Calculate a portfolio's weighted return

A portfolio holds more than one investment, so its one-period return depends on both what each holding earned and how much of the portfolio was invested there. The weighted-return calculation captures both. A 20% position has twice the effect of a 10% position when their returns differ by the same amount.

The one-period formula

For asset i, multiply its return by its beginning portfolio weight. Add the contributions across the assets: portfolio return = Σ(wᵢ × rᵢ). A weight can be written as a decimal, such as 0.60, or a percentage, such as 60%, as long as the calculation uses one convention consistently. The weights should represent the portfolio at the start of the measurement period and add to 100% when all assets are included.

Worked example

Suppose a portfolio begins the period with 60% in stocks and 40% in bonds. Stocks return 8% and bonds return 3%. The stock contribution is 0.60 × 8% = 4.8 percentage points; the bond contribution is 0.40 × 3% = 1.2 percentage points. Add them: the portfolio's one-period return is 6.0%.

You can verify the result with dollar values. If the portfolio begins at $100,000, the starting positions are $60,000 and $40,000. An 8% gain adds $4,800 and a 3% gain adds $1,200. The $6,000 total gain divided by the original $100,000 equals 6%. This check catches weight and percentage errors.

A short exam calculation

Common mistakes

• Taking the simple average of asset returns without using the portfolio weights.
• Multiplying by 60 instead of 0.60, or by 8 instead of 0.08 when using decimal arithmetic.
• Using ending weights after assets have already gained or lost value instead of the beginning weights for the period.
• Leaving out cash or another holding so the weights do not sum to the total portfolio.
• Adding the weighted contributions but reporting them as dollars when the calculation produced percentage points.
• Using a single-period weighted average to answer a multi-period performance question without compounding or handling cash flows.

When a portfolio changes during the period

The simple formula assumes the weights and asset returns refer to a matching measurement period. If the portfolio is rebalanced, receives outside contributions, or has withdrawals during the period, one beginning-weight calculation may not describe the investor's actual experience. For successive subperiods, calculate the portfolio return for each subperiod using the relevant weights, then geometrically link the subperiod returns when a time-weighted result is required.

A time-weighted return removes the effect of the timing and size of external cash flows to assess investment performance across periods. A money-weighted return, such as an internal rate of return, is affected by when and how much cash the investor contributed or withdrew. Those measures answer different questions; neither is calculated by simply averaging the asset returns for the full period.

Weights and return contribution

The weighted-return formula also explains an asset's contribution to the total. A small holding with a large gain can contribute less than a larger holding with a modest gain. In a portfolio of multiple asset classes, increasing the weight of one class changes how strongly its return affects the whole portfolio. Return contribution describes arithmetic, not whether the allocation was suitable for the client's risk tolerance or goal.

Exam method

1. Write each asset's beginning weight and period return in matching rows.
2. Check that the weights sum to 100%, or identify the missing holding or cash balance.
3. Multiply each weight by its return, keeping percentage and decimal notation consistent.
4. Add the contributions and state the result as the portfolio's one-period percentage return.
5. If the stem includes changing weights, contributions, withdrawals, or several periods, decide whether a time-weighted or money-weighted calculation is being tested instead.

For a single period, think contribution by contribution: weight times return, then sum. For multiple periods or external cash flows, stop and identify the performance measure first. That distinction is often what the question is really testing.

Confirm the weights describe the same starting point

The weighted-return formula assumes the portfolio weights correspond to the beginning of the measurement period or to another explicitly defined allocation. If weights are measured at the end, after one asset has already outperformed, applying those weights to the period’s full returns produces a different answer. State the timing before calculating. Use market values, not account counts or number of holdings, to calculate capital weights.

For a two-asset portfolio with 60% in a fund returning 8% and 40% in bonds returning 3%, the one-period portfolio return is (0.60 × 0.08) + (0.40 × 0.03) = 0.060, or 6%. Check that weights sum to 100%, preserve the sign on negative returns, and use consistent decimal or percentage notation. If cash flows occur during the period, the simple beginning-weight result may not equal the investor’s money-weighted return.

Rebalance and cash flows change the calculation

If a portfolio is rebalanced during a period, break the period into segments using each segment’s weights and returns, then geometrically link subperiod returns. If contributions or withdrawals occur, time-weighted performance neutralizes the timing of external cash flows by measuring returns over subperiods; money-weighted return reflects the investor’s actual cash-flow timing. A weighted average of fund returns does not capture every performance-reporting problem.

Rounding can cause small differences. Keep at least several decimal places in intermediate steps and round only the final percentage. A negative return in one holding can offset gains in another: 70% at +10% and 30% at -8% produces 4.6%, not 18% and not the simple average of 1%. Interpret a negative weight only if the scenario explicitly includes short positions or derivatives.

Distinguish return from contribution

An asset’s contribution to portfolio return equals its weight multiplied by its return for the period. In the example above, stocks contribute 4.8 percentage points and bonds contribute 1.2 points. Contribution analysis explains which allocation drove the result, but it does not measure skill or risk. A holding can contribute positively because it had a large starting weight, not because it had the highest return.

Use the formula for a single period with stable stated weights and aligned returns. For multiple periods, compound each portfolio period return: (1+r1)(1+r2)…−1, then annualize if needed. Do not average annual asset returns first and apply current weights if allocations changed. For exam questions, label weight, holding return, contribution, and portfolio return separately before multiplying.