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Reconcile starting weights to portfolio gain

Starting balances 60 and 40 earning 10% and −5% give a portfolio return of 4%.

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Calculate currency amounts first

The fictional portfolio begins with assets A = 60 and B = 40. Over one common period, A gains 6 and B loses 2. Ending values are 66 and 38, totaling 104. There are no flows, costs or currency differences.

Divide each gain by total initial capital

A contributes 6/100 = 6 percentage points; B contributes −2/100 = −2 percentage points. The contributions sum to 4%. Asset B’s own −5% return is not its portfolio contribution.

Asset and portfolio measures
AssetOwn returnPortfolio contributionEnding balance
A10%6 percentage points66
B−5%−2 percentage points38

Update the next starting allocation

Ending weights are 66/104 ≈ 63.461538% and 38/104 ≈ 36.538462%. They become the next period’s starting weights if nothing is rebalanced or transferred. They are not the original 60/40 weights used for the completed period.

Keep timing in a multi-period model

If the portfolio is rebalanced within a period, a simple starting-weight formula may no longer describe all transactions. Separate the intervals or use a stated transaction-aware method. The original weighted sum assumes one fixed initial allocation for this interval.

Further references