Robust Construction of a Multi-Asset Index Including Bitcoin

Abstract

In recent years, investors have shown growing interest in diversified multi-asset indices that incorporate crypto assets, with Bitcoin at the forefront. The launch of exchange-traded products, the growing acceptance of Bitcoin among institutional investors, and its increasing weight in financial markets all highlight the strategic importance of this asset. Bitcoin has exhibited extraordinary returns in the past, yet as a standalone investment it appears less attractive to risk-averse investors due to extreme volatility and severe drawdowns. The relevant question is therefore whether including Bitcoin in a diversified multi-asset portfolio can enhance performance without deteriorating its overall risk profile, and what allocation methods provide a credible way to achieve this balance. Classical allocation methods offer contrasting perspectives. Mean–variance optimisation explicitly incorporates expected returns, but it is highly sensitive to estimation error, which often results in unstable allocations. Empirical evidence even shows that simple rules such as the naïve 1/N portfolio often outperform mean–variance optimisation out of sample [DeMiguel et al., 2007]. Risk-based approaches, such as minimum variance or risk parity, are more stable but ignore expected returns altogether, which is problematic when dealing with an asset that exhibits an unusually high mean return. Robust optimisation provides a natural way to reconcile these two approaches. By incorporating parameter uncertainty directly into the optimisation problem, robust methods allow expected returns to influence the allocation while penalising excessive reliance on noisy estimates. This framework is particularly well-suited for Bitcoin, whose characteristics amplify estimation risk. The aim of this thesis is to study the construction of a multi-asset index including Bitcoin, with a particular focus on the use of robust optimisation techniques. More specifically, the objective is both to assess whether the inclusion of Bitcoin can enhance the performance of a diversified portfolio without materially worsening its risk profile, and to evaluate whether robust optimisation provides more stable and credible allocations than classical approaches such as mean–variance, risk parity, or equal-weighting. Performance and stability are examined through backtests and Monte Carlo simulations.