Risk of Ruin: The Math Behind Account Survival

Every trader who's been around long enough has watched someone blow up. A funded account, gone in a week. An evaluation, failed on day three. The pattern repeats: aggressive sizing, a bad streak, and suddenly it's over.

This isn't bad luck. It's math.

Risk of ruin is a concept from probability theory that calculates the likelihood of losing your entire stake given your edge, win rate, and position sizing. Understanding it won't make you immune to losses, but it will show you exactly why some approaches are doomed before they start.

What Is Risk of Ruin?

Risk of ruin is the probability that you'll lose enough money to stop trading - whether that's hitting zero, breaching your prop firm's drawdown limit, or falling below the minimum required to take positions.

The formula considers:

• Your win rate
• Your average win vs. average loss
• Your position size as a percentage of capital
• Your maximum acceptable loss (your "ruin point")

The key insight: even with a positive edge, you can still go broke if you size incorrectly.

The Surprising Math

Let's say you have a strategy with:

• 55% win rate
• 1:1 risk-reward (average win equals average loss)
• A clear edge - you'll make money over time

Sounds profitable. And it is. But here's what happens at different position sizes:

Risking 2% per trade: Risk of ruin is approximately 0.1% Risking 5% per trade: Risk of ruin jumps to about 4% Risking 10% per trade: Risk of ruin climbs to around 13% Risking 25% per trade: Risk of ruin exceeds 50%

Read that last one again. With a winning strategy, risking 25% per trade gives you worse than coinflip odds of survival.

This is why aggressive traders blow up. Their edge is real, but their sizing makes survival unlikely.

Why Small Edges Need Small Sizes

Your edge is the difference between your expected value and breakeven. Most retail trading edges are small - a few percentage points better than random.

Small edges require many trades to realize. If your edge is 2%, you need hundreds of trades for that edge to show up reliably in your results. But if you're sized so aggressively that you blow up before those hundreds of trades, your edge never gets a chance to play out.

The paradox: The smaller your edge, the smaller your position size needs to be to survive long enough to profit from it.

Prop Firm Implications

Prop firms give you strict drawdown limits. TopstepX might allow 3% daily loss and 6% trailing drawdown. These aren't suggestions - hit them and you're done.

Your position sizing needs to account for:

• The daily loss limit: Can you survive your worst expected day without breaching it?
• The trailing drawdown: Can you survive your worst expected week or month?
• Multiple concurrent losers: What if several positions go against you simultaneously?

Most traders size for average conditions. They calculate: "I usually have 3 trades per day, so I'll risk 0.8% per trade, which gives me 2.4% exposure."

But what about the day you have 5 trades and they all lose? That's 4% drawdown - beyond your daily limit from normal trading, not even counting a bad streak.

Size for worst-case scenarios, not average ones.

Calculating Your Personal Risk

Here's a simplified approach to sizing:

Step 1: Define Your Ruin Point

For prop trading, this is usually your maximum drawdown limit. Let's say it's 6%.

Step 2: Determine Your Worst Expected Losing Streak

With a 55% win rate, a 7-trade losing streak isn't unusual over a few months of trading. With a 45% win rate, expect 10+ consecutive losses eventually.

Step 3: Size So Your Worst Streak Doesn't Kill You

If you might have 7 consecutive losses and your ruin point is 6%, you need to risk less than 0.85% per trade (6% / 7 = 0.85%).

In practice, add buffer. The actual worst streak might be worse than expected. Size for 10 losses even if you expect 7.

Step 4: Reality Check

If your calculation says you can only risk 0.5% per trade, and that makes your strategy unprofitable after costs... your strategy might not be viable for prop trading. Better to know now.

The Psychology of Conservative Sizing

Here's what nobody tells you about small position sizes: they're psychologically easier.

When you're risking 0.5% per trade, a losing streak feels like a minor setback. You're down 2-3%, it's uncomfortable but manageable. You can think clearly, follow your rules, and let the edge work.

When you're risking 5% per trade, a losing streak feels like an emergency. You're down 20%, you're panicking, you're questioning everything, and you start making emotional decisions that make things worse.

Conservative sizing isn't just about math. It's about keeping you in a mental state where you can actually execute your strategy.

Common Sizing Mistakes

"I'll Size Up When I'm Winning"

This feels logical: you have a cushion, so you can take more risk. But winning streaks don't predict future wins. Sizing up after winners increases your exposure right when mean reversion might kick in.

"I'll Size Down When I'm Losing"

The opposite mistake: reducing size during drawdowns. This locks in losses and reduces your ability to recover. If your edge is real, drawdowns are when you need to trust it, not abandon it.

"I'll Risk More On High-Confidence Setups"

Your confidence isn't a good predictor of outcome. Studies show traders' confidence correlates weakly with actual results. The setup that "feels right" isn't measurably better than your normal setups.

The fix for all three: Use consistent sizing based on your risk-of-ruin calculations, not your feelings.

Building Survival Into Your System

When you set up automation in Algo Bread, build in hard stops:

Per-trade limits: Never risk more than X% regardless of your conviction

Daily loss limits: Stop trading if you hit Y% down for the day

Drawdown circuit breaker: Pause the strategy if you reach Z% total drawdown

These aren't signs of weakness. They're acknowledgment that even good strategies have bad periods, and surviving those periods is how you eventually profit.

The Long View

Trading is an infinite game. Your goal isn't to maximize today's profits - it's to stay in the game long enough for your edge to compound.

A trader making 0.5% per day with low risk of ruin will crush a trader making 2% per day with high risk of ruin. The first trader is still trading in year three. The second trader blew up in month four.

Run your risk-of-ruin numbers. Be honest about your edge. Size conservatively. The math doesn't lie, and it doesn't care about your confidence.

Survival first. Profits follow.