This Repo contains a small working example of portfolio optimisation through exploting numerical optimisation algorithms. This was implemented as part of UCL's COMPGV19 course, in 2018.

optimise.py introduces implementations of Steepest Gradient Descent, Newton's Method and BFGS algorithms, largely following the scipy.optimize.minimize syntax (although of the three, only BFGS is available through SciPy).

linesearch.py offers a simple way to switch different procedures for finding appropriate step lengths. Default is backtracking line search satisfying Armijo condition.

Run main.py to perform the full analyis involving:

• Quadratic Minimisation with penalty terms to trace the efficient frontier
• Monte Carlo analysis of feasible portfolios
• KKT formulation and solution for globally-optimal portfolio (maximising Sharpe Ratio)

Run Jupyter notebook to see interactive version of above, plus trajectory analysis and function surface plot comparision of constrained and unconstrained penalty optimisation.