Learning outcomes

After this module you should be able to:

1. Derive $\operatorname{Cov}(\Delta p_t, \Delta p_{t-1}) = -s^2/4$ in the Roll model, estimate the spread from trade prices, and state when the estimator fails (Proposition 5.1).
2. Compute Glosten–Milgrom bid and ask quotes by Bayes' rule and show that the spread equals the adverse-selection loss to informed traders (Proposition 5.2).
3. Derive the linear equilibrium of the one-period Kyle model, $\lambda = \sigma_v/(2\sigma_u)$, $\beta = \sigma_u/\sigma_v$, and its implications for profits and price informativeness (Proposition 5.3).
4. State the square-root impact law, estimate the impact of an order from daily volatility and volume, and explain why concave impact makes splitting orders worthwhile.
5. Define VWAP, TWAP and implementation shortfall, and prove that a volume-proportional schedule achieves VWAP (Proposition 5.4).
6. Derive the Almgren–Chriss expected cost and variance and the optimal $\sinh$ trajectory, in discrete and continuous time, and verify it numerically (Proposition 5.5).
7. Translate a published predictive $R^2$ into expected basis points per trade, and compute the Sharpe drag of costs for intraday versus swing holding periods (Propositions 5.6–5.7).
8. Quote, with sources, the base rates of retail intraday trading in Taiwan, Brazil, the US and India, and explain them with this module's models.