Permanent Versus Temporary Impact

A desk buys 50,000 shares of a stock trading at $100.00. They slice it into ten child orders and work it over twenty minutes. By the time the last slice fills, the stock is at $100.18. Ten minutes after the algo stops, it has drifted back down to $100.07 — and it stays there for the rest of the day. The trader who has to explain this fill to a portfolio manager needs an answer to one question: was that 18 cents of move "real," or did the desk just pay a temporary tax for trading fast?

The answer is both, and the split matters. Define the pre-trade price $p_0$ (the $100.00 you started at), the peak price $p_{\text{peak}}$ reached during execution ($100.18), and the post-trade settled price $p_{\infty}$ once the market has had time to absorb the trade and move on ($100.07). Then

$\text{temporary impact} = p_{\text{peak}} - p_\infty$

$\text{permanent impact} = p_\infty - p_0$

In words: temporary impact is the part of the move that reverses once you stop trading — the price concession you paid for immediacy, for eating through the book faster than natural liquidity would replace it. Permanent impact is the part that never comes back — the market's read that your order contained information, so the price re-settles at a new, higher fair value.

For the example: temporary impact is $100.18 - 100.07 = 0.11$, i.e. 11 cents. Permanent impact is $100.07 - 100.00 = 0.07$, i.e. 7 cents. Total impact was 18 cents; three-fifths of it was the toll for speed, two-fifths was the market genuinely repricing the stock.

A second worked example: two execution speeds

Same order, same stock, two different clocks. Fast execution (10 minutes): price runs up to $100.24, decays back to $100.07. Temporary = $100.24 - 100.07 = 0.17$. Permanent = still $0.07 — permanent impact is a property of the information in the order (you bought 50,000 shares that someone had to sell you), not of how fast you traded it, so it barely changes with speed. Slow execution (60 minutes): price only runs up to $100.10, and because the order dribbles in near the pace of natural volume there's almost no concession to unwind, so it settles near $100.07 directly. Temporary = $100.10 - 100.07 = 0.03$.

Same permanent cost either way, wildly different temporary cost. That is the entire trade-off execution algorithms are built around: trading faster does not change how much information you reveal, it only changes how much you pay in temporary concession for demanding liquidity on your own schedule.

Where this gets used

• Transaction cost analysis. A TCA report that only shows arrival-price slippage can't tell a trader whether they overpaid for speed (fixable — trade slower next time) or correctly paid for alpha (not fixable — that's the cost of being right). Decomposing into permanent and temporary is what makes the report actionable.
• Calibrating execution algorithms. Almgren-Chriss style optimizers need both numbers separately: temporary impact enters the cost function as a convex penalty on trading rate, while permanent impact is rate-independent and gets treated as a sunk cost you can't trade around.
• Sizing metaorders. A portfolio manager deciding how large a position to build sometimes cares more about permanent impact than temporary, because temporary cost is a one-time toll but permanent impact changes the price everyone else in the fund transacts at afterward.

In interviews

If asked to decompose impact, draw the price path first: a rise during execution, a partial decay after, a settled plateau. Label the three prices $p_0$, $p_{\text{peak}}$, $p_\infty$ and write the two differences — that's the whole answer, the trick is remembering which difference is which. The natural follow-up is "does trading faster reduce total cost?" — the correct answer is that it reduces neither the permanent component nor your certainty about it, it only trades temporary cost for timing risk, which is exactly the tension Pre-Trade Cost Models are built to quantify. See The Square-Root Impact Law for how the temporary piece typically scales with size.