Portfolio return is the gain or loss generated by a portfolio over a stated period, expressed relative to its invested capital. For a total return, that gain includes investment income as well as changes in the value of the holdings. A quant needs this portfolio-level result to judge a strategy: a winning stock may contribute little if the portfolio held very little of it.
With positive starting wealth , no external deposits or withdrawals, and ending wealth that includes all retained investment income,
State the holding period, reporting currency and treatment of costs. The result is a return for that interval; it is an annual return only if the interval is one year.
Follow the holdings and the cash
Start a synthetic portfolio with USD 1,000: USD 600 in asset A and USD 400 in asset B. Hold the positions without interim trading. Over the same period, A's price rises 10% and B's price falls 5%. A also pays a USD 20 cash dividend at period end, retained inside the portfolio. There are no fees, taxes or external cash flows.
| Portfolio component | Starting value (USD) | Ending value (USD) |
|---|---|---|
| A shares | 600 | 660 |
| B shares | 400 | 380 |
| Dividend cash | 0 | 20 |
| Total wealth | 1,000 | 1,060 |
The portfolio gains USD 60, so its return is
Original synthetic USD example for one common holding period. The dividend is paid at period end and retained as cash. The separate deposit arrives after the investment returns; there are no interim trades, fees or taxes.
The price return alone is 4%: the share values rise by USD 40 in aggregate. The dividend contributes another 2 percentage points. Adding the dividend again after using USD 1,060 as ending wealth would count it twice.
Why the weights belong at the start
For unchanged holdings over the period, each position's total return is weighted by its fraction of starting portfolio value:
Here the starting weights are 60% and 40%. A's total return includes its dividend:
Therefore,
A contributes 8 percentage points to portfolio return and B contributes −2 percentage points. These contributions are each position's dollar gain divided by the same USD 1,000 portfolio denominator. A's 13.3333% standalone return is not its contribution to the whole portfolio.
An unweighted average of the two asset returns gives approximately 4.1667%, answering the question for an equally weighted allocation instead. Ending weights also answer a different question: they describe the allocation after returns have occurred. With trading during the interval, calculate returns using the actual holdings and cash-flow timing rather than applying one initial weight vector to the entire interval's asset returns.
A deposit changes the balance
Now suppose the investor deposits USD 200 immediately after the period's investment returns, at the ending boundary. The account balance becomes USD 1,260. Calling its raw 26% increase a portfolio return would treat the investor's new capital as profit.
Because this particular deposit had no time to earn a return, removing it recovers the investment result:
This end-boundary adjustment is not a general formula for flows arriving during the period. A contribution made earlier can itself earn gains or suffer losses. Time-weighted return separates performance into subperiods around external flows and compounds their growth factors. Money-weighted return reflects the amounts and timing of the investor's flows. Choose the measure that answers the performance question being asked.
The Risk-Adjusted Performance Measures lesson develops time-weighted measurement before moving to risk-adjusted comparisons. Its public preview is available; the full lesson requires membership. A positive realised portfolio return alone does not establish manager skill or identify how much risk produced it.
Sources
- Edwin J. Elton, Martin J. Gruber, Stephen J. Brown and William N. Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition (Wiley, 2014), Chapter 4, pp. 50–51, “Characteristics of Portfolios in General”: portfolio return as the value-weighted combination of constituent returns, followed by the expected-return counterpart.
- FINRA, “Key Concepts: Return and Rate of Return”: income plus value change, the invested-capital denominator, and the need to state the measurement period and expenses.
- CFA Institute, GIPS Standards Handbook for Firms, Section 2, discussions of provisions 2.A.28–2.A.29: true time-weighted calculation around external flows and the timing-and-size interpretation of money-weighted return. The example above is an original synthetic ledger, rather than a claim of GIPS compliance.