Learning outcomes

After this module you should be able to:

1. Derive the global minimum-variance, frontier and tangency portfolios by Lagrangians, and prove two-fund separation.
2. Quantify why sample mean–variance optimisation fails out of sample, and derive the optimal shrinkage intensity toward a structured covariance target.
3. 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.
4. Derive the Sharpe ratio of a combination of two strategies with correlation $\rho$, and of $N$ strategies with average correlation $\bar\rho$.
5. State prospect theory's value and weighting functions with the Tversky–Kahneman (1992) parameters, and prove that the value function generates the disposition effect.
6. Design position-level and portfolio-level risk limits and a drawdown-control rule with a provable drawdown bound.
7. 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.
8. Write a complete trading plan with graduation and scaling criteria that a third party could audit.