not always the amount risked.

Correlations move.

Ruin, streaks and the way back.

A few hundred futures at the same odds.

The same trades at five sizes.

A long run of losses is ordinary.

Several holdings, or one in disguise?

The way back is longer than the way down.

Weights, rebalancing, and what borrowing changes.

The same exposure with borrowed money

What this machine assumes

What the machines assume.

Every trade is independent.

The odds never change.

The risk is a share of the account as it stands.

The streak figure is exact; the fan is a count.

The holdings are bell-curve steps.

The portfolio is three invented holdings over 120 months.

The stress stretch and the exchange rate are assumptions.

Borrowed money is a fixed loan that ends at zero.

Real trading is not a row of fixed bets.

Real trades are not independent.

Nobody knows their odds.

A loss is not always the amount risked.

Correlations move.

Ruin, streaks and the way back.