Market Impact Estimation

1. In the Kyle (1985) single-period model, the equilibrium price impact coefficient is $\lambda = \frac{1}{2\sigma_u}\sqrt{\Sigma_0}$, where $\sigma_u$ is the noise trader volume and $\Sigma_0$ is the prior variance of the asset value. What happens to $\lambda$ as $\sigma_u \to \infty$ (very noisy market), and what does this mean economically?

2. The square-root law of market impact states $\mathrm{Impact}(Q) \approx Y\sigma\sqrt{Q/V}$, where $Q$ is the order size, $V$ is ADV, and $\sigma$ is daily volatility. A trader executes $Q = 0.01V$ (1% of ADV). If $Y = 1$ and $\sigma = 1\%$/day, what is the expected price impact in basis points?

3. Estimating Kyle's lambda from tick data by regressing mid-price changes on signed order flow can produce upward-biased estimates. The Lee-Ready algorithm is used to assign trade signs. Which of the following is the primary source of bias in this regression?

4. The permanent impact component of a trade measures the price move that persists after the trade is complete. A permanent impact close to zero implies that the trade was uninformative — the price reverts to its pre-trade level because no new information was revealed.

5. A trader is considering whether to execute a large sell order using TWAP over 1 day or to execute it immediately. The square-root impact model gives $h(v) = \eta\sigma\sqrt{v/V}$ (temporary impact only; ignore permanent). For TWAP with constant rate $v_0 = Q/T$, the total temporary impact cost is $\int_0^T h(v_0)\,dt = T \cdot h(Q/T)$. For immediate execution at rate $v_0 \to \infty$ (a single market order of size $Q$), the cost is $h(Q/\Delta t)\cdot\Delta t$ for small $\Delta t$. Which statement correctly compares these costs?

6. In the context of market impact estimation, what is a 'meta-order' and why is correctly identifying meta-order boundaries important for estimating the square-root law?