Module 6 · Lesson 12 of 17 · Risk, process, and mindset · About 5 minutes
Risk of Ruin: How Losing Streaks and Bet Size Interact
On this page
Before you read: Risk Management Arithmetic: Position Size, Risk-Reward, Drawdown
What you will learn
- What risk of ruin means and why it depends on the definition of “ruin”.
- How losing streaks happen even when wins and losses are balanced.
- Why the share of the account lost per trade matters so much, using fixed-fractional sizing as the example.
What is risk of ruin?
At what point would an account be too small to continue?
Risk of ruin is the probability that a series of results takes an account down to a level where it can no longer continue as planned, the ruin threshold. Some definitions use zero. Others use a drawdown of 50%, or the point where the account falls below a broker minimum. The number depends heavily on that choice.
How likely are losing streaks?
If each trade is a coin flip, how long can a run of losses get?
First define the event and sequence length. In a stipulated independent, constant 50% loss-probability model, five specified consecutive trades all losing has probability (1/2)^5=1/32=3.125%. This includes a run beginning at a fixed specified place; it does not require the previous trade to be a win, and it does not mean “at least one five-loss run anywhere.”
For ten trades, the anywhere event includes overlapping candidate starts. Exact enumeration gives 112 of 1024 equally likely win/loss strings with at least one five-loss run: 112/1024=7/64=10.9375%. Multiplying six possible starts by 3.125% would double-count histories with overlapping runs. Under the SAME toy assumptions, exact sequence counting for 100 trades gives approximately 81.010960%. That is a different event/horizon, not a new estimated win/loss rate.
One reproducible counting rule keeps states 0–4 for the current trailing losses while forbidding five. Start counts [1,0,0,0,0]. For every next result, a win moves all allowed paths to state 0; a loss moves old states 0–3 to states 1–4; discard a loss from state 4. After N steps, sum remaining paths; any-run probability=1−allowed/2^N. It gives 912 allowed at N 10 and 112 with a run. These calculations were also checked against exhaustive enumeration through N 15.
Do not say eight/ten losses occur “regularly” without a horizon and dependence model. A run probability is not yet a probability of ruin: payoff magnitudes, costs, position rules and the chosen threshold must also be defined. Real outcomes need not be independent or stationary.
A small separate ordering counterexample, zero costs, fixed ±1 balance unit per result, starting 20: LLLLLWWWWW and LWLWLWLWLW both have 5 wins/5 losses and finish 20. Their lowest balances are 15 and 19 respectively; peak-to-trough drawdowns are 25% and 5%. Identical outcome counts do not specify the path. This is not fixed-fraction sizing and is not merged with the next section’s example.
Risk of ruin diagram
Read the diagram step by step
- f is a fraction of CURRENT balance lost each trade. Starting normalized balance 100; ten straight losses; no fees/gaps.
- Fraction of CURRENT balance, not a fixed dollar loss from the starting balance.
- No ruin-probability axis or arbitrary threshold line.
- Three calculated ending balances, not three supplied historical paths or probabilities. 100×0.99^10, 100×0.95^10 and 100×0.90^10 give the shown amounts. A ruin threshold must be declared separately.
Illustrative diagram constructed for teaching. Not real market data.
Three calculated ending balances, not three supplied historical paths or probabilities. 100×0.99^10, 100×0.95^10 and 100×0.90^10 give the shown amounts. A ruin threshold must be declared separately.
Why does the fraction lost per trade matter?
Two accounts lose the same ten trades in a row. One lost a small share each time, the other a large share. How far apart are they?
Under fixed-fractional sizing, each loss is a set share of the current account. In a fictional sequence of ten straight losses, losing 1 percent of the account each time leaves about 90% of the starting balance. Losing 5 percent each time leaves about 60%. Losing 10 percent each time leaves about 35%. The deeper the hole, the larger the gain needed to recover, as the drawdown and recovery math shows.
What assumptions sit underneath?
Are real trading results independent coin flips?
Simple independent-trial models stipulate fixed probabilities and a particular loss/payoff process. Actual outcomes need not satisfy those assumptions; conditions, dependence, costs, slippage, gaps and execution can differ. The numbers are a way to see how streaks and sizing interact, not an estimate of anyone’s real chances.
What this does not tell you about risk of ruin
- No empirical probability of anyone’s ruin is supplied. Actual outcomes need not satisfy this example’s independence, constant-odds, payoff, cost or position assumptions.
- What fraction anyone should lose per trade. That is a personal decision.
- Whether a losing streak will end soon. Past streaks do not change the next result’s odds in the model.
- Nothing here suggests any sizing method, strategy or trade.
Check yourself
- Why can 3.125% and 10.9375% both be correct under the same 50% iid model? Hint: how many starting points are there?
- Does 81.010960% for N 100 estimate a real trader’s ruin risk? Hint: costs, changing odds, gaps.
- What does the 5% endpoint bar mean?
- Why can two readers quote different ruin probabilities from the same summary results? Hint: how did each define ruin?
Reflect on your own process
- What ruin threshold, in plain numbers, does your written plan define for your own account?
- Where does your plan state the most you will lose per trade, and when did you last review that rule?
- How does your journal track your longest losing streak so you can compare it with your plan's assumptions?
Sources
This lesson’s numbers are invented teaching examples. Their arithmetic was checked; no outside source is needed.