Using Convex Optimisation to Balance Trading Returns, Costs, and Risk
Summary
This article develops intuition for using convex optimisation to turn forecasts into portfolio positions under practical constraints. It begins with a long-only, unlevered return-maximisation example, then adds existing holdings and transaction costs to show why a small forecast improvement may not justify switching assets. Further examples incorporate risk and portfolio constraints, using CVXR to express objectives and constraints in R. The discussion frames optimisation as a way to manage the trade-offs among expected returns, turnover, costs, and risk.
The article also describes an alternative downside constraint based on historical portfolio losses, alongside a mean-variance formulation. Its examples illustrate how risk and trading-cost parameters affect chosen weights, but they do not establish future performance. Covariance estimates can be sensitive, and a historical-loss constraint assumes past outcomes are informative about future ones. Optimisation structures decisions around forecasts; it does not create predictive edge, and parameter selection requires further work.
Key ideas
- A return-only objective under long-only and leverage limits concentrates weight in the asset with the strongest forecast.
- Transaction costs and current holdings can make retaining a position preferable to switching to a slightly better forecast.
- Convex optimisation can encode portfolio constraints and risk estimates directly alongside return objectives.
- Historical downside constraints offer a risk formulation that avoids covariance estimates but depend on past returns being informative.
- Optimisation helps implement forecasts and does not generate alpha by itself.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.