A twenty-percent turnover with four basis points of drag

Name the denominator first

The constructed portfolio begins at drifted pretrade weights of 60% and 40%, measured against one starting net asset value. Its target is 40% and 60%. Both vectors use the same two asset positions in the same order. There is no subscription, withdrawal, leverage change or explicit cash leg. These conditions matter because the half-sum turnover convention is only a concise description of this particular self-financing comparison.

The example assumes a symmetric charge of ten basis points per unit of traded notional on each side. This is an invented parameter, not a broker quote, spread estimate or evidence about actual execution. A round-trip rate, one-way rate and commission-only rate are different inputs even when each is expressed in basis points.

Reconcile trades and the half sum

The first exposure changes by -0.2 and the second by +0.2. Their signed sum is zero. Absolute traded weights sum to 0.4, while the conventional half sum is 0.2. A report using one-way turnover can therefore say twenty percent without contradicting a cost calculation that charges both buys and sells on forty percent of NAV. The names and denominator must travel with each number.

Apply the stated rate once

Ten basis points equals 0.001 in decimal terms. Multiplying by the gross traded weight 0.4 yields 0.0004, or four basis points of starting NAV. Subtracting that assumed drag from a hypothetical gross period return of 0.02 gives 0.0196. This is an additive one-period approximation. The calculation does not spend the fees from a separate cash account or recompute the post-cost target weights.

Using the same ten-basis-point per-side rate with half-sum turnover would produce two basis points of drag and undercount the stated charge. Using a rate already quoted for a whole round trip on both individual sides could instead overcount it. The arithmetic cannot determine which commercial convention a source intended; that must be documented before the rate is entered.

Preserve the model boundary

The cost card deliberately excludes market impact, participation constraints, taxes, financing and opportunity cost. It is useful for validating units and denominator choices, not forecasting the cost of an institutional order. The downloadable example includes the before and after vectors, cost rate and gross return so that the deduction is inspectable. Extending it to actual execution requires instrument-level trade records and an appropriate cost model; simply increasing the number of decimal places would not supply that evidence.

Reproduce the referenced calculations

Primary references

These sources support methods and conventions. The example values are original constructions, not observations extracted from these documents.

• Cvxportfolio: proportional transaction costs
• Cvxportfolio: turnover conventions

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