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📖 Book Value

💡 What is Book Value?

Book Value represents the historical accounting cost of your portfolio — open cost basis plus cash reserves and in-transit book value. It does not fluctuate with market prices — only cash held in another currency follows its exchange rate, in Book as in NAV — and it is distinct from Price Resolution.

🧮 Formula

\[ \boxed{\mathrm{Book}(t) = \mathrm{OCB}(t) + \mathrm{Cash}(t) + \mathrm{InTransitBook}(t)} \]

Where Open Cost Basis:

\[ \mathrm{OCB}(t) = \sum_{\substack{(a,b) \in S \\ q > 0}} q(a,b,t) \cdot w^{C^*}(a,b,t) \]

Here \(w^{C^*}(a,b,t)\) is the WAC kept directly in the requested currency \(C^*\): each acquisition entered it at the rate of its own date \(d_i\), as \(P_i \cdot \mathrm{fx}(\mathrm{ccy}(P_i), C^*, d_i)\) for an amount \(P_i\) actually paid. OCB therefore uses no exchange rate at the valuation date \(t\): it is the sum of historical costs — what was paid — and it does not move when exchange rates move.

Cash, instead, is each broker's cash kept in the currencies it was recorded in and valued at the rate of \(t\):

\[ \mathrm{Cash}(t) = \sum_{b \in S} \sum_{c} N_{b,c}(t) \cdot \mathrm{fx}(c, C^*, t) \]

Here \(N_{b,c}(t)\) is the balance broker \(b\) holds in currency \(c\) on \(t\) — its movements in \(c\) dated on or before \(t\), scaled by the broker's ownership share — and \(\mathrm{fx}(c, C^*, t)\) is the latest rate on or before \(t\), with \(\mathrm{fx}(C^*, C^*, t) = 1\). Unlike OCB, Cash moves with exchange rates: 1,000 USD are worth €900 at 0.90 EUR per USD and €950 at 0.95. Each movement was still booked at the rate of its own date, and the capital flows among them entered the capital baseline at that rate; only the balance held afterwards follows the rate.

In the in-transit term, cash in transit is converted at \(t\) too, like the cash at rest, while assets in transit carry their frozen cost converted at their arrival date.

Incomplete cost

When part of a position's cost is unknown — no exchange rate on or before an acquisition date, or a transfer or adjustment without cost basis — OCB includes only the known part, and the position itself is flagged: its average cost and unrealized gain/loss are not shown.

🔗 See Portfolio Engine — §3 Position State for full derivation.

⚖️ Unrealized Gain/Loss

\[ \mathrm{Unrealized}(t) = \mathrm{NAV}(t) - \mathrm{Book}(t) \]

Because NAV values the assets at the day's market price and exchange rate while Book keeps historical costs, the unrealized gain/loss of an asset priced in another currency includes the effect of the exchange rate. For example, 10 units bought for €400 when they were worth 500 USD keep an OCB of €400; if they are worth 550 USD on a day when 1 USD = €0.75, their market value is €412.50 and the unrealized gain is €12.50 — the units' own gain (+€37.50) less the dollar's fall (−€25.00). Period P&L shows how the Dashboard splits the two.

Cash held in another currency is different: \(\mathrm{Cash}(t)\) is the same term in NAV and in Book, valued at the rate of \(t\) on both sides, so its exchange-rate effect cancels in the difference and Unrealized excludes it. It is a result all the same: the engine books it as the exchange result on cash, it is part of the Total P&L, and over a period it is the FX on cash part of Other. For example, 1,000 USD deposited at 0.90 EUR per USD and held while the rate rises to 0.95 count €950 in both NAV and Book: Unrealized does not move, while the Total P&L gains €50 over the €900 of capital.

📝 Example

Component Amount
Open Cost Basis €27,000
Cash €600
In-Transit Book €0
\[ \mathrm{Book} = 27\,000 + 600 = 27\,600 \text{ EUR} \]

With NAV = €33,000:

\[ \mathrm{Unrealized} = 33\,000 - 27\,600 = +5\,400 \text{ EUR} \]