Portfolio return

Portfolio return is the percentage change in its economic value over a defined interval. It becomes interpretable only after stating what it includes: price changes, dividends and coupons, costs, taxes, currency hedges and external cash flows. Base currency, valuation times, frequency and compounding rules are also part of the measure.

A higher final balance does not prove positive performance; it may reflect a deposit. A lower balance may reflect a withdrawal rather than a loss. The economic perimeter is reconstructed first, then a method appropriate to the cash flows is applied.

The measurement contract

Two series called “return” may legitimately differ when one is a local-currency price return and another a net total return in euros. The problem is an undisclosed difference, not the existence of different measures.

Simple return and total return

For an asset with no external flow during the period, opening value V₀, closing value V₁ and income I not already included in V₁, simple total return is:

Price return includes only price movement. Total return also includes income under a reinvestment convention. If closing value already contains the income cash, adding I again double-counts it.

For a self-financing portfolio formed at the period start with no interim trading or flows:

Each weight and return must share the same interval, currency and income basis. In a long–short portfolio, weights may be negative and may sum to one only relative to a specified capital base. NAV, gross exposure, leverage and denominator must therefore be disclosed.

When trading occurs inside the period, opening weights no longer describe all return units. Subperiod weights or a reconstruction from quantities, prices and cash is required. Final weights cannot retrospectively explain the path.

Log return: useful but not interchangeable

When R > −100%, the log return of the same total-return path is:

Consecutive log returns on the same wealth process add over time, and the corresponding cumulative simple return is exp(Σgₜ) − 1. This does not make log returns the answer to every question. A portfolio's log return is not generally the weighted average of component log returns. Aggregate assets with simple returns first, then transform the portfolio result if needed.

Simple return cannot fall below −100%, while log return is undefined when wealth reaches zero. Labels must remain visible when the two representations are used.

Compounding through time

Simple returns over consecutive periods compound geometrically:

Adding them is only an approximation. A +10% return followed by −10% gives 1.10 × 0.90 − 1 = −1%, not zero. Recovering from −10% requires about +11.11% on the smaller base. This is arithmetic, not an operating threshold.

The arithmetic mean answers “what was the sample's average period return?”. The geometric mean answers “what constant rate links the endpoints?”. Frequency, number of observations and partial periods must accompany any annualisation.

External and internal cash flows

An external cash flow crosses the measured boundary: subscription, withdrawal, contribution or redemption. A purchase funded by selling another holding is internal. Dividends and coupons remain internal when credited to portfolio cash; they become external only if the chosen perimeter sends them outside.

With external flows, (V₁−V₀)/V₀ confuses market performance and capital. Two main families answer different questions:

• time-weighted return divides the period at cash flows and geometrically links the subperiods;
• money-weighted return incorporates the size and timing of flows, commonly through an internal rate of return.

TWR better isolates a strategy path when flows are externally controlled; MWR describes the experience of the capital actually invested. They are not rival estimates of one identical object.

Contributions and attribution

In the simple opening-weight case, wᵢ,₀ × Rᵢ is component contribution; contributions sum to portfolio return when weights, data and residuals share one methodology. Contribution answers “how much did this position add?”. It does not prove skill.

Performance attribution instead compares portfolio and benchmark and assigns active return to represented decisions such as allocation and selection. With intra-period trading, derivatives, cash and currencies, reconciliation may include price P&L, income, FX, hedges, costs and an explicitly controlled residual.

Costs, tax and base currency

“Gross” and “net” need definitions. A series may be net of transaction costs but gross of management fees; another may include custody, administration or tax. Costs affect the compounding path and cannot always be subtracted as one annual percentage at the end.

For an unhedged foreign position under consistent conventions:

The interaction term means local return and FX cannot always be added. A hedge adds its own P&L, carry, collateral and costs. Price currency, account currency and reporting currency are not synonyms.

Reproducible example

A hypothetical portfolio starts with €60 in asset A and €40 in B. Their consistent total returns are +5% and −2%, with no trading or flow:

Contributions are +3.00 and −0.80 percentage points. If booked costs equal 0.10% of NAV on the same basis, net return is approximately 2.10%; the qualification recognises that precise cost timing may matter.

If €50 is deposited halfway through, opening weights no longer measure the full path. A TWR needs a valuation at the flow; an MWR needs its date and amount. The contribution is not return and must not be attributed to assets.

Quality control

A publishable series preserves opening and closing values and timestamps; included quantities, prices, accrued income, cash and liabilities; each dated external flow; income and reinvestment rules; costs and taxes; base currency, FX and hedges; formula, frequency and compounding; corrections, estimated data and residual reconciliation.

Stale prices, missed corporate actions, duplicate dividends, unsynchronised FX and rounding can produce a formally valid but economically false series. Historical return describes an observed path; it is not a forecast or an allocation recommendation.

Sources

• CFA Institute, Rates and Returns — 2026 refresher reading — holding-period returns, compounding, log returns, TWR and MWR.
• U.S. Securities and Exchange Commission, Form N-1A, total-return instructions — ending value, reinvested distributions, cost and annual compounded rate for covered funds.
• S&P Dow Jones Indices, Index Mathematics Methodology — price, total-return and net-total-return indices and dividend reinvestment.
• U.S. Securities and Exchange Commission, How Fees and Expenses Affect Your Investment Portfolio — official investor bulletin on the compounded effect of costs.
• CFA Institute, GIPS Standards Handbook for Firms — inputs, external flows, valuation and consistent performance methods.

Related entries

• Portfolio construction and performance
• Portfolio construction
• Time-weighted return (TWR)
• Money-weighted return (MWR)
• CAGR and annualisation
• Performance attribution