Part II · Trading equities · M05 · week 3 · 16 h

Intraday trading and execution

Microstructure models (Roll, Glosten–Milgrom, Kyle), price impact, execution benchmarks and Almgren–Chriss optimal execution; the evidence on intraday strategies, the mathematics of cost drag and why most retail day traders lose.

Start reading · Learning outcomes

Builds on M01 Market structureM02 Statistics of returnsM03 Kelly and ruinM04 Systematic research

Prerequisites M01 (order book, auctions, the cost algebra of 1.7), M02 (autocovariance, variance of sums), M03 (expectancy), M04 (hypothesis tests, multiple testing, deflated Sharpe). Mathematics: conditional expectation for jointly Gaussian vectors, Bayes' rule, linear difference equations, a little calculus of variations. Time: ~16 hours (10 reading and derivations, 6 on problems and code). Primary texts: Joel Hasbrouck, Empirical Market Microstructure (OUP, 2007), Ch. 3 (Roll), Ch. 5 (sequential trade), Ch. 7 (strategic trade); Robert Almgren and Neil Chriss, "Optimal execution of portfolio transactions", Journal of Risk 3(2), 2000; Albert Kyle, "Continuous auctions and insider trading", Econometrica 53(6), 1985.

Intraday trading is where the gap between how a strategy looks on a chart and what it earns is widest. This module explains that gap from first principles. The spread exists because some of the people you trade with know more than you (Glosten–Milgrom, Kyle). Prices bounce between bid and ask, and that bounce shows up as negative autocorrelation you can measure (Roll). Large orders move prices, in a concave way (the square-root law), and the optimal response trades off impact against risk (Almgren–Chriss). Then we put numbers on the edge a strategy needs to survive Indian costs, review the best published intraday evidence, and set it against the base rates of people who actually tried.

Learning outcomes

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).
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).
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).
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.
Define VWAP, TWAP and implementation shortfall, and prove that a volume-proportional schedule achieves VWAP (Proposition 5.4).
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).
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).
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.

Sections ≈ 2 h 25 min of study

Foundation 5 sections · ≈ 40 min
Core 6 sections · ≈ 50 min
Advanced 4 sections · ≈ 55 min

Learning outcomes Foundation 5′
5.1 The intraday landscape Foundation 5′
5.2 The Roll model: spread from bid–ask bounce Core 10′
5.3 Sequential trade: Glosten–Milgrom Advanced 10′
5.4 Strategic informed trading: the Kyle model Advanced 15′
Figure Kyle model: price impact and the insider's optimal intensity
5.5 Price impact and the square-root law Advanced 10′
Figure The square-root law of market impact
5.6 Execution benchmarks: VWAP, TWAP and implementation shortfall Foundation 10′
5.7 Optimal execution: Almgren–Chriss Advanced 20′
Figure Optimal execution: Almgren–Chriss
5.8 Intraday strategies: what the evidence says Core 10′
5.9 The mathematics of cost drag Core 10′
Figure Cost drag against holding period
5.10 Why most retail intraday traders lose: base rates Foundation 10′
5.11 Case studies Core 10′
Summary of key results Foundation 10′
Readings and resources Core 5′
Facts that change Core 5′