Calculate portfolio weights from a holdings ledger, include cash and financing, and distinguish valuation weights from targets, active weights and derivatives exposure.
Portfolio weight
A portfolio weight is a position's share of a specified portfolio value at a specified time. For an ordinary investment account, it is the position's signed market value divided by the account's net value. Weights connect a holdings ledger to investment decisions: they show how much capital sits in each position and how strongly each position's return affects the whole portfolio.
The denominator and the valuation time are part of the definition. “A has a 50% weight” is incomplete unless we know 50% of which account, including which cash and financing balances, and measured when.
Start with values, including cash
Let vi,t be the signed value of component i at time t, expressed in one reporting currency. If the components reconcile to positive net portfolio value Vt, then
Vt=i∑vi,t,wi,t=Vtvi,t,i∑wi,t=1.
For a directly held security, its value is quantity times current price. A weight therefore measures money committed, rather than a fraction of the number of shares or contracts. Holdings denominated in different currencies must first be valued in the same reporting currency.
Consider this hypothetical account at the beginning of one holding period:
Component
Value in USD
Exact portfolio weight
Investment A
6,000
1/2
Investment B
4,000
1/3
Cash
2,000
1/6
Net portfolio value
12,000
1
The displayed percentage weights are 50.00%, 33.33% and 16.67%. Cash belongs in the denominator even when it earns no return. Excluding it would give A and B weights of 60% and 40% within the invested sleeve, which answers a different question from their shares of the whole account.
Weights drift even without trading
Suppose A returns +10%, B returns −5% and cash returns 0% over the same period. There are no trades, distributions, external contributions or withdrawals, fees or taxes. The ending ledger is:
Component
Ending value in USD
Exact ending weight
Ending weight, rounded
A
6,600
33/62
53.23%
B
3,800
19/62
30.65%
Cash
2,000
5/31
16.13%
Net portfolio value
12,400
1
100% exactly
Rounded component percentages total 100.01%; the exact fractions sum to one. Cash's dollar value has stayed constant, but its weight has fallen because the denominator grew.
Beginning USD values are A 6,000, B 4,000 and cash 2,000, totalling 12,000. Ending values are 6,600, 3,800 and 2,000, totalling 12,400. Exact ending weights are 33/62, 19/62 and 5/31.
Original synthetic single-period USD ledger. Each bar is normalised to its own total value; unchanged cash occupies a smaller share at the end. No trading or external cash flows occur.
For this unchanged-holdings setting, the portfolio return uses beginning weights:
The independent value check is (12,400−12,000)/12,000=1/30. A adds 5 percentage points to the account return; B subtracts 5/3 percentage points. Ending weights already contain the effects of these returns, so using them to calculate the same period's return gives the wrong attribution.
When each component's ending value is vi,0(1+Ri), its weight updates according to
wi,1=1+Rpwi,0(1+Ri),V1>0.
If all components earn the same return and ending value remains positive, their weights are unchanged. For an initially positive holding, its weight rises when its return exceeds the portfolio's return. With income payments, trading or external flows, track their timing and destination explicitly; the simple ledger above cannot silently absorb those events. Use a consistent total-return convention when distributions are reinvested.
Current, target and active weights answer different questions
A current weight describes the marked holdings. A target weight states an intended allocation. The initial weights in the example could also be chosen as targets, but the observed ending weights would still be 33/62, 19/62 and 5/31 until an allocation change occurs. Rebalancing is the trading or cash-allocation process used to move towards a target. The SEC's allocation guide explains why unequal investment growth creates this drift.
An active weight compares a portfolio with a benchmark: ai=wi−bi, where bi is the benchmark weight on the same asset universe and valuation basis. If both complete weight vectors sum to one, active weights sum to zero. An underweight can still be a positive holding; it means holding less than the benchmark.
Choosing targets is a separate modelling problem from calculating current weights. For that next step, Mean-Variance Optimisation develops weight constraints, cash balances and benchmark-relative allocations. The public preview introduces the lesson; the full derivations require membership.
A capital share is not a complete exposure measure
For an unleveraged long-only account, every component weight lies between zero and one. With borrowing, an investment can exceed 100% of equity. For example, USD 15,000 of investments financed by USD 3,000 of borrowing leaves USD 12,000 of equity: the investment weight is 125% and financing cash is −25%. The signed weights still sum to 100%. A short position has a negative signed security value. Financing, collateral and short-sale proceeds must be accounted for consistently rather than discarded to make the percentages look familiar. Weights based on net equity are undefined when that equity is zero.
Derivatives require an additional distinction. A newly entered futures contract can have a near-zero marked value while creating substantial price exposure. Its notional value, margin and sensitivity are separate quantities. CME's notional-value explanation describes the contract-unit and price calculation. Dividing notional by portfolio equity produces an exposure ratio, rather than the valuation weight defined here; it need not share the same sum-to-one budget identity.
Nor is a 50% capital weight necessarily 50% of risk. Portfolio variance depends on the positions' volatilities and covariances as well as their weights. A report should identify whether “weight” means market value, target allocation, benchmark difference, notional exposure or a risk allocation before those numbers are compared.
Sources
Elton, Gruber, Brown and Goetzmann, Modern Portfolio Theory and Investment Analysis, 9th edition, Wiley, 2014, Chapter 4, “Characteristics of Portfolios in General,” printed pp. 50–51. Value fractions and portfolio-return aggregation; examples and figure here are original.
