Making portfolio optimisation understandable for humans

Optimising a portfolio of investments means coming up with the mix of assets that maximises the return expected from the portfolio. The composition of the portfolio is adjusted for the level of risk the investor is willing to take. It involves applying mathematical models to balance the risk-return trade-off efficiently. 

In our most recent paper, “From Black Box to Explainable Portfolio Optimization: Tracing Allocations to Views and Constraints”, we present a framework that makes portfolio optimisation fully transparent. It turns a traditionally complex process into one that is structured, interpretable, and ready for real‑world implementation. 

Why isn’t everyone using portfolio optimisation?

Portfolio optimisation has been around since Harry Markowitz introduced the Modern Portfolio Theory in the 1950s. While those early models often produced unrealistic portfolios, today’s ‘Robust Portfolio Optimisation’ techniques can deliver stable, practical, and usable portfolios that remain faithful to investment views and manage risk exposures more efficiently than ad-hoc or heuristic approaches. 

Yet, despite these advances, portfolio optimisation has still not achieved widespread adoption. 

In practice, optimisers are still often treated as black boxes. This is precisely the gap we address in our paper: we provide a framework that makes portfolio optimisation fully explainable and apply it to the construction of tactical asset allocation portfolios benchmarked against a given strategic asset allocation. 

Tactical asset allocation portfolios

Building a tactical asset allocation portfolio is much harder than it looks: tactical views are often expressed on broad market indices, while implementation of those views often involves funds invested a way that does not always align with the composition of the indices. 

There are many hurdles including: 

• The portfolio’s strategic benchmark is built from indices which can have a composition misaligned with the funds selected. 
• Active funds, added because of their expected positive alpha, bring additional risks. 
• Every fund, active or passive, introduces ongoing costs. 
• Constraints can include no short positions, no leverage, exclusions and caps. 

Addressing the challenges

In our paper, we start by showing how ‘Robust Portfolio Optimisation’ can tackle these challenges. Then, instead of only producing the final tactical asset allocation to the funds shortlisted for implementation, we show how to get the transparent breakdown of the weights of the proposed tactical asset allocation portfolio: 

• How much of each fund allocation comes from replicating the strategic benchmark 
• How much tactical views tilt allocations away from that replication 
• How much the expected fund alpha net of costs tilts it further away 
• How much binding constraints, e.g. on sustainability, tilt it further 
• How much the funding constraint require a final tilt. 

In short: an investor does not just get a ‘do this’. You get the ‘why you should do this’.

Examples from the paper 

No tactical views, just net fund alpha

In this example, we used ‘Robust Portfolio Optimisation’ to build a benchmarked tactical asset allocation with only the shortlisted active and passive funds, but without applying any tactical views. 

The optimiser works under the simplest real‑world constraints: no short positions, no leverage, and the portfolio must be fully invested. With no tactical views pushing the portfolio in any direction, we show how the allocation is driven by two forces: staying close to the strategic benchmark (SAA Replication), then tilting away toward funds with higher expected alpha net of costs (Alpha). 

The breakdown shows a transparent and intuitive composition that mirrors the benchmark as much as possible while then tilting in favour of funds with the largest expected alpha net of costs. 

Tactical views and a constraint on sustainability

In this example, we added tactical views and a requirement for a minimum allocation of 30% to sustainable investments. We applied five tactical views: a negative view on euro sovereign bonds, a slightly negative view on emerging market debt in hard currency, and positive views on EMU equities, euro investment-grade bonds, and USD high-yield bonds. 

These views and the sustainability constraint reshape the portfolio. For example, the optimiser finds that a positive view on EMU equities is most effectively implemented through an overweight in a Europe mid‑large cap equity ETF, complemented by a smaller overweight in its active counterpart. The allocation to these two funds is the most faithful implementation of the positive EMU equity view when it comes to replicating its underlying exposures to risk factors. 

The 30% sustainable investment floor pushes the portfolio toward funds with a higher sustainable investment exposure. For European equity funds, this shifts the balance further in favour of the Europe mid‑large cap equity ETF with a 40% exposure to sustainable investment and away from its active counterpart with just 30%.

Conclusions

Our framework removes a large obstacle to adopting portfolio optimisation at scale: the black box is gone. Once every view and constraint can be traced and explained, institutional investors, portfolio managers, and robo‑advisors should be able to embrace these methods. 

Transparency also enables automation: once every portfolio tilt is explainable, the entire construction process can be industrialised, customised for clients, and even provide the required inputs for Large Language Models, opening the door to next‑generation interactive investment advisory tools and robo‑advice.