Multiple funded accounts are one position, not several

A trader runs three funded accounts at the same firm, same instrument, same strategy, and treats them as three independent shots at a payout. Then a single bad session takes all three at once. The accounts were not three positions. They were one position, tripled, with three drawdown floors reporting the same loss.

The diversification a trader thinks they own from multiple accounts is a function of correlation between the account strategies, not the number of accounts. Getting this wrong is one of the most expensive modelling errors available, because it converts what looks like risk reduction into concentrated risk with three times the fee surface.

Why the independence assumption is so tempting

Three accounts feels safer than one for an obvious reason: three floors means three separate opportunities for at least one to survive. That intuition is correct if the strategies are independent. The arithmetic is the same as any portfolio:

• One account, probability of breach on a given day: p.
• Three accounts, probability that all breach on a given day: p³ (if independent).

At p = 0.2, that is 0.8% — reassuring. But the same three accounts trading the same strategy on the same instrument in the same session have correlated daily returns. In the limit of perfect correlation, all three breach together:

• Three perfectly correlated accounts, probability all breach: p = 20%.

The two scenarios have identical account counts and identical per-account risk. They differ only in correlation, and the difference in joint-breach probability is a factor of twenty-five.

That is the whole point: accounts are not the unit of diversification; strategies are.

Where the correlation actually comes from

It is worth naming the sources, because they are all avoidable and none of them is visible on a dashboard:

1. Same instrument, same direction. Two accounts long the same index in the same session is one bet, expressed twice.
2. Same strategy, same signals. A mean-reversion system run on three accounts generates the same entries. The trades are duplicates.
3. Same session. Two different edges traded in the same overlapping hours share the market regime, and regimes are the dominant risk factor.
4. Same firm's shared constraint. If the firm applies a portfolio-level or per-trader rule, three accounts at one firm are not even independent at the rule level.

Only the first is obvious. The second and third are the ones that actually bite, because a trader running a breakout strategy on three accounts in the same 90-minute window is, mechanically, running one breakout strategy at triple size.

The measurable version

If you keep trade logs per account, the correlation is computable and it is not hard:

// Pearson correlation of daily returns between two accounts.
function corr(a, b) {
  const n = Math.min(a.length, b.length);
  const ma = mean(a.slice(0, n));
  const mb = mean(b.slice(0, n));
  let num = 0, da = 0, db = 0;
  for (let i = 0; i < n; i++) {
    const xa = a[i] - ma;
    const xb = b[i] - mb;
    num += xa * xb;
    da += xa * xa;
    db += xb * xb;
  }
  return num / Math.sqrt(da * db);
}

function mean(xs) {
  return xs.reduce((s, x) => s + x, 0) / xs.length;
}

Run it on the daily P&L of account A against account B. A value near 1.0 means the two accounts are one position. A value near 0 means the second account is genuinely diversifying. Most "multiple accounts" setups measure above 0.8, which is why the downside arrives correlated even when the accounts look independent on paper.

For more than two accounts, the object you want is the correlation matrix, and the useful summary is its largest eigenvalue: if one factor explains most of the variance, you have one strategy wearing several hats.

The consequences for drawdown

Correlation does not just change the probability of a joint breach. It changes the shape of the loss you have to survive:

• Independent accounts: losses arrive at different times. One account can be funded and paying while another is recovering. The equity curve of the portfolio of accounts is smooth.
• Correlated accounts: losses arrive together. Every account is down on the same day, against floors that are all measured from peaks that all rose together. The worst day in one account is the worst day in all of them.

Because drawdown is a function of the worst path, not the average, correlated accounts concentrate exactly the event that ends them. The trailing-floor mechanic makes this worse: a good run raises all three floors simultaneously, so all three accounts are at maximum vulnerability at the same moment.

What to do about it

None of this means multiple accounts are a mistake. It means the diversification has to be engineered rather than assumed:

1. Measure the correlation before adding the third account. Two accounts at 0.9 are one account with double fees.
2. Diversify the strategy family, not the instrument. Two correlated instruments (an index and its futures) are not diversifying; an intraday momentum system and an overnight mean-reversion system may be.
3. Stagger the session, not just the signal. If both accounts trade the same hours, they share the regime.
4. Check the firm's portfolio-level rules. Some firms cap aggregate risk across a trader's accounts, which makes the accounts correlated by policy regardless of strategy.
5. Reserve the uncorrelated account for the worst day. The value of the second account is highest when it is the one not in the drawdown. That only happens if it holds a different bet.

A funded account is a small business with a hard floor. Running three of them is running three businesses — and three businesses selling the same thing in the same market on the same day are one business with three sets of overheads. Correlation is the number that tells you which you have.

The practical firm-level detail — per-trader account caps, whether one firm's accounts share a risk limit, and how the rules treat multiple accounts at the same or different firms — is in the multiple accounts at one firm breakdown.