Hedging Immediately After You Get Hit

The scenario: you just got hit — a counterparty sold you a large block, and you now hold inventory you didn't want to hold indefinitely. Do you hedge it immediately, all at once, or work out of it gradually over the next few minutes? The instinct to "get flat as fast as possible" is common but not automatically correct — hedging fast and hedging slow trade off two different costs.

The two costs in tension

Hedge immediately, all at once, and you pay a larger market impact cost, because pushing a big order through the market quickly moves the price against you — you're demanding liquidity faster than the market naturally supplies it. Hedge slowly, spreading the trade out over time, and you reduce that impact cost, but you're now exposed to the market moving against your unhedged position while you wait, which is pure price risk with no offsetting benefit. The right speed balances these two costs rather than minimizing either one alone.

Worked example: a simple square-root impact model

A common approximation says impact cost from executing a quantity $Q$ over time $T$ scales like $\text{impact} \propto Q / \sqrt{T}$ — trading twice as fast (half the time) costs roughly $\sqrt{2} \approx 1.41\times$ more in impact, not 2x, because the market has some natural absorption capacity. Meanwhile, holding the position unhedged for time $T$ exposes you to price risk that grows like $\sqrt{T}$ (standard random-walk variance scaling), so expected risk cost also scales like $\sqrt{T}$ if you have a fixed risk-aversion penalty per unit of variance.

Suppose impact cost is $\text{Impact}(T) = \dfrac{100}{\sqrt{T}}$ (in $, with $T$ in minutes) and risk cost is $\text{Risk}(T) = 5\sqrt{T}$. Total cost is $C(T) = \dfrac{100}{\sqrt{T}} + 5\sqrt{T}$. Try a few values:

$T$ (minutes)	Impact	Risk	Total
1	$100.0	$5.0	$105.0
4	$50.0	$10.0	$60.0
16	$25.0	$20.0	$45.0
20	$22.4	$22.4	$44.7
25	$20.0	$25.0	$45.0
100	$10.0	$50.0	$60.0

The total cost bottoms out around $T = 20$ minutes, where impact and risk costs are roughly equal — this is a general property of this kind of square-root-in-both-directions model: the optimum sits where the two costs cross. Hedging in 1 minute costs more than twice what hedging in 20 minutes costs, purely from impact; hedging over 100 minutes also costs more, this time from accumulated risk exposure.

What this means in practice

Trading desks formalize this exact tradeoff (most directly in the Almgren-Chriss optimal execution framework) to set hedging schedules rather than hedging purely on instinct. The interview-relevant point is recognizing that "hedge immediately" and "hedge patiently" are both wrong as universal rules — the right answer depends on the relative size of impact costs (driven by liquidity in the name) versus risk costs (driven by volatility and your risk aversion), and a good answer names that tradeoff explicitly rather than picking a side.