Transaction cost modeling — the edge that costs eat

The cost stack, with numbers

Recall D4-01's list, now as a model you can compute with. For a retail-scale trader in liquid US large-caps:

The half-spread convention: if the quote is bid 100.00 / ask 100.04 (4 bps spread), a marketable buy pays about 2 bps above mid, and the later sell pays 2 bps below mid — half the spread per side, the full spread per round trip. Market impact is the one that grows with you: doubling order size raises per-share impact by roughly the square root of two (Almgren et al. 2005), which is why backtests of small accounts do not scale to large ones.

Cost-adjusted returns

From D4-02, turnover at time $t$ is $\tau_t = |p_t - p_{t-1}|$. With a one-way cost of $c$ (as a decimal, e.g. 5 bps = 0.0005) per unit of turnover:

$r^{\text{net}}_t = r^{\text{gross}}_t - c \cdot \tau_t$

That's the whole model. Its honesty lives entirely in the value of $c$ — which is why $c$ must be stated, justified, and stress-tested, never defaulted to zero.

The sensitivity table

Never report one net number. Report net performance as a function of assumed cost. For a strategy earning 10% gross with 250 round trips per year:

The same backtest is a good strategy, a coin flip, or a disaster depending on one assumption. A strategy whose sign flips inside the plausible cost range is not a strategy; it is a bet on your cost model. Contrast a 10%-gross strategy doing 5 round trips per year: even at 10 bps it loses only 0.5% to costs.

Document or it didn't happen

Any backtest claim must state: the assumed cost per unit turnover, where that number came from (measured spreads? broker fill data? guess?), and the sensitivity table. This is the "realistic transaction costs" checkbox from the D4-01 checklist made concrete — an undocumented cost assumption is indistinguishable from an optimistic one.

Try it

Explain it

Your generative activity: explain out loud, to an imaginary friend who just showed you a backtest with Sharpe 2 and daily trading, why their result might be an artifact of a zero-cost assumption. Use the 10-percent-gross, 250-round-trip example, and tell them exactly what two numbers you'd ask for (turnover and assumed cost per round trip).

Predict before the next lesson

D4-04 covers walk-forward testing and out-of-sample discipline. Predict:

• If you tune a parameter to maximize Sharpe on 2010–2020 data and then report the Sharpe on 2010–2020, what's wrong?
• How much of an in-sample Sharpe do you think typically survives out of sample: 100%, 70%, or less than half?