Free module · Systematic strategy development
Portfolio Theory: Estimation, Risk Budgets & Rebalancing
Allocate across uncertain forecasts, shared risks and implementation constraints.
mean–variance · shrinkage · risk contributions · Bayesian views · turnover
The building blocks
An allocator converts forecasts and risk estimates into positions. Understand a weighted average and two-asset risk before solving a large optimization problem.
- Read return, variance and covariance inputs
- Balance reward, risk and trading costs
- Add uncertainty, regimes and constraints
Lessons in this module
- Mean–variance theory and the efficient frontier
- Covariance estimation, shrinkage and fragile allocations
- Regime uncertainty: combine scenarios before allocating
- Marginal risk, risk contributions and strategy overlap
- Bayesian views, forecast uncertainty and robust decisions
- Turnover, no-trade regions and dynamic portfolio management
Practice and apply
- Solve a diagonal allocation — Expected return .04, variance .04, risk aversion 2 for one independent asset.
- Shrink a covariance entry — Sample covariance .018, diagonal-target off-diagonal zero, intensity .5.
- Mixture mean — Regime probabilities [.75,.25] have daily means [.01,−.03]. Find the overall mean.
Work through the practice exercises · Quant development tools