Part VI · Prediction and synthesis · M14 · week 8 · 20 h

Portfolio construction, risk, psychology and going live

Mean–variance and its failure, shrinkage, risk parity, volatility targeting, combining strategies, expected shortfall and stress tests, prospect theory and trading psychology, the written trading plan, and the Jhunjhunwala playbook.

Start reading · Learning outcomes

Builds on M02 Statistics of returnsM03 Kelly and ruinM04 Systematic researchM06 ValuationM09 Volatility tradingM13 Forecasting

Prerequisites M02 (moments, covariance, estimation error), M03 (R-multiples, expectancy, fixed-fractional sizing, Kelly, drawdowns), M04 (hypothesis tests, multiple testing, deflated Sharpe), M06 (CAPM sketch, valuation), M09 and M13 (volatility estimation). Lagrange multipliers, matrix calculus, Jensen's inequality, the Student- $t$ distribution. Time: ~20 hours (end of week 8), plus the written trading plan, which you should draft here and revise after paper trading. Primary texts: Markowitz (1952); Cochrane, Asset Pricing (rev. ed., 2005), ch. 5; Roncalli, Introduction to Risk Parity and Budgeting (CRC, 2013), chs. 1–2; Kahneman, Thinking, Fast and Slow (2011), part IV; Tversky & Kahneman (1992); Barber & Odean (2000).

This module closes the course. It answers three questions. How do you combine positions and strategies so that the whole is better than the parts, given that you cannot estimate the inputs well? Why do intelligent people, knowing all of M01–M13, still lose money, and what formal models describe the failure? And how do you go from paper to real money without fooling yourself about whether you have an edge?

Learning outcomes

Derive the global minimum-variance, frontier and tangency portfolios by Lagrangians, and prove two-fund separation.
Quantify why sample mean–variance optimisation fails out of sample, and derive the optimal shrinkage intensity toward a structured covariance target.
Prove that Euler risk contributions sum to portfolio volatility, characterise when inverse-volatility weights are equal-risk-contribution weights, and compute ERC weights by convex optimisation.
Derive the Sharpe ratio of a combination of two strategies with correlation $\rho$ , and of $N$ strategies with average correlation $\bar\rho$ .
State prospect theory's value and weighting functions with the Tversky–Kahneman (1992) parameters, and prove that the value function generates the disposition effect.
Design position-level and portfolio-level risk limits and a drawdown-control rule with a provable drawdown bound.
Derive the number of trades needed for an expectancy $t$ -statistic of 2, with and without a power requirement, and estimate the false-positive rate of an "edge" by simulation.
Write a complete trading plan with graduation and scaling criteria that a third party could audit.

Sections ≈ 4 h 55 min of study

Foundation 7 sections · ≈ 1 h 30 min
Core 12 sections · ≈ 2 h 45 min
Advanced 4 sections · ≈ 40 min

Learning outcomes Foundation 5′
14.1 Mean–variance portfolios Core 15′
Figure Efficient frontier, tangency portfolio and capital market line
14.2 Estimation error: why sample mean–variance fails Core 10′
Figure Estimation error: sample tangency portfolios
14.3 Shrinkage covariance (Ledoit–Wolf) Advanced 10′
14.4 Risk parity: Euler contributions and equal risk contribution Advanced 10′
Figure Capital weights against risk contributions
14.5 Volatility targeting Core 5′
14.6 Correlation in crises Core 5′
Lab Correlation in crises: Nifty, gold in rupees and US yields
14.7 Combining strategies Advanced 5′
Figure What combining strategies buys
14.8 Risk limits and drawdown control Foundation 10′
14.9 Psychology with formal models Foundation 20′
Figure Prospect theory: value and probability weighting
14.10 Going live Foundation 15′
14.11 Synthesis: the Jhunjhunwala playbook mapped onto the course Foundation 10′
14.12 Case studies Core 10′
14.13 Expected Shortfall and coherent risk measures Core 25′
14.14 Scenario P&L: full revaluation versus the delta–gamma–vega expansion Advanced 15′
14.15 A mixed Indian book: rupee Greeks, stress table and margin utilisation Core 20′
14.16 Cash-market leverage in India: the Margin Trading Facility and pledged collateral Foundation 15′
14.17 Short selling and securities lending (SLB) Core 15′
14.18 The mathematics of leverage: drawdowns and margin calls Core 20′
14.19 Hedging a stock portfolio with Nifty options Core 30′
Summary of key results Foundation 15′
Readings and resources Core 5′
Facts that change Core 5′