Methodology

The reasoning behind every number

What we measure. How we calculate it. Where the evidence ends.

Portfolio intelligence should be open to examination. This reference explains the calculation rules, the populations they measure and the assumptions behind them. Read measured facts, estimates and scenarios on their own terms.

Method reviewed

November 11, 2026

Reviewed calculation methods. Prices, fund holdings and individual analyses carry their own data dates; the date here describes this reference.

The essentials in two minutes

Choose the question you want to answer. Each chapter connects the calculation to its scope, limitations, sources and available public code.

Check which accounts are included
Start with the included assets, currency and valuation date. A securities account, your wider wealth and a modeled selection of holdings can cover different parts of your finances.
Match the number to your question
Returns describe investment history. A mandate score checks your holdings against your signed rules. Projections explore possible outcomes under assumptions. A cash plan checks whether you can fund the contributions.
Notice what is missing
A missing value is different from zero. The holdings we can identify may already exceed a limit, while missing details can prevent us from confirming that the portfolio meets its limits. Simulation ranges depend on stated assumptions.

Find your question

What is included in this number?
Start with the portfolio boundary, then compare the wider wealth and data scopes.
Also read: Net worth & currencies Data sources
How was my return measured?
Separate the investment path from cash timing, costs and the German tax estimate.
Also read: Costs and after-tax performance Tax calculation
Where could losses come from?
Read historical variation alongside shared issuers and specified stress scenarios.
Also read: Concentration & look-through Stress tests and historical scenarios
Am I following my plan?
Understand the mandate score before comparing possible rebalancing actions.
Also read: Rebalancing & optimization
Can I fund and reach my goal?
Distinguish a feasible contribution schedule from conditional investment outcomes.
Also read: When Investboard declines to answer Limits & transparency

Evidence, reproduction and validation

Know what kind of evidence you are reading

Start with the population and denominator. Then distinguish what was observed, what was reconstructed, what was assumed and what was chosen. The same number can answer very different questions under a different scope.

Recorded

Positions, transactions, prices and fund disclosures describe dated observations. Their completeness, currency, income basis and age determine what can be measured.

Reconstructed

A ledger and historical prices can reconstruct a past book. Missing valuations, inferred opening positions and carried prices remain approximations; reconstruction is not an audited account statement.

Modeled

Proxies, covariance estimates, cost estimates and future paths depend on assumptions. A model can reconcile arithmetically and still omit a material source of uncertainty.

Policy

Mandate weights, score curves, coverage floors and trading thresholds encode a chosen rule. Research can inform the decision without validating that particular setting or your investment policy.

What reproduction requires

Keep the valuation and transaction snapshot, dated price and FX inputs, classifications, scope, settings and calculation version. Simulations also need the random seed and path count. Public module links below pin a specific revision; a README, implementation and test each answer a different question. Licensed market histories and connected-account orchestration are not made public by publishing a calculator.

What has actually been established

Worked examples show identities and edge cases. Implementation tests check declared behavior. The reference-risk review also records arithmetic, matrix and selected sensitivity checks. None of these alone establishes predictive accuracy, optimal policy, investment suitability or an independent platform audit. Open each chapter's details for the important counterexamples and remaining limitations.

Read the denominator first

Read the denominator first
Reading	What is measured
Portfolio intelligence	All imported depots owned by the customer, pooled in one reporting currency. The depot named by an analysis route does not narrow this population. Accounts and assets you have not supplied remain outside the measurement.
Equity X-Ray	The underlying equity population. Whole-portfolio exposure and equity-only concentration use different denominators; bonds, cash and physical assets do not become companies.
Mandate issuer limit	The equity portion of the core portfolio across imported depots. Satellite holdings are excluded before look-through.
Net worth	The supported recorded wealth categories, less liabilities. This broader wealth view is not the denominator of the portfolio mandate score.

Portfolio analysis

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Portfolio analysis follows a structured process that runs automatically and deterministically.

Data import & aggregation

CSV import: transaction data from common banks and brokers is read in and normalized
Transactions update quantities and acquisition lots. FIFO selects the oldest eligible lots when calculating realized disposal gains; it is not a return formula
Imported identifiers, currencies and classifications are normalized and matched where evidence is available. Unresolved instruments require review
Duplicate-file and transaction checks reduce repeat booking. Overlapping exports or incomplete broker identifiers still require review of the import result

Allocation calculation

The actual allocation is based on the current market value of all holdings
Categorization by asset class, region, sector, and currency
Weighting relative to the total portfolio value
Overlaps between ETFs are taken into account (look-through)

Performance tracking

Time-weighted return (TWR) approximates performance after adjusting for external capital movements
Money-weighted return (MWR) for the actual investor experience, accounting for timing effects
Benchmark comparison against four references: MSCI World, DAX, S&P 500 or a cash rate
Recorded distributions are included according to their gross or fallback evidence; observed NAV already reflects embedded fund expenses

Calculation

Market value and allocation

value = quantity × usable price × FX conversion factor weight = value / total valued assets in the stated scope

Convert into one currency before adding values. An unknown asset classification stays unknown; a missing price is not a zero-value holding. An incomplete valuation qualifies the scope of any subtotal.

Illustrative example, not market data

If the measured portfolio contains 6,000 in equities and 4,000 in bonds, the equity allocation is 60%. This says nothing about a property or account outside that portfolio.

Return measurement

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A return starts with a defined book: its assets, valuations, funding and income. TWR describes the investment path after adjusting for funding. MWR describes the experience of money invested on particular dates.

Scope and assumptions

We link subperiod returns using available valuations and a declared funding-boundary convention. Missing valuations limit the result even when the arithmetic reconciles. Contributions, currency effects and benchmark differences answer separate questions.

Our decision and its limits

Funding-date valuations determine TWR precision. Book, currency and income basis must match before returns or benchmarks can be compared.

Calculation details and limitations

The book and its missing valuations

Purchases and sales are funding legs relative to the securities book. They are not necessarily new savings or withdrawals across your whole wealth. An internal rotation needs offsetting legs; cash included as an asset needs its corresponding leg too. Distributed income is added separately only when absent from NAV. Dividends use recorded gross income, with net income as the fallback when gross is unavailable.

Every funding date opens a boundary, so the Modified Dietz calculation normally has no strictly interior funding to time-weight. An observed post-flow NAV is adjusted for funding. Without that observation, the preceding value is carried and funding is folded into the next opening value. This approximation differs from whole-period Modified Dietz and cannot recover an unobserved market path. In the formula, V₀ and V₁ are boundary-adjusted values; C is strictly interior funding, w its remaining-period time weight, and D distributed income absent from NAV. A zero denominator without dividend income contributes zero by engine convention; zero-base dividend income or a negative denominator leaves the subperiod undefined.

Calculation

rₜ = (V₁ − V₀ − ΣC + D) / (V₀ + Σ(w × C)) TWR = Πₜ(1 + rₜ) − 1

Illustrative example, not market data

Observe 100 on January 1, add 100 on January 11 without a valuation, then observe 220 on January 21. Our carry convention gives 0% followed by 10%, linked to 10%. Whole-period Modified Dietz gives 20 / (100 + 50) = 13.33%. True TWR depends on the missing January 11 value; neither approximation establishes it.

Money-weighted return and solver limits

XIRR includes opening wealth, dated funding and distributions, and terminal wealth on the last measured valuation date. It discounts actual elapsed days over a fixed 365-day year. Same-day flows are netted in cents; an accepted rate must also satisfy the net-present-value condition.

We search between −99.9% and 1000% iteratively. Failure does not prove that no mathematical root exists, and irregular flows can have multiple roots. We withhold MWR below 365 days as a presentation policy. TWR annualization has the same minimum span but uses a separate 365.25-day exponent.

Calculation

Σᵢ CFᵢ / (1 + r)^(elapsed daysᵢ / 365) = 0

Illustrative example, not market data

Across two 365-day years, 100 grows to 110, another 900 is invested, then the resulting 1,010 falls to 909. TWR is −1%; annual MWR is about −8.34%. More money was exposed during the loss.

How contributions link through time

A holding's period contribution divides its adjusted value change and income by the portfolio's opening value. We multiply each contribution by all later portfolio return factors. This equals reversed Frongello linkage against a zero-return benchmark. Original Frongello uses a different assignment of compounding effects; reconciliation alone does not select a unique interpretation.

These are absolute return contributions, not allocation or selection skill. Changing the end date can change an earlier contribution. It is neither a standalone return nor a causal share of profit. Unsupported explanation stays in the residual, with recorded standalone costs separate. Reconciliation does not authenticate prices or ledger completeness.

Calculation

Cᵢ = Σₜ[cᵢ,ₜ × Πᵤ>ₜ(1 + rᵤ)]

Illustrative example, not market data

Suppose A explains a first-period gain of 10% and B a second-period loss of 10%. Our linked contributions are +9 and −10 percentage points, totaling −1%. Past-wealth scaling would assign +10 and −11 points. Both reconcile; they assign the compounding interaction differently.

Quote-currency effects and their interaction

Local value and currency translation multiply. We average both calculation orders, assigning half their interaction to each leg; distributed income enters the local leg. This describes translation from quote currency to reporting currency, not underlying economic currency exposure, forward-contract returns or hedging skill.

The decomposition needs independent dated price and FX evidence with an explicit conversion direction. Because local values are derived from reporting values and supplied rates, an incorrect rate pair can still reconcile perfectly. Contributions grouped by quote currency are also different from the FX effect itself.

Illustrative example, not market data

100 USD at 0.90 EUR/USD is 90 EUR; 110 USD at 0.81 EUR/USD is 89.10 EUR. Local price rises 10% and FX falls 10%, producing −1% together. The symmetric contributions are +9.5 points from local price and −10.5 from FX.

What a benchmark comparison establishes

The difference is cumulative portfolio TWR minus benchmark return in percentage points, without beta adjustment or annualization. It is not CAPM alpha. We withhold it for currency or income-basis mismatches and unsupported date gaps. We do not silently convert an incompatible comparator. Passing these guards does not establish mandate suitability.

Some equity comparators use ETF proxies with their own expenses, tracking and trading line. A total-return label does not establish matching tax assumptions or closing times. The cash comparator compounds a configured nominal rate daily across the selected history. It is an illustrative constant-rate curve, not historical deposit rates or an available bank offer.

Sources and further reading

GIPS Handbook: cash flows and return measurement Read the source note ↓: GIPS Handbook: cash flows and return measurement
XIRR: dated cash flows and iterative roots Read the source note ↓: XIRR: dated cash flows and iterative roots
Linking Single Period Attribution Results Read the source note ↓: Linking Single Period Attribution Results
Linking contributions and the order of returns Read the source note ↓: Linking contributions and the order of returns
MSCI Index Calculation Methodology Read the source note ↓: MSCI Index Calculation Methodology

Risk, drawdown and correlation

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Volatility shows how much returns vary. The Sharpe ratio compares return above a cash-rate reference with that variation. Drawdown measures the fall from a previous peak. Each describes a different part of historical risk; none captures every way a plan can fail.

Scope and assumptions

Realized account risk, weekly holdings correlations, reference covariance, issuer concentration and future goal scenarios use different evidence and assumptions. Issuer breadth does not establish low market risk. Historical covariance does not measure future risk.

Volatility and Sharpe use consecutive cash-flow-adjusted simple valuation returns; drawdown uses the TWR unit-wealth curve. Weekly diversification uses aligned instrument histories. Window, currency, data basis and coverage qualify every reading.

Our decision and its limits

Daily account statistics, weekly holdings correlations and mapped reference covariance are separate calculations. Read the calendar, window and coverage for each.

Calculation details and limitations

Realized variability and the observation calendar

Returns compare consecutive valuations after removing recorded net funding on the closing date. Volatility uses the n−1 divisor: the returned Performance window or last 30 returns in the recent-risk tile. Distributed dividends are not separately reinvested here.

Recorded and reconstructed observations can include calendar days, carried prices and irregular gaps. The engine still applies √252 without inferring a trading calendar or normalizing interval lengths. These conventions qualify annualized comparisons. Fewer than two usable returns withholds sample volatility.

Calculation

rᵢ = (closing valueᵢ − closing-date net fundingᵢ) / opening valueᵢ − 1 annualized volatility = sample standard deviation(r) × √252

Sharpe: an estimate with sampling uncertainty

Sharpe uses 252 times the arithmetic mean return, less the configured annual cash rate, over annualized volatility. The 3.5% fallback is a maintained assumption, not a historical interest-rate series.

Thirty returns and nonzero volatility permit display, not statistical confidence. Serial dependence alters annualization; non-normality affects inference. There is no autocorrelation correction or estimation interval. Alternative estimators introduce choices and estimation noise requiring their own evidence.

Calculation

Sharpe = (252 × mean(r) − configured annual risk-free rate) / annualized volatility

Drawdown depends on the observed path

Drawdown tracks linked TWR unit wealth against its running peak. Undefined return subperiods withhold the curve; stale-pricing gaps can leave it sparse. Falls between observations can remain unseen. Recovery means regaining the observed peak, not purchasing power. Drawdown and volatility use different return constructions.

Weekly co-movement is descriptive

The holdings lens uses completed Friday-anchored weeks, aligned simple returns and unshrunk Pearson correlations. Admission needs three eligible holdings covering 60% of book value and 80% common weekly observations. Missing histories can exclude holdings; value coverage is not risk coverage.

Fisher intervals are approximate, without time-series dependence or multiple-comparison adjustment. Bands and grouping thresholds are interpretation rules. Weak linear correlation establishes neither independence nor crash protection. Non-overlapping intervals across windows signal a difference; they are not a formal test of changing dependent correlations.

A separate reference covariance model

Reference risk uses three years of common weekly observations, an n−1 divisor, 52-period scaling and fixed 10% shrinkage toward the sample diagonal. Every accepted row contains every reference. For p references, admission requires at least max(104, 4p) common observations, 80% common coverage, no gap over three consecutive weeks, endpoints within 14 days and a valid covariance matrix. This is not fitted Ledoit–Wolf shrinkage.

Euler contributions reconcile to modeled volatility, retaining negative signs when covariance offsets risk. They do not represent selling and reallocating a holding. Whole-wealth risk requires usable valuation and reviewed mapping for every position, unlike the partial correlation lens.

Calculation

Σ = 52 × [0.9S + 0.1 diag(S)] portfolio volatility = √(wᵀΣw) volatility contributionᵢ = wᵢ(Σw)ᵢ / portfolio volatility

Regularization has a cost, and validation has a scope

Diagonal shrinkage preserves individual variances while moving covariances toward zero. Target bias trades against estimation noise; the adjustment is not uniformly conservative. The recorded September 30, 2026 review covers 32 references, ten cutoff/currency cases and 400 fixed portfolios, using independent 50-digit decimal arithmetic. It checks matrix validity, signed decomposition and selected 0%/20% shrinkage sensitivity. It does not establish out-of-sample forecasting accuracy or crisis probabilities.

Illustrative example, not market data

If two separately modeled references have identical returns, each has variance σ² and their covariance is σ². Shrinking covariance to 0.9σ² gives their equal-weight combination modeled variance 0.95σ². Duplication cannot itself reduce economic risk; the difference comes from the target.

Sources and further reading

The Sharpe Ratio (1994)Read the source note ↓: The Sharpe Ratio (1994)
The Statistics of Sharpe Ratios Read the source note ↓: The Statistics of Sharpe Ratios
Portfolio Selection Read the source note ↓: Portfolio Selection
Honey, I Shrunk the Sample Covariance Matrix Read the source note ↓: Honey, I Shrunk the Sample Covariance Matrix
Capital allocation to business units and sub-portfolios Read the source note ↓: Capital allocation to business units and sub-portfolios

Concentration & look-through

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Equity look-through measures the companies behind direct shares and eligible equity funds. It does not turn every asset class into equity exposure.

Look-through

Eligible equity funds are decomposed into constituents and merged with direct equity holdings. Bond, cash, gold and crypto funds remain whole
Verified issuer identities can join share classes and depositary receipts with their ordinary shares; uncertain identities remain unresolved
Unattributed equity mass stays in the equity denominator and out of named issuer numerators. It is never redistributed to visible companies
Coverage distinguishes missing constituent data from inherently opaque fund exposure; provider dates describe the age of the evidence

What incomplete coverage can establish

The private issuer-limit check cannot claim compliance below 80% equity coverage. A measured lower-bound breach can still be reported at any coverage
Even above that floor, unknown equity can prevent a compliant mandate verdict when it could conceal a cap breach. The public snapshot API has its own stricter section-availability guards
Not measurable stays unavailable. A verified lower-bound breach and partial coverage can both be true
The mandate issuer cap measures core equities across all imported depots, excluding satellites before look-through. The X-Ray also pools all imported depots; the depot in its route is an address, not a filter

Limits of the grouping

Issuer identity is not a complete parent-subsidiary or corporate-group map
Verified company names and supported identifier mappings determine joins. Without sufficient identity evidence, separate lines are not silently combined
Unresolved identity can understate observed concentration. A receipt without a verified issuer name does not become safely diversified by using its listing identifier
Bond funds are not dissolved into equity constituents. The separate company-risk analysis may combine identified corporate bonds with shares and names its own population

What you set and what is fixed

You set the limit for your largest single issuer in your mandate
The separate 5/40 diagnostic groups issuers above 5% and compares their combined share with 40%. It is an analytical reference, not a legal UCITS-compliance certificate for your personal portfolio
Effective issuer count is descriptive context. The equity denominator retains unattributed equity; cash is outside that denominator and cannot make equity concentration safer

Fund constituent data comes from provider disclosures and is cached. What is shown is the provider's own as-of date, not the time of retrieval.

Calculation

Underlying exposure and pairwise overlap

company exposure = direct weight + Σ(fund weight × constituent weight) overlap(A, B) = Σ shared securities min(weight in A, weight in B)

Exposure is weighted by what you own. Pairwise fund overlap describes the two funds themselves and is independent of the amounts you hold. Incomplete constituent lists can understate both; an empty overlap list does not prove zero overlap.

Illustrative example, not market data

A fund at 60% of your portfolio with 5% in a company contributes 3% exposure. A direct 2% holding brings the total to 5%.

Calculation

Concentration and coverage

issuer weight = attributed issuer value / equity-book value HHI = Σ issuer weights²; effective issuer count = 1 / HHI

Unattributed equity remains in the denominator. HHI and its inverse describe concentration, not statistically independent bets or a probability of loss. With incomplete identity coverage, observed weights are lower bounds and concentration can look too low. The separate company-risk reading includes eligible corporate bonds and has its own denominator.

Illustrative example, not market data

With full coverage, two issuers at 50% each give HHI 0.5 and an effective count of 2. Twenty fund wrappers do not necessarily mean twenty independent exposures.

Our decision and its limits

Unresolved equity stays in the denominator, so observed issuer weights are lower bounds. A coverage floor alone cannot prove a limit is satisfied.

Calculation details and limitations

Unknown equity stays in the denominator

Attributable direct equity and fund constituents share the valued equity-book denominator, including unresolved fund mass that may contain equity. Named weights are lower bounds under those values and scope. A measured breach can be certain while missing mass prevents reassurance. The 80% coverage floor does not remove uncertainty.

Effective issuer count is not independent bets

HHI measures issuer-size concentration, not return independence. Unresolved mass can make observed HHI understate concentration and its reciprocal overstate breadth. Two half-weight issuers have identical HHI whether their returns move together or offset each other.

Calculation

HHI = Σᵢ wᵢ² effective issuer count = 1 / HHI

Illustrative example, not market data

An 80% known issuer and 20% unresolved equity give observed HHI 0.64 and reciprocal about 1.56. If the unknown part belongs to that issuer, complete-book HHI and effective count are both 1.

A legal-inspired diagnostic has a narrower purpose

The 5/40 diagnostic sums issuers individually above 5% and flags a bucket above 40%, with strict comparisons. Approaching begins at 30% by product policy. Fund law has separate conditions and exceptions; this diagnostic does not test full UCITS compliance.

Sources and further reading

Concentrate on concentration risk Read the source note ↓: Concentrate on concentration risk
KAGB § 206: issuer limits for UCITS Deutsch Read the source note ↓: KAGB § 206: issuer limits for UCITS

The portfolio mandate score

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The mandate score measures the imported portfolio against your signed rules. It does not assess whether those rules suit your needs.

Scope and assumptions

Version 8 combines measured rules with limits on compensation between strong and weak results. Read individual verdicts, scopes and coverage alongside the score. It does not predict returns or loss probabilities.

Weights, curves and guardrails are Investboard policy choices. Composite-indicator research informs their disclosure; it does not validate these settings or establish that a higher score improves investment outcomes.

Our decision and its limits

Weights, curves and ceilings are product policy. Coverage belongs with the score: losing evidence for a weak rule can raise a partial result.

Calculation details and limitations

Target distance and compliance answer different questions

Signed ranges determine compliance. The allocation grade also measures distance from the target inside the range, so a compliant allocation need not earn 100. Distances use percentage points, not relative percentage changes.

For each class, d is absolute target distance, b is distance outside the range, and s is the larger of the target-to-boundary margin on that side and 5 percentage points. Aggregation emphasizes large deviations using the larger of actual and target weights. These settings are maintained calibration, not estimated loss probabilities.

Calculation

q = (d / s)² / 9 + (b / s)² class grade = 100 / (1 + q) allocation grade = 100 / (1 + √Σ[max(actual %, target %) × q² / 100])

Illustrative example, not market data

With a 60% target and a 55–65% permitted range, 65% remains compliant. Its individual class grade is 90; the aggregate allocation grade also depends on the other classes.

Raw weights are only part of the calculation

Raw weights are allocation 60, core-equity issuer limit 30, satellite allowance 10, direct-stock position cap 30 and cash floor 30. Only measured applicable rules enter the average. With all five measured, allocation receives 60/160, or 37.5%. Core-equity concentration uses a different denominator from whole-portfolio allocation.

The weakest averaging rule caps the headline at its grade plus 20. Exclusions and exposure bands have no averaging weight but can impose stricter ceilings. With a binding ceiling, improving another rule may leave the headline unchanged. Raw weights therefore do not describe actual influence everywhere.

Calculation

average = Σ(raw weight × measured grade) / Σ(measured raw weights) headline = min(average, weakest averaging grade + 20, applicable exposure ceilings, 100)

A strict verdict can sit beside a graduated grade

Verdicts use signed boundaries; grades express severity through continuous curves. The cash-floor grade is quadratic: half the required cash earns 25. A confirmed breach prevents a displayed 100 despite rounding. For upper-limit grades, excess is max(0, observed − limit). Scale is max(limit, 5 percentage points); the direct-stock position cap instead uses max(limit, 1 percentage point). Optional behavior and review history have zero headline weight.

Calculation

cash-floor grade = 100 × min(recorded cash / required cash, 1)² upper-limit grade = 100 / [1 + (excess / scale)²]

Illustrative example, not market data

Recorded cash of €500 against a €1,000 floor scores 25 and caps the headline at 45, even if every other measured rule is perfect.

Missing evidence can increase a partial score

Unmeasurable rules leave the average, changing the remaining weights. Losing a weak rule can raise the partial score, even to 100. That is an evidence change, not demonstrated improvement. Unknown cash differs from recorded zero; incomplete exposure evidence can establish a breach without establishing compliance.

Coverage must travel with the number. Comparable history requires complete coverage and compatible method, signed rules and scope. Household assets outside the imported portfolio do not enter the score.

Scenario previews use a separate score

Some rebalancing before-and-after scenarios use a separate 40/30/30 proxy combining allocation, concentration and structural allocation risk. Its change is not a change in the live version-8 score. Predictive validity for financial outcomes and robustness to alternative weights, curves, caps and missing-data assumptions have not been established here.

Sources and further reading

Elements of an investment policy statement Read the source note ↓: Elements of an investment policy statement
Handbook on Constructing Composite Indicators Read the source note ↓: Handbook on Constructing Composite Indicators

Costs and after-tax performance

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Observed returns already reflect fund expenses embedded in fund value and the costs present in recorded flows. We preserve that return and explain estimated embedded expenses separately. Recorded sale proceeds can already include tax, so the starting return is not uniformly before tax.

Scope and assumptions

The German after-tax estimate uses transaction and tax-profile evidence, accounting for embedded sale tax before adding further modeled drag. These estimates are not broker settlements or tax certificates.

Calculation

Known annual ongoing fund cost

known annual cost = Σ(covered fund value × annual cost rate) covered-fund TER = known annual cost / covered fund value

This is a current annualized estimate. Unknown charges remain outside the known subtotal, with coverage disclosed. It does not imply the same rates applied throughout the past.

Illustrative example, not market data

A 10,000 EUR portfolio with 6,000 EUR in a fund at 0.20% and 4,000 EUR cash has 12 EUR of known annual fund cost. The fund TER is 0.20%; the whole-portfolio known cost rate is 0.12%.

Our decision and its limits

A current TER applied to past capital is an estimate. Missing transaction or tax-profile evidence can withhold the German after-tax result.

Calculation details and limitations

Historical exposure, currently recorded rates

We reconstruct positions, including sold funds, and apply currently recorded expense rates to supported opening values over each interval. Intervals longer than seven days do not support an estimate. Rate dates and capital-days coverage describe evidence, not a historical archive of charges.

An unknown rate is not zero expense. A classified non-fund can have a known zero fund expense; missing capital can make coverage unknown. The covered subtotal cannot reconstruct an audited gross return or the future returns lost to costs. We never deduct it again from observed performance.

Calculation

estimated expense = Σ(value × current annual rate × interval days / 365)

Fund expenses are part of total investment cost

TER and ongoing-charge fields do not capture every spread, transaction cost, performance fee, financing, custody or advisory charge. ESMA distinguishes product costs from distribution services and shows that distributor remuneration can already sit inside product expenses. Adding overlapping disclosures would double-count it. We distinguish recorded fees from estimated fund expenses; missing charges cannot be inferred from a fund rate.

Sources and further reading

Total costs of investing in UCITS and AIFs Read the source note ↓: Total costs of investing in UCITS and AIFs
Fund fees, expenses and NAV Read the source note ↓: Fund fees, expenses and NAV
EStG § 32d: special tax rate Deutsch Read the source note ↓: EStG § 32d: special tax rate

Net worth & currencies

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The net-worth view sums six categories and converts everything into euro as the single reporting currency.

What is counted

Securities, real estate, pensions, precious metals and other assets make up gross assets
Net worth is gross assets less liabilities
The same figures are additionally split into liquid and tied-up wealth
Securities are not read from a stored value but revalued at the moment of retrieval

Currency conversion

Conversion runs through two legs: from the holding's currency into the portfolio's base currency, and from there into euro
Portfolios with different base currencies are therefore never added as if they were the same unit
Exchange rates come from the European Central Bank's reference rates first, with market-data providers only as a fallback. The source is stored alongside every rate
Reference rates are one daily fixing, not the rate at which anyone actually traded
Where fresh spot FX is unavailable, the wealth calculation can use a stored historical fixing and reports its effective date. Without usable conversion evidence, a complete valuation cannot be claimed; currencies are never silently treated as equal

What is not included

Separate bank-balance and crypto-account categories are not included in this wealth rollup. This differs from asset-class labels within imported securities analytics
Only securities are multi-currency. Real estate, pensions, precious metals, other assets and liabilities carry no currency field: the amount you enter is treated as euro
There is no automatic property valuation. The value is the one you enter

Once a day one level per user is written, freshly recomputed and never from a cache. The run is skipped when the price refresh has not succeeded within the last 24 hours.

Calculation

Wealth and foreign exchange

net worth = supported gross assets − liabilities value in EUR = native value × native-to-depot FX × depot-to-EUR FX

Wealth reporting uses EUR. Portfolio analytics may use the portfolio or selected scope's reporting currency. Historical transactions and valuations need dated currency evidence; today's FX rate is not a substitute for a missing historical fixing. A listing currency is also different from a company's economic currency exposure.

Illustrative example, not market data

A hypothetical 1,000 USD holding at 0.90 EUR per USD contributes 900 EUR. Adding 1,000 USD directly to 1,000 EUR would mix units.

Our decision and its limits

Only supported recorded categories and liabilities enter the total. Valuation dates can differ; the securities mandate uses a narrower population.

Calculation details and limitations

A balance sheet has valuation boundaries

Supported securities, property, pension, precious-metal and other recorded asset categories are added before recorded liabilities are deducted. Property is ownership-adjusted; pensions use recorded current values, not an assumed capitalization of every future entitlement. Non-securities amount fields are treated as EUR.

A net total does not establish liquidity, realizable sale value, borrowing capacity or complete household coverage. Valuation dates can differ across categories. The HFCS methodology is useful for defining wealth and pension boundaries; we do not reproduce its survey population, imputation or valuation process.

Sources and further reading

Household Finance and Consumption Survey: methodology Read the source note ↓: Household Finance and Consumption Survey: methodology
Framework for euro foreign exchange reference rates Read the source note ↓: Framework for euro foreign exchange reference rates

Projections

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Goal projections calculate outcomes under specified growth, volatility, contribution, inflation and tax assumptions. Their probabilities are conditional model frequencies.

Scope and assumptions

Independent normal shocks affect monthly log growth before contributions arrive. Annual growth anchors median compounding for an untaxed lump sum. This differs from deterministic calculator scenarios, recorded performance and cash affordability.

Percentile lines summarize each month; success counts terminal target outcomes. Fixed model parameters omit some uncertainty about future wealth.

Our decision and its limits

Bands depend on growth, volatility, contributions, tax and inflation assumptions. Pointwise outcomes under fixed parameters do not describe a guaranteed path.

Calculation details and limitations

The growth input describes a median

For annual rate g above −100%, log-growth volatility σ and standard normal shock Z, growth factors stay positive. The 8%, 15% and 22% volatility tiers are maintained assumptions, not measured portfolio volatility. Contributions and tax complicate the lump-sum lognormal distribution.

Calculation

Vₘ = Vₘ₋₁ × exp[ln(1+g)/12 + σZₘ/√12] + contributionₘ untaxed lump-sum median after T years = V₀(1+g)ᵀ untaxed lump-sum mean = V₀(1+g)ᵀ × exp(Tσ²/2)

Illustrative example, not market data

At fixed median growth, higher volatility worsens the lower tail but can increase success for an above-median target. It is not uniformly conservative for the reported probability.

Cash timing, nominal tax and purchasing power

A supplied feasible contribution schedule replaces declared saving; a declaration alone does not prove affordability. Nominal values and German fund advance tax at 12-month boundaries, per sleeve, are simulated first, without awarding each goal another personal allowance. A recorded non-assessment certificate suppresses the modeled advance-tax deduction. Fees and later realized-gain tax are excluded.

A fixed 2% annual factor deflates purchasing-power bands and inflates today's-money target for deadline comparison. This is an assumption, not an inflation forecast. Joint projections make both portfolios move in lockstep; no diversification between the two is credited.

Illustrative example, not market data

Start at 100 and add 100 after each period. Returns of +50%, then −50% end at 225; reversing them ends at 325. Without contributions both end at 75. Equal compounded returns do not imply equal savings outcomes.

A percentile line is not one simulated path

Values are sorted each month for P10, P25, P50, P75 and P90; a line can join different paths. Pointwise P10–P90 bands do not give an 80% probability of staying inside throughout, or a forecast confidence interval. Deadline success differs from earlier target contact, interim affordability and retirement survival.

More paths cannot resolve uncertain assumptions

The default 1,000 paths give 0.1-percentage-point frequency increments. Near 50%, idealized Monte Carlo standard error is about 1.6 percentage points under fixed assumptions: simulation noise, not real-world accuracy. A seed and fingerprint permit replay; more paths do not validate parameters.

Normal log shocks omit empirical tails, volatility clustering and crisis dependence. Fixed growth, volatility and inflation omit parameter uncertainty. Historical resampling and richer volatility models address different omissions but introduce sample and estimation risks. Complexity alone does not establish better calibration.

A missing future deadline, confirmed EUR units, admitted current valuation, target, contribution or risk/return assumption can withhold the projection. An absent parameter is not silently replaced by a measured zero.

Sources and further reading

The lognormal distribution Read the source note ↓: The lognormal distribution
Empirical properties of asset returns: stylized facts Read the source note ↓: Empirical properties of asset returns: stylized facts
Are Stocks Really Less Volatile in the Long Run?Read the source note ↓: Are Stocks Really Less Volatile in the Long Run?
The ECB’s two percent inflation target Read the source note ↓: The ECB’s two percent inflation target

Stress tests and historical scenarios

Back to contents ↑

Stress replay applies a named historical episode or assumed shock to today's valued holdings. It describes vulnerability under that scenario, without assigning a probability or reproducing your actual past portfolio.

Scope and assumptions

Direct security history, sector proxies, asset-class assumptions and FX evidence retain different meanings. A complete current valuation is required; scenario coverage can still be partial. Read the modeled subtotal and excluded holdings before treating the percentage as a whole-wealth loss.

Our decision and its limits

Complete current valuation is required, while scenario coverage can be partial. Read the modeled-loss denominator together with the excluded holdings.

Calculation details and limitations

Two denominators, two valid readings

Modeled loss percentage divides impact by modeled pre-stress value. Coverage divides modeled value by all known valued holdings, including explicitly excluded positions. An excluded holding is not assumed to survive unchanged. Partial coverage withholds a complete-book interpretation.

Calculation

modeled loss % = modeled impact / modeled starting value coverage = modeled starting value / all known valued holdings

Illustrative example, not market data

With 8,000 modeled and 2,000 excluded, a modeled loss of 2,000 is −25% on the modeled book at 80% coverage. It is not evidence of a −20% complete-portfolio loss; the excluded outcome is unknown.

A proxy is a different claim from a price

Accepted direct history needs compatible dates, instrument, price basis and currency. Sector proxies and asset-class shocks fill different evidence gaps. A crypto scenario before that asset's inception, or a stand-in for property or commodities, is an assumption about exposure rather than that holding's historical return.

Asset and FX gross factors multiply. Quote currency does not establish underlying economic exposure or hedging. A selected window's endpoint loss differs from its maximum interim drawdown. Replay omits changing holdings, emergency sales, market impact and liquidity constraints. Save the scenario definition and accepted dataset as well as its name.

Calculation

combined return = (1 + asset return) × (1 + FX return) − 1

Illustrative example, not market data

A −50% asset move and −10% FX move produce −55% together. A 1,000 holding becomes 450, before any separately modeled effects.

Sources and further reading

BCBS stress-testing principles, consolidated RMA30 Read the source note ↓: BCBS stress-testing principles, consolidated RMA30

Tax calculation

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The tax calculation models the German tax waterfall for capital income in detail:

Gross capital income

Dividends, realized capital gains, advance lump sums (Vorabpauschale)

Partial exemption (Teilfreistellung)

Depending on fund type: 30% (equity funds), 15% (mixed funds), 60% (real-estate funds), 80% (foreign real-estate funds)

Loss offsetting (Verlustverrechnung)

Equity losses offset only equity gains, other losses offset all remaining capital income

Saver's allowance (Sparerpauschbetrag)

EUR 1,000 (individual) or EUR 2,000 (joint filing) is deducted

Flat capital-gains tax (Abgeltungsteuer)

The base special rate is 25%; eligible foreign-tax credits and church-tax deductibility modify the calculation under § 32d EStG

Solidarity surcharge (Solidaritätszuschlag)

5.5% on the Abgeltungsteuer

Church tax (optional)

8% or 9% of the resulting capital-income tax, where applicable. The tax base is adjusted for church-tax deductibility rather than adding this to an unchanged 25% rate

This is a German private-investor tax model for capital income under EStG §20, not a universal tax calculation for every supported website language. Fund classification, tax year, loss pools, allowances and the recorded profile determine the result. Vorabpauschale uses the relevant annual base rate, statutory cap and acquisition-year adjustment. Estimates do not replace an individual tax review or a broker certificate.

Our decision and its limits

This model uses German private-investor rules in every reading language. Fund classification, tax year, losses and remaining allowances determine the result.

Calculation details and limitations

Order matters in the German model

The fund classification determines partial exemption, symmetrically for gains and losses. Relevant loss pools are applied before the remaining personal allowance. Previously assessed Vorabpauschalen reduce a fund's disposal gain in full before partial exemption, under §19(1) InvStG; they are not deducted again as a second tax credit.

The special-rate relationship accounts for church tax and eligible foreign-tax credits. Solidarity surcharge and church tax apply to the resulting capital-income tax. Tax residency, fund eligibility, cost basis, loss restrictions and assessment choices remain individual prerequisites.

Calculation

capital-income tax = (taxable income − 4 × eligible foreign tax) / (4 + church-tax rate)

Illustrative example, not market data

For a qualifying equity fund, a disposal gain of 1,000 and prior assessed advance lump-sum bases of 100 leave 900 before the 30% exemption, hence 630 before loss offsetting and allowance. This is an ordering example, not a complete tax assessment.

An annual official rate is not a future forecast

The BMF letter of January 13, 2026 sets the 2026 Basiszins at 3.20%; the corresponding advance lump sum is deemed received on January 4, 2027. Section 18 also specifies the base-yield factor, annual gain cap, distribution adjustment and acquisition-year treatment. The rate alone does not determine an investor's tax.

A projection must assume future rates and law that are not yet known. Website language never changes the German jurisdiction of this calculation. Estimated after-tax performance, hypothetical tax effects and a broker's actual settlement remain distinct results.

Sources and further reading

Data sources

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Investboard sources market data from specialist market-data providers:

Price data

Price sources and access depend on the instrument, listing and provider entitlement
A current quote, an end-of-day close and a historical adjusted series are different observations
Exchange holidays, market hours and provider delays affect freshness
A carried price retains its age and quality state; unavailable valuation remains explicit

Closing prices & fundamental data

Company fundamentals and fund constituents are supplied by specialist providers, including Financial Modeling Prep where supported
A provider reporting date, a retrieval time and an analytical computation time are different timestamps
Plausibility and identity checks reduce errors but cannot guarantee provider data is correct
Sector, country and industry are classifications. Company domicile is not revenue geography; a listing currency is not measured economic FX sensitivity

Data quality is monitored continuously. The user is informed of discrepancies or missing data points.

Our decision and its limits

Observation dates govern the evidence; retrieving a file does not refresh its contents. Carry and fallback choices retain their own data basis.

Calculation details and limitations

Four dates that should not be confused

Price observation, fund-holdings reporting date, provider retrieval and calculation time describe different events. A newly retrieved holdings file can still describe an old portfolio. An adjusted price series, distributed dividend and total-return series also need compatible treatment to avoid double-counting income.

Provider names and schema documentation establish provenance, not independently verified accuracy. A fallback can change source, freshness or modeling basis. Replay needs the accepted input values and conventions; the current provider response may differ from the saved result. Public engines accept evidence under their input contracts and do not publish our licensed feeds.

Sources and further reading

Twelve Data API documentation Read the source note ↓: Twelve Data API documentation
Financial Modeling Prep API documentation Read the source note ↓: Financial Modeling Prep API documentation
Framework for euro foreign exchange reference rates Read the source note ↓: Framework for euro foreign exchange reference rates

Rebalancing & optimization

Back to contents ↑

Rebalancing restores a chosen allocation under stated constraints. It does not guarantee higher returns or protection from falling markets.

Scope and assumptions

A policy specifies review timing, trading triggers, destinations and acceptable costs. Investboard applies signed corridors, available funding, sale restrictions, minimum trades and tax evidence. Generated scenarios remain conditional on those inputs.

Calculation

Drift is measured in percentage points

drift = actual weight − target weight target amount after contribution = target weight × (portfolio value + contribution)

A signed target range and distance from the target are separate readings. Rebalancing scenarios depend on budget, minimum transaction size, sale restrictions and tax evidence. A calculated scenario is not proof of a globally optimal allocation or an executable order.

Illustrative example, not market data

An equity weight of 65% against a 60% target is 5 percentage points overweight. Whether that breaches your plan depends on the signed range.

Our decision and its limits

A scenario applies the signed policy, budget, trading restrictions and tax assumptions. It does not establish a globally optimal allocation.

Calculation details and limitations

Trigger and destination are separate choices

Signed corridor breaches trigger correction; quantities aim toward targets. Calendar policies instead review or trade at scheduled intervals. Threshold policies tolerate drift until a boundary is crossed. Costs and uncorrected drift depend on both monitoring and trading rules.

Returning to target creates distance from the next boundary but requires larger trades. Trading only to a boundary can reduce proportional costs; fixed charges may favor fewer, larger adjustments. Research supports comparing alternatives under an explicit objective, not a universally optimal frequency or band. Constant-mix rebalancing behaves differently in trending and reversing markets.

New contributions help only within their capacity

Contribution-only planning allocates money toward shortfalls using the post-contribution portfolio value, while protecting the cash floor. Minimum trades, rounding and restrictions can leave cash or drift. Avoiding sales can reduce realized taxes, but available funding limits the correction.

Illustrative example, not market data

A €100,000 portfolio holding €70,000 equities and €30,000 bonds needs about €16,667 added entirely to bonds to reach 60/40 without sales, before costs. A €1,000 contribution cannot do so.

Tax-aware describes a heuristic, not an optimum

One sale filter can skip a trade when estimated tax exceeds 3% of trade value and absolute allocation deviation is at most 15 percentage points. These are product thresholds, not research-established optima. Missing cost basis stays unknown. Purchasing capacity depends on the applicable tax calculation and net proceeds.

Tax-aware planning does not establish minimum lifetime taxes or a globally optimal allocation. Those claims require comparison with alternative policies under realistic spreads, fees, taxes, cash flows and adverse market paths. That empirical validation has not been established here.

Sources and further reading

Elements of an investment policy statement Read the source note ↓: Elements of an investment policy statement
Dynamic Strategies for Asset Allocation Read the source note ↓: Dynamic Strategies for Asset Allocation
Best Practices for Portfolio Rebalancing Read the source note ↓: Best Practices for Portfolio Rebalancing

Use of AI

Back to contents ↑

Financial calculations and language-model explanations have different reliability boundaries. Deterministic services produce the measured inputs; AI turns supplied evidence into an explanation that still requires scrutiny.

Scope and assumptions

A fluent answer, matching number or linked source does not by itself establish that the interpretation is correct. The calculation method, source data and explanation each need their own evidence.

Our decision and its limits

Severe recognized patterns can block output; unmatched numbers are logged. Numeric or source matching alone cannot verify an explanation’s meaning.

Calculation details and limitations

What the output guardrail actually checks

Severe recognized patterns can replace an answer; advice-like patterns can append a disclaimer. Numbers unmatched to supplied facts are logged, rather than automatically blocking the answer. Pattern checks do not prove factual completeness. A matching number can still be paired with the wrong denominator, period or meaning.

There is no accuracy percentage established here for generated explanations. NIST's confabulation and evaluation guidance and ESMA's financial-sector statement explain why controls, evidence and human scrutiny matter. They do not certify these controls or establish Investboard's regulatory status.

Processing terms and factual correctness differ

AWS documents data handling for the built-in Bedrock inference route, including model-provider access boundaries. A separately connected external provider has its own terms. Processing safeguards do not establish whether an explanation, financial inference or citation is true.

Sources and further reading

Generative AI Profile · NIST AI 600-1 Read the source note ↓: Generative AI Profile · NIST AI 600-1
AI in retail investment services Read the source note ↓: AI in retail investment services
Data protection in Amazon Bedrock Read the source note ↓: Data protection in Amazon Bedrock

When Investboard declines to answer

Back to contents ↑

The hardest number is the one you do not have. Investboard is built to show nothing in that case rather than something plausible.

No value is invented as a substitute

Loading and empty are separate states. While a query is in flight a fixed-width placeholder stands there, not a zero
A withheld value appears as an en-dash, never as a zero. The formatter deliberately returns nothing, so the placeholder has to be placed consciously
Negative amounts carry a typographic minus sign, not a hyphen

Automated checks and their limits

Automated source checks look for fabricated financial state and selected unsupported claims. Labeled illustrative examples are permitted
Additional rules look for common fallbacks that turn missing data into a number and timestamps that misrepresent the age of the data
Count-up animation on monetary values is prohibited. Numbers appear fully formed rather than counting up
Promotional promises and exclamation marks are blocked in the copy dictionaries
Fixture tests and scan-coverage checks help detect regressions in these rules. They do not certify every result or sentence

Refusals in live operation

Below 80% equity coverage the issuer-limit check cannot establish compliance. A known lower-bound breach may still be shown with its coverage qualification
Missing FX does not justify one-to-one conversion. Supported carry-forward uses dated evidence and remains distinguishable from a fresh spot rate
A holding without a usable price is not valued at zero but listed by name as unvalued
Below one year of history no return is extrapolated, and below 30 observations no Sharpe ratio is reported
A concentration alert is withheld while prices in the core portfolio are older than 72 hours

Where this commitment ends

AI output checks can block serious safety violations. Unsupported-number checks can also log rather than withhold; pattern checks and notices cannot prove every sentence is correct
Where an AI answer reads like a recommendation, a note is placed beneath it rather than the sentence being removed
This protective layer works on patterns and is explicitly not watertight
On the home page example figures are permitted and marked as such in the code. They are illustration, not measurement

These rules are not a promise to always be right. They are the commitment to show the gap rather than fill it.

Our decision and its limits

Partial evidence can establish a breach while leaving compliance unproven. Unavailable, partial and measured zero remain different results.

Calculation details and limitations

Unavailable, partial and zero are different results

A measured zero carries evidence. Unavailable means prerequisites are missing; partial means a supported subset is known. A minimum coverage threshold permits a qualified calculation, not a favorable conclusion about the rest.

At 95% issuer coverage, an observed 8% weight can reach 13% if all unresolved equity belongs to that issuer. A 10% limit is therefore not proven satisfied. An observed 11% already establishes a breach. The same asymmetric reasoning applies when a missing rule can remove a weak grade and increase a partial mandate score.

Sources and further reading

GIPS Handbook: cash flows and return measurement Read the source note ↓: GIPS Handbook: cash flows and return measurement
Generative AI Profile · NIST AI 600-1 Read the source note ↓: Generative AI Profile · NIST AI 600-1

Limits & transparency

Back to contents ↑

Investboard communicates clearly what the platform does and does not do. Honesty about its own limits is part of the product promise.

No investment advice

Investboard is an analysis tool. The platform does not provide individual investment advice within the meaning of the WpHG (the German Securities Trading Act). All information is for illustration only.

No trade execution

Investboard does not carry out securities transactions and does not route orders to banks or brokers. Bank and custody connections are used solely to read your holdings. Strategy and analysis, not execution.

No future forecasts

The platform analyses historical and current data but makes no forecasts about future price movements or returns.

No return guarantees

Simulations and projections show ranges, not promises. Investboard names the assumptions a calculation rests on and marks what is measured against what is modeled.

Our decision and its limits

Versions and data dates belong to each result. Public modules expose the calculation contracts documented for those modules.

Calculation details and limitations

Compare results only after comparing their contracts

A changed result can come from new market prices, a corrected transaction, revised holdings, a different denominator or a changed method. Compare data cutoffs, population, currency, income basis, coverage and versions before interpreting a change as an investment outcome.

The public performance, stress, rebalancing and cash-scheduling modules expose particular input and calculation contracts. They do not expose every native risk, score, tax or AI service. The public goal-planning module schedules cash and measures no-growth funding gaps; it is not the probabilistic goal simulation described above. A reproducible module is a valuable audit surface, not an audit of the full application.

Sources and further reading

Elements of an investment policy statement Read the source note ↓: Elements of an investment policy statement
BCBS stress-testing principles, consolidated RMA30 Read the source note ↓: BCBS stress-testing principles, consolidated RMA30

Example edition 1.0.0

Reproduce the arithmetic

Six synthetic cases connect declared inputs, calculation steps and expected results. Use them to understand what a number answers and what it leaves unknown.

Download the replay bundle · ZIP ↓Download all inputs · JSON ↓Download expected results · JSON ↓

Explanations on this page use your reading language. JSON field names, program code and the technical README use English so the same versioned files can be shared across all editions.

In JSON, returns and coverage are decimal fractions: 0.10 means 10%. Fields ending in Pp are percentage points; amounts are EUR unless another currency is specified.

01 · Synthetic worked example

The return of investments and the return of your money

The same two-period history produces different time-weighted and money-weighted returns when most money arrives before the loss.

Read the method: Return measurement ↑

Open inputs, calculation and result

Calculation steps

Start with 100. After the first 365-day year, +10% produces 110. Add 900, giving 1,010. The next year loses 10%, leaving 909.
Link the investment returns: 1.10 × 0.90 − 1 = −1% over the two years.
For annual money-weighted return r, solve −100 − 900/(1+r) + 909/(1+r)² = 0. The positive growth-factor root gives approximately −8.34% per year.

Inputs

{
  "id": "funding-and-mwr",
  "currency": "EUR",
  "openingDate": "2021-01-01",
  "fundingDate": "2022-01-01",
  "closingDate": "2023-01-01",
  "openingValue": 100,
  "observedValueBeforeFunding": 110,
  "contribution": 900,
  "observedValueAfterFunding": 1010,
  "closingValue": 909
}

Expected result

{
  "periodReturns": [
    0.1,
    -0.1
  ],
  "timeWeightedReturn": -0.01,
  "moneyWeightedAnnualRate": -0.083359,
  "investmentResult": -91,
  "linkedPeriodContributions": [
    0.09,
    -0.1
  ]
}

What it means

Most capital was invested during the losing year. The cumulative TWR and annual MWR use different periods of expression; do not compare them as interchangeable annual rates.

02 · Synthetic worked example

A missing valuation changes what can be measured

A funding date without a valuation prevents an exact reconstruction of the investment path.

Read the method: Return measurement ↑

Open inputs, calculation and result

Calculation steps

Observe 100 on January 1, add 100 on January 11 without a valuation, then observe 220 on January 21.
The carry/fold convention assigns 0% before the funding boundary and 220/200 − 1 = 10% afterward.
Whole-period Modified Dietz instead gives (220 − 100 − 100)/(100 + 0.5 × 100) = 13.33%.

Inputs

{
  "id": "missing-valuation",
  "currency": "EUR",
  "openingDate": "2026-01-01",
  "fundingDate": "2026-01-11",
  "closingDate": "2026-01-21",
  "openingValue": 100,
  "contribution": 100,
  "closingValue": 220,
  "observedValueOnFundingDate": null,
  "alternativeUnobservedPreFundingValues": [
    120,
    80
  ]
}

Expected result

{
  "carriedBoundaryValue": 100,
  "nextOpeningValue": 200,
  "carriedBoundaryTimeWeightedReturn": 0.1,
  "wholePeriodModifiedDietz": 0.133333,
  "alternativeTrueTimeWeightedReturns": [
    0.2,
    -0.022222
  ]
}

What it means

Both calculations need a convention. The missing January 11 value prevents either approximation from establishing the true TWR.

03 · Synthetic worked example

A price gain can become a reporting-currency loss

Separate a USD price move from its EUR translation without allocating their interaction twice.

Read the method: Return measurement ↑

Open inputs, calculation and result

Calculation steps

100 USD at 0.90 EUR/USD is 90 EUR. Later, 110 USD at 0.81 EUR/USD is 89.10 EUR.
Local price gains 10% and FX loses 10%: 1.10 × 0.90 − 1 = −1% in EUR.
Split the −1 percentage-point interaction equally: local contribution +9.5 points and FX contribution −10.5 points. Their euro changes are +8.55 and −9.45, totaling −0.90 EUR.

Inputs

{
  "id": "price-and-fx",
  "reportingCurrency": "EUR",
  "quoteCurrency": "USD",
  "quantity": 1,
  "openingLocalPrice": 100,
  "closingLocalPrice": 110,
  "openingReportingPerQuote": 0.9,
  "closingReportingPerQuote": 0.81,
  "distributedIncome": 0
}

Expected result

{
  "openingValueEur": 90,
  "closingValueEur": 89.1,
  "localPriceReturn": 0.1,
  "quoteFxReturn": -0.1,
  "combinedReturn": -0.01,
  "localPriceDeltaEur": 8.55,
  "quoteFxDeltaEur": -9.45,
  "localContributionPp": 9.5,
  "fxContributionPp": -10.5,
  "investmentResultEur": -0.9,
  "componentSumGapEur": 0
}

What it means

The components reconcile to the supplied values and rates. This is quote-currency translation; it does not measure a company's economic currency exposure.

04 · Synthetic worked example

A breach can be certain while compliance remains unproven

An issuer's observed weight is a lower bound while part of the equity book remains unresolved.

Read the method: Concentration & look-through ↑

Open inputs, calculation and result

Calculation steps

Value the equity book at 10,000, with 500 unresolved and 800 attributed to issuer A. Other identified issuers account for 8,700.
The observed weight is 800/10,000 = 8%. Assigning all unresolved equity to A gives a possible upper bound of 13%.
A 10% cap is not proven satisfied. If A is already observed at 11%, the breach is established regardless of the unresolved allocation.

Inputs

{
  "id": "concentration-coverage",
  "currency": "EUR",
  "totalEquityValue": 10000,
  "resolvedEquityValue": 9500,
  "observedIssuerValue": 800,
  "alternativeObservedIssuerValue": 1100,
  "issuerLimit": 0.1
}

Expected result

{
  "coverage": 0.95,
  "unresolvedEquityValue": 500,
  "observedIssuerWeight": 0.08,
  "maximumPossibleIssuerWeight": 0.13,
  "verdict": "not_proven_within_limit",
  "alternativeObservedIssuerWeight": 0.11,
  "alternativeVerdict": "breach"
}

What it means

95% identity coverage does not settle every limit. The missing part matters relative to the rule being assessed.

05 · Synthetic worked example

A scenario loss and its coverage use different denominators

A modeled subtotal cannot silently stand in for the whole portfolio.

Read the method: Stress tests and historical scenarios ↑

Open inputs, calculation and result

Calculation steps

Known valued holdings total 10,000. Scenario evidence covers 8,000; holdings worth 2,000 are explicitly excluded.
A modeled impact of −2,000 is −2,000/8,000 = −25% on the modeled holdings.
Coverage is 8,000/10,000 = 80%. The excluded outcome is unknown.

Inputs

{
  "id": "stress-coverage",
  "currency": "EUR",
  "modeledStartingValue": 8000,
  "excludedStartingValue": 2000,
  "modeledImpact": -2000,
  "excludedImpact": null
}

Expected result

{
  "knownStartingValue": 10000,
  "modeledReturn": -0.25,
  "coverage": 0.8,
  "modeledImpactOverKnownValue": -0.2,
  "wholeBookReturn": null
}

What it means

The result is −25% on a modeled book at 80% coverage. It does not establish a −20% complete-portfolio loss.

06 · Synthetic worked example

New money has a limited capacity to correct drift

Funding an underweight can avoid sales, but a small contribution may leave most of the deviation.

Read the method: Rebalancing & optimization ↑

Open inputs, calculation and result

Calculation steps

Start with 70,000 in equities and 30,000 in bonds. Target 60/40; assume unchanged prices, no costs, no taxes and no cash-floor constraint.
If x goes entirely to bonds, solve 70,000/(100,000 + x) = 0.60. The continuous solution is approximately 16,666.67.
A contribution of only 1,000 leaves the equity share at 70,000/101,000, approximately 69.31%.

Inputs

{
  "id": "contribution-only-rebalance",
  "currency": "EUR",
  "equityValue": 70000,
  "bondValue": 30000,
  "targetEquityNumerator": 3,
  "targetEquityDenominator": 5,
  "availableContribution": 1000,
  "allNewMoneyGoesToBonds": true,
  "salesAllowed": false,
  "feesAndTaxes": 0
}

Expected result

{
  "startingValue": 100000,
  "requiredContributionFraction": {
    "numerator": 50000,
    "denominator": 3
  },
  "requiredContribution": 16666.666667,
  "minimumWholeCentContribution": 16666.67,
  "valueAfterAvailableContribution": 101000,
  "equityWeightAfterAvailableContribution": 0.693069,
  "bondWeightAfterAvailableContribution": 0.306931,
  "availableContributionReachesTarget": false
}

What it means

Contribution-only planning can move toward the target without reaching it. Actual tradable quantities, minimum trades and costs can create further residual drift.

Run the examples yourself

The bundle contains the inputs, expected results and a small offline JavaScript program. It uses no account, API key or downloaded market history.

Download and unpack the bundle. Keep its files together.
With Node.js 22 or newer installed, open a terminal in the unpacked folder and run the command below.
Compare the printed JSON with expected.json. The README describes rounding and the separate public-module replay.

node replay.mjs

These cases reproduce defined arithmetic and documented input conventions. They do not certify connected-account imports, missing-data decisions, future probabilities or the complete platform. The optional public-module replay uses the pinned performance package; it is distinct from the standalone arithmetic program.

Sources and method changes

Back to contents ↑

Selected original papers, authoritative methods, official law and provider contracts are linked to the decisions they inform. Descriptions identify relevant sections and the limits of each source. Older foundational work is paired with research on estimation and model uncertainty. Publication prestige does not validate our implementation, parameters or platform.

Research

Linking Single Period Attribution Results
Andrew S. B. Frongello · Journal of Performance Measurement · 2002
Frongello (2002), especially p. 13; original paper’s publisher record. Its original recursion differs from our reversed zero-benchmark convention. The detailed formula and public attribution source establish the convention actually used here.
Used in: Return measurement ↑
Linking contributions and the order of returns
The Spaulding Group · Performance Perspectives · 2014-01
The original publisher’s January 2014 newsletter, pp. 2–4, demonstrates future-return scaling and order-dependent contributions; it also cites Frongello’s 2002/2003 “The Recursive Family Dilemma.” Reconciliation does not select a unique attribution.
Used in: Return measurement ↑
The Sharpe Ratio (1994)
William F. Sharpe · Stanford · 1994
The author’s “Ex Post Sharpe Ratio” and “Time Dependence” sections distinguish historical estimation, expected differential returns and sampling assumptions. They do not validate our observation calendar or configured cash rate.
Used in: Risk, drawdown and correlation ↑
The Statistics of Sharpe Ratios
Andrew W. Lo · Financial Analysts Journal · 2002
Lo (2002), pp. 38,40–42 and equations (19)–(20): estimation uncertainty and serial-correlation effects on annualization. Explains why an observation threshold and square-root rule do not establish precision.
Used in: Risk, drawdown and correlation ↑
Portfolio Selection
Harry Markowitz · Journal of Finance · 1952
Markowitz (1952), pp. 80–83 and 89–91: variance, covariance and diversification, with estimation and practical input limits. Establishes the framework, not the correctness of our reference mappings or future covariance.
Used in: Risk, drawdown and correlation ↑
Honey, I Shrunk the Sample Covariance Matrix
Olivier Ledoit · Michael Wolf · 2003/2004
Ledoit–Wolf, 2003 working version of the 2004 paper, §§ 3.1–3.3: target construction and estimated intensity. Our fixed 10% shrinkage to a diagonal is a different estimator; citing this paper does not make it fitted Ledoit–Wolf shrinkage.
Used in: Risk, drawdown and correlation ↑
Capital allocation to business units and sub-portfolios
Dirk Tasche · 2008
Tasche, § 3.1, equation (3.4a), p. 8: Euler volatility contributions and their additive identity. Signed contributions describe a fixed modeled portfolio; they do not equal the impact of selling a position.
Used in: Risk, drawdown and correlation ↑
Total costs of investing in UCITS and AIFs
ESMA · 2025-11
November 2025 report, pp. 7–9 and methods pp. 53–55: product and distribution costs, estimation and overlapping remuneration. Survey findings are not an account invoice or a universal fee estimate.
Used in: Costs and after-tax performance ↑
Household Finance and Consumption Survey: methodology
ECB · Household Finance and Consumption Network · 2023
Statistics Paper 45, § 2.2, especially pensions in § 2.2.6 and the reference-period discussion. Supports careful wealth definitions and valuation boundaries, not equivalence to our supported categories or the survey.
Used in: Net worth & currencies ↑
Empirical properties of asset returns: stylized facts
Rama Cont · Quantitative Finance · 2001
Cont (2001), § 2 and §§ 5–6: heavy tails, volatility clustering and dependence across time scales. Explains omissions of independent normal log shocks; it does not supply or validate our volatility tiers.
Used in: Projections ↑
Are Stocks Really Less Volatile in the Long Run?
Ľuboš Pástor · Robert F. Stambaugh · Journal of Finance · 2012
Pástor–Stambaugh (2012), §I equations (3)–(4) and §VI: predictive variance and parameter uncertainty. Conditional simulated paths with fixed parameters omit uncertainty that can grow with the horizon.
Used in: Projections ↑
Dynamic Strategies for Asset Allocation
André F. Perold · William F. Sharpe · 1988/1995
Perold–Sharpe (1988), 1995 reprint pp. 151–154,158–160; footnote 8 excludes transaction costs. Explains path-dependent differences between constant-mix and buy-and-hold, without establishing a universal winner.
Used in: Rebalancing & optimization ↑
Best Practices for Portfolio Rebalancing
Vanguard · Jaconetti, Kinniry, Zilbering · 2010
Jaconetti, Kinniry and Zilbering (2010), pp. 10–11: cash-flow use and cost-dependent destinations. Historical findings are conditional on the study portfolio and assumptions. Original authored paper hosted by Indexa Capital.
Used in: Rebalancing & optimization ↑

Methodological guidance

GIPS Handbook: cash flows and return measurement
CFA Institute · GIPS · 2020/2021
2020 standards, 2021 handbook: printed pp. 100–105 for TWR and Modified Dietz; pp. 109–111 for MWR; pp. 85–86 for short-period annualization. These conventions do not establish GIPS compliance or exact TWR from missing valuations.
Used in: Return measurement ↑When Investboard declines to answer ↑
Elements of an investment policy statement
CFA Institute · 2010
Individual-investor guidance, pp. 11–17; rebalancing § 4c, p. 17. Objectives, constraints and governance support a written mandate. These pages do not prescribe our score weights or a universally optimal trading policy.
Used in: The portfolio mandate score ↑Rebalancing & optimization ↑Limits & transparency ↑
Handbook on Constructing Composite Indicators
OECD · European Commission JRC · 2008
OECD/JRC (2008), pp. 24,31–35,83–85,102–108 and117–123: missing data, normalization, weights, compensation and sensitivity. Supports disclosure and robustness analysis; does not validate version 8’s curves or ceilings.
Used in: The portfolio mandate score ↑
The lognormal distribution
NIST · Engineering Statistics Handbook
NIST gives the mean, median and distribution functions implied by normal log growth. This mathematical identity does not establish market realism, parameter calibration or forecast confidence.
Used in: Projections ↑
BCBS stress-testing principles, consolidated RMA30
Basel Committee · BIS · 2026
January 2026 version, §§ 30.27–31, 30.40–50 and 30.55–64: objectives, scenarios, data, model limits and review. Banking principles inform disclosure, without equating retail replay to supervisory testing.
Used in: Stress tests and historical scenarios ↑Limits & transparency ↑
Generative AI Profile · NIST AI 600-1
NIST · AI 600-1 · 2024
§ 2.2 on confabulation and MEASURE 2.5 actions 001, 003, 006 on grounded evidence and evaluation. The guidance explains failure modes and assessment needs; it does not certify our controls.
Used in: Use of AI ↑When Investboard declines to answer ↑
AI in retail investment services
ESMA · 2024-05-30
ESMA statement of May 30, 2024, paragraphs 5, 8–16 and 21–24: output reliability, data, oversight and client interests. Its investment-firm scope does not establish Investboard’s regulatory status or compliance.
Used in: Use of AI ↑

Law and official tax guidance

KAGB § 206: issuer limits for UCITS Deutsch
Bundesministerium der Justiz
The fund-law origin of the 5/40 diagnostic, including legal conditions and exceptions that the diagnostic does not fully test.
Used in: Concentration & look-through ↑
EStG § 32d: special tax rate Deutsch
Bundesministerium der Justiz
The German capital-income tax rate relationship, including church tax and creditable foreign tax under the statutory conditions.
Used in: Costs and after-tax performance ↑Tax calculation ↑
EStG § 20: capital income Deutsch
Bundesministerium der Justiz
German income categories, loss offsetting and the private-investor allowance.
Used in: Tax calculation ↑
InvStG § 18: Vorabpauschale Deutsch
Bundesministerium der Justiz
The advance lump-sum assessment, annual limit and acquisition-year adjustment.
Used in: Tax calculation ↑
InvStG § 19: disposal gains Deutsch
Bundesministerium der Justiz
Section 19(1) reduces disposal gains by previously assessed advance lump sums in full before the partial exemption. The statutory ordering prevents treating them as a second independent tax credit.
Used in: Tax calculation ↑
InvStG § 20: partial exemptions Deutsch
Bundesministerium der Justiz
Fund and investor classification determine the applicable German partial exemption.
Used in: Tax calculation ↑
BMF: Basiszins for the 2026 Vorabpauschale Deutsch
Bundesministerium der Finanzen · 2026-01-13
Official letter dated January 13, 2026: 3.20% for 2026 and deemed receipt on January 4, 2027. A dated annual rate is neither a forecast of future rates nor a complete personal tax calculation.
Used in: Tax calculation ↑

Provider documentation

Framework for euro foreign exchange reference rates
European Central Bank · 2026-06
June 2026 framework, pp. 1–4: construction, publication and informational purpose. Reference fixings are not executable transaction rates, a complete historical feed or evidence of economic currency exposure.
Used in: Portfolio analysis ↑Net worth & currencies ↑Data sources ↑
XIRR: dated cash flows and iterative roots
Microsoft
Microsoft’s Syntax and Remarks document the actual/365 convention and iterative nature of a familiar XIRR implementation. This is a comparison reference, not the code or convergence policy of our solver.
Used in: Return measurement ↑
MSCI Index Calculation Methodology
MSCI · 2026-09
September 2026 edition, §§ 1.7 and 2.2 and Appendix III: price, gross/net income and tax conventions. A latest-edition URL can change; matching an index name or total-return label alone does not establish a comparable benchmark.
Used in: Return measurement ↑
The ECB’s two percent inflation target
European Central Bank
A medium-term euro-area policy objective. It contextualizes the fixed inflation assumption without forecasting future prices, national inflation or household purchasing power.
Used in: Projections ↑
Twelve Data API documentation
Twelve Data
Provider definitions for prices, time series and instrument metadata. Availability and delay depend on the dataset and instrument.
Used in: Data sources ↑
Financial Modeling Prep API documentation
Financial Modeling Prep
Provider definitions for fundamentals and fund holdings. A retrieval timestamp does not make the holdings observation current.
Used in: Data sources ↑
Data protection in Amazon Bedrock
Amazon Web Services
AWS's processing and model-provider access boundaries for Bedrock. These terms do not cover a separately connected external AI provider.
Used in: Use of AI ↑

Investor education

Asset allocation, diversification and rebalancing
SEC · Investor.gov
Investor education on time horizon, risk tolerance, fund overlap and restoring an allocation. It does not prescribe a universal target or trading schedule.
Used in: Portfolio analysis ↑
Concentrate on concentration risk
FINRA
Why correlated holdings and overlapping funds can leave a portfolio concentrated despite many positions.
Used in: Concentration & look-through ↑
Fund fees, expenses and NAV
SEC · Investor.gov
Accessible SEC explanation of fund expenses already embedded in returns. It is a companion to ESMA’s cost analysis, not a historical TER archive or evidence of the costs on a particular account.
Used in: Costs and after-tax performance ↑

Calculator and public API methodology
The separate reference for calculator conventions and caller-supplied portfolio snapshots. Their populations and assumptions can differ from connected-account analysis.

Reference edition · November 11, 2026

This review clarifies equity and core-portfolio denominators, reconstructed versus recorded history, mandate-score version 8, cost double-counting, stress evidence and the boundary between deterministic calculations and AI explanations. Calculation versions and data dates belong to each result; this page's review date never replaces them. When inputs, classifications or methods change, a recalculated figure can change without a market move.

The standard

Strategy, not trading. Clarity, not noise.

See these methods in a sample portfolio

Explore a sample case file to see the calculations, evidence and limitations together.

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The essentials in two minutes

Choose the question you want to answer. Each chapter connects the calculation to its scope, limitations, sources and available public code.

Check which accounts are included

Start with the included assets, currency and valuation date. A securities account, your wider wealth and a modeled selection of holdings can cover different parts of your finances.

Match the number to your question

Returns describe investment history. A mandate score checks your holdings against your signed rules. Projections explore possible outcomes under assumptions. A cash plan checks whether you can fund the contributions.

Notice what is missing

A missing value is different from zero. The holdings we can identify may already exceed a limit, while missing details can prevent us from confirming that the portfolio meets its limits. Simulation ranges depend on stated assumptions.

Read the denominator first

Read the denominator first
Reading	What is measured
Portfolio intelligence	All imported depots owned by the customer, pooled in one reporting currency. The depot named by an analysis route does not narrow this population. Accounts and assets you have not supplied remain outside the measurement.
Equity X-Ray	The underlying equity population. Whole-portfolio exposure and equity-only concentration use different denominators; bonds, cash and physical assets do not become companies.
Mandate issuer limit	The equity portion of the core portfolio across imported depots. Satellite holdings are excluded before look-through.
Net worth	The supported recorded wealth categories, less liabilities. This broader wealth view is not the denominator of the portfolio mandate score.

{ "id": "funding-and-mwr", "currency": "EUR", "openingDate": "2021-01-01", "fundingDate": "2022-01-01", "closingDate": "2023-01-01", "openingValue": 100, "observedValueBeforeFunding": 110, "contribution": 900, "observedValueAfterFunding": 1010, "closingValue": 909 }

{ "periodReturns": [ 0.1, -0.1 ], "timeWeightedReturn": -0.01, "moneyWeightedAnnualRate": -0.083359, "investmentResult": -91, "linkedPeriodContributions": [ 0.09, -0.1 ] }

{ "id": "missing-valuation", "currency": "EUR", "openingDate": "2026-01-01", "fundingDate": "2026-01-11", "closingDate": "2026-01-21", "openingValue": 100, "contribution": 100, "closingValue": 220, "observedValueOnFundingDate": null, "alternativeUnobservedPreFundingValues": [ 120, 80 ] }

{ "carriedBoundaryValue": 100, "nextOpeningValue": 200, "carriedBoundaryTimeWeightedReturn": 0.1, "wholePeriodModifiedDietz": 0.133333, "alternativeTrueTimeWeightedReturns": [ 0.2, -0.022222 ] }

{ "id": "price-and-fx", "reportingCurrency": "EUR", "quoteCurrency": "USD", "quantity": 1, "openingLocalPrice": 100, "closingLocalPrice": 110, "openingReportingPerQuote": 0.9, "closingReportingPerQuote": 0.81, "distributedIncome": 0 }

{ "openingValueEur": 90, "closingValueEur": 89.1, "localPriceReturn": 0.1, "quoteFxReturn": -0.1, "combinedReturn": -0.01, "localPriceDeltaEur": 8.55, "quoteFxDeltaEur": -9.45, "localContributionPp": 9.5, "fxContributionPp": -10.5, "investmentResultEur": -0.9, "componentSumGapEur": 0 }

{ "id": "concentration-coverage", "currency": "EUR", "totalEquityValue": 10000, "resolvedEquityValue": 9500, "observedIssuerValue": 800, "alternativeObservedIssuerValue": 1100, "issuerLimit": 0.1 }

{ "coverage": 0.95, "unresolvedEquityValue": 500, "observedIssuerWeight": 0.08, "maximumPossibleIssuerWeight": 0.13, "verdict": "not_proven_within_limit", "alternativeObservedIssuerWeight": 0.11, "alternativeVerdict": "breach" }

{ "id": "contribution-only-rebalance", "currency": "EUR", "equityValue": 70000, "bondValue": 30000, "targetEquityNumerator": 3, "targetEquityDenominator": 5, "availableContribution": 1000, "allNewMoneyGoesToBonds": true, "salesAllowed": false, "feesAndTaxes": 0 }

{ "startingValue": 100000, "requiredContributionFraction": { "numerator": 50000, "denominator": 3 }, "requiredContribution": 16666.666667, "minimumWholeCentContribution": 16666.67, "valueAfterAvailableContribution": 101000, "equityWeightAfterAvailableContribution": 0.693069, "bondWeightAfterAvailableContribution": 0.306931, "availableContributionReachesTarget": false }