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💸 Deposited Capital, Total PnL and Cash Pools

⬅️ Back to Performance Metrics Overview

💡 Concept Overview

Deposited Capital = cumulative net external capital contributed since inception:

\[ \mathrm{DepCap}(t) = \sum_{\tau \leq t} D(\tau) - \sum_{\tau \leq t} W(\tau) \]

Total PnL = all value generated above external contributions:

\[ \boxed{\mathrm{TotalPnL}(t) = \mathrm{NAV}(t) - \mathrm{DepCap}(t)} \]

🎯 What Counts

Transaction Effect on DepCap
DEPOSIT / WITHDRAWAL (unlinked) ✅ Yes
CASH_TRANSFER linked-external ✅ Yes
CASH_TRANSFER linked-internal ❌ No
BUY, SELL, DIVIDEND, INTEREST, FEE, TAX ❌ No

📊 Three-Pool Cash Model

The Growth Chart decomposes current cash into two visible aggregates plus a hidden global tracker:

\[ \mathrm{Cash}(t) \approx \sum_b K_b(t) + \sum_b R_b(t) \]
Pool Scope Meaning
\(K_b\) Per-broker External capital still at broker \(b\)
\(R_b\) Per-broker Generated returns still at broker \(b\)
\(W\) Global Returns that left the system (restorable on re-deposit)

Key properties

  • \(\mathrm{DepCap}\) = historical sum of all flows. \(\sum K_b\) = how much current cash is external capital. They diverge after BUY/SELL.
  • A BUY on broker \(b_1\) only consumes \(R_{b_1}\), never \(R_{b_2}\).
  • Cash transfers between brokers move \(R\) and \(K\) from source to destination without touching \(W\).

🔗 Full per-broker update rules: Portfolio Engine — §6 Three-Pool Model

📝 Worked Examples

A — Deposit → Buy → Sell in Gain

Step Tx \(K\) \(R\) Cash
1 DEPOSIT €1,000 1,000 0 1,000
2 BUY €1,000 0 0 0
3 SELL P=€1,200, C=€1,000 1,000 200 1,200

TotalPnL = 1,200 − 1,000 = +€200 ✓

B — Dividend then Withdrawal

Step Tx \(K\) \(R\) \(W\) Cash
1 DEPOSIT €1,000 1,000 0 0 1,000
2 DIVIDEND €50 1,000 50 0 1,050
3 WITHDRAWAL €100 (K first) 900 50 0 950
4 WITHDRAWAL €950 (K=900→0, R=50→0, W+=50) 0 0 50 0
5 RE-DEPOSIT €30 (restore min(30,W=50)=30) 0 30 20 30

After step 5: Cash=30, K=0, R=30 ✓ (returns restored from W)

C — Full Sell Regression

Step Tx \(K\) \(R\) Cash
1 DEPOSIT €1,000, BUY 1@€1,000 0 0 0
2 SELL 1@€1,005 (C=1000, G=5) 1,000 5 1,005

Capital correctly returns to \(K\); only €5 gain to \(R\). Not all €1,005 to \(R\).

⚙️ Implementation

The 3-pool model runs in a single per-transaction loop (event-driven, not daily-delta):

  1. Read WAC before pool mutation
  2. Update K/R/W per transaction type rules
  3. Then reduce WAC pool (for SELLs)

🔗 See Portfolio Engine — §6 for all formal rules.