• The AILA methodology typically generates allocation opportunities for a given asset, e.g. the WTI Dec25 futures.
• The allocation opportunities are based on signals representing predictions of favorable market risk-reward conditions.
• Long or short opportunity signals are based on the output from classification models (hereinafter referred to as models), where several opportunity signals from different models can be considered for the same given asset.
• This raises the question of which models to be used, with the best choice typically assessed by past performance and covariance.
• Just like in optimal portfolio allocation, past results typically reflect future expectation with large uncertainties.
• In this exercise we therefore compare a few simple methods of combining multiple-model signals within the AILA approach.
• For this study 10 different models were used, representing a range of varying model types and complexity.

• Each model is assigned a Sharpe ratio (SR) reflecting expected performance, e.g. model m1 consistently better than m2.
• Any SR estimation is a very uncertain, i.e. not to be taken at face value.
• An optimal SR portfolio typically suggest to allocate proportional to the expected future performance [e.g. Markowitz], however, with large uncertainty over-allocating has an adverse effect [e.g. Thorp].
• Therefore, using the Rank instead of the estimated SR is a common choice that offers some regularization.
  • Monotonic function increasing with expected performance.
  • Ensure positive values, also for negative “fluctuations”.
  • Reduce (increase) impact from large (small) differences.
• => Ranked weights provide a simple reference approach.
• => Follow idea of increasing impact from models with higher expected performance but also account for large uncertainty.

Portfolio Setup:

• Diversified commodity portfolio, only changed by aspect relevant for the given comparison.
• Covering 25 commodity futures markets, including from 2 to12 contracts per markets.
• SR calculated at signal level for direct comparison, i.e. excluding portfolio/execution logic and costs.

Results:

• Given this diverse portfolio, the differences between using Ranked vs Shrunk SR, as well as including correlations or not, were small.
• The simple ranked method showed slightly higher SR across the comparisons, including some variations of the portfolio, with a SR difference around 0.28.
• Including the correlation factor indicated a difference of about 0.06 and typically indicating no added benefit.
• => Only small differences were observed between the scenarios compared, and with low statistical significance.