The expected-return vector is the dirtiest input in portfolio choice: its standard error falls with the length of the sample in years, not with the number of observations, so ten years of data cannot distinguish a risk premium of zero from one of 8%. Mean–variance optimisation then amplifies that error through the inverse covariance matrix, and the Merton solution assumes the drift is known. This project looks at both sides of that fact.
Eleven SPDR sector ETFs, 2010–present, 252-day estimation window rolled forward 21 days at a time. Equal-weight versus unconstrained minimum-variance, with the sample covariance and the Ledoit–Wolf shrinkage estimator; turnover, condition number and out-of-sample volatility as the diagnostics. The data loader and its tests are written; the backtest is in progress.
Itô's formula, the wealth process, the dynamic-programming principle, the HJB equation and the CRRA solution of the Merton problem, worked by hand; then the half-page extension where the drift lies in an interval and the control problem becomes a sup–inf.
No results to report yet. The data loader and its tests are written; the rolling-window backtest is in progress.
I wrote the data loader and its tests, and worked through the theory exercises by hand. The empirical backtest is still in progress.
Learning project, in progress. The backtest is unfinished, so there are no completed empirical results to interpret yet.