Computing a Strategy's Transaction-Cost Threshold — the four-step check that decides whether a documented edge is tradable

Every strategy page in this wiki reports a gross effect. This page turns that number into the only one that decides anything: the cost per round trip at which the edge reaches zero. Above that number the strategy is a documented fact and an unprofitable trade — the two are not the same thing, and conflating them is the most common way a real anomaly loses money.

Proof regime: attested. The four steps are our procedure, stated so it can be refuted. The inputs are all verified elsewhere in this wiki and linked where they are used. If a step is wrong, it is wrong for a reason you can name — that is what makes it worth writing down.

The identity

$$\text{breakeven cost per round trip} = \frac{\text{gross annual alpha}}{\text{annual turnover}}$$

It follows directly from the turnover-adjusted return identity in Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one: cost scales linearly with the sum of absolute weight changes, so the cost that consumes the whole alpha is simply the alpha divided by how many times you pay it. Nothing is estimated here; the estimation lives entirely in the two inputs.

Step 1 — Take the gross alpha *after* publication decay, not from the original paper

The number in the abstract is almost never the number you can trade. Use the post-publication figure if the wiki has one.

For cross-sectional equity momentum, the original documented effect is ~1% per month, and the post-publication realised figure is ~1.5%/year — roughly 50% of the alpha disappeared after publication (Cross-Sectional Momentum in Equities — the strongest documented anomaly, and how much of it survives costs, Out-of-Sample vs Post-Publication Decay: The Two Numbers That Tell You If a Premium Is Real). Starting this calculation from 12%/year instead of 1.5%/year makes the strategy look eight times more robust to cost than it is.

Step 2 — Take turnover *one-sided and annual*, and check which convention the source used

Turnover conventions differ by a factor of two, and this is where the arithmetic usually breaks. State which you are using. This wiki uses one-sided annual: the fraction of the portfolio replaced per year, counting one side.

Momentum's is 90% one-sided annual, which is why it is the standard example of a real effect with a cost problem: Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one records its 48.4 bps/month cost burden against 5.5–5.7 bps/month for value and size.

Step 3 — Divide, then compare against a *measured* cost for your actual universe

$$\frac{1.5\%}{0.90} = 1.67\% = \mathbf{167\ bps}$$

That is the round-trip cost at which post-publication momentum earns exactly nothing. Now compare it to what execution actually costs in the segment you would trade:

| Universe | Measured round-trip cost | Verdict against the 167 bps threshold | |---|---|---| | US large-cap | 23 bps | survives — 1.27% net remains | | US small-cap | 32 bps | survives on this arithmetic | | Institutional momentum traders, 1995–97 | 204 bps | dead — above the threshold |

The first two rows and the third come from the same wiki and disagree by an order of magnitude. That is not an error to be averaged away: it is the finding. Cost is not a property of the strategy, it is a property of the strategy at a given size, in a given decade, executed by a given desk. A 23 bps assumption and a 204 bps reality are both documented, and only one of them describes you.

Step 4 — Ask what size breaks the answer

Steps 1–3 assume cost is a constant. It is not. Above modest size the dominant term is permanent market impact — the price moves against you because your own order reveals information — and it grows with trade size (Almgren & Chriss; see the components section of Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one).

So the threshold has a capacity attached. Momentum's documented capacity is $5B, against $50B for value and $170B for size. Below capacity, step 3's answer holds. Above it, the cost input in step 3 is no longer the number you measured, and the calculation must be redone with an impact model rather than a flat basis-point figure.

The honest output of this procedure is therefore three numbers, never one: the breakeven cost, the measured cost for your universe, and the size beyond which the second number stops being true.

What does NOT work

Comparing gross alpha directly to a cost figure. "The effect is 1.5% and costs are 23 bps, so it survives" happens to reach the right verdict here and is the wrong calculation: it omits turnover entirely. At 300% turnover the same two numbers give a dead strategy. The division in step 3 is not decoration.

Using the paper's own cost estimate. Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one documents the spread in the literature — some papers ignore costs, some fill at the midpoint (which is not an executable price), and Frazzini et al. found live institutional costs an order of magnitude below prior academic estimates. A cost number inherited from the same paper that reports the alpha is not independent evidence.

Treating the threshold as a pass/fail gate. A strategy that clears its breakeven cost by 40% has no margin for a regime in which spreads widen, and spread widening correlates with exactly the periods when a momentum book is already losing. Clearing the threshold is necessary, not sufficient — What Counts as an Edge Here: The Evidence Bar This Wiki Applies to Every Technique states the other three legs.

Related

- Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one — the cost components and the identity this page operationalizes; go there for where each number comes from. - Cross-Sectional Momentum in Equities — the strongest documented anomaly, and how much of it survives costs — the worked example's source, and the clearest documented case of a real effect constrained by implementation cost. - Out-of-Sample vs Post-Publication Decay: The Two Numbers That Tell You If a Premium Is Real — why step 1 uses the decayed figure. - What Counts as an Edge Here: The Evidence Bar This Wiki Applies to Every Technique — cost survival is one of four legs, and this page is only the one leg.