Questions:

• Can we construct a given amount of correlation to an index like GSCI for an AiLA long/short index?
• Could we express the correlation preference directly in terms of weights?
• How does this impact the AiLA index returns?

Approach:

• Start from a long/short target portfolio, with equal risk assigned to all assets (𝑤^𝑇𝑎𝑟𝑔𝑒𝑡).
• Express correlation as an angle (𝛼^𝐺𝑆𝐶𝐼) between the AiLA and GSCI index weight vectors.
• Find AiLA weights (𝑤) most similar to 𝑤^𝑇𝑎𝑟𝑔𝑒𝑡 and satisfying a constraint: cos⁡(𝛼^𝐺𝑆𝐶𝐼 )> correlation preference.

• However, the AiLA and GSCI indices include different assets and returns are correlated.
• Associate assets through a simple risk model with asset correlations treated as 1 or 0, e.g. Wheat H vs Wheat N -> 1 and Wheat H vs Zinc Z -> 0.
• Group AiLA and GSCI assets into a common risk space, reflecting high market correlations, e.g. WTI and RBOB grouped together as Oil due to high correlation.
• Group Risk in buckets,
  • Ags & Meat: 7 risk groups.
  • Metal: 8 risk groups.
  • Soy Complex: 2 risk groups.
  • Wheat Complex: 1 risk group.
  • Power & Gas: 3 risk groups.
  • Oil: 1 risk group.
• Calculate 𝛼^𝐺𝑆𝐶𝐼angle based on (22) risk group weights.

• GSCI risk weights are relatively stationary and concentrated to the oil risk group.
• AiLA signals are only active at certain times and do not always cover the prevailing GSCI markets and contracts.
• The AiLA target index used here involve 102 market/contracts selected by being the most liquid.
• Being able to construct a high correlation to GSCI requires enough AiLA signals for relevant assets, which was confirmed by adjusting weights in favor of GSCI only considering assets with active AiLA signals at the time.
• The exercise indicates a maximum possible correlation of about 86% and confirm that the cos⁡(𝛼) metric follow the high correlation of the manually adjusted AiLA index.

(* The dips in cos⁡(𝛼) value indicate periods when the available AiLA assets are too different to achieve a close match with the GSCI weight vector.)

• The described approach, using a cos⁡(𝛼) constrain for the AiLA long/short index weights, result in desired correlation to GSCI.
• The unconstrained AiLA long/short index show slight negative correlation (-14%) to GSCI, which increase with tighter constraints and saturates inline with suggested maximum (<86%).
• Given the long-only nature of an index like GSCI the constrained AiLA index effectively converge towards a pure long signal index, concentrated to the main GSCI risk groups, with an increasingly positive correlation constraint.
• However, these results are produced in a context where asset capacity constraints are not relevant.
• In case of tight capacity constraints, the AiLA index will be concentrated to certain high liquidity assets, which both affect the ability to control correlation as well as the performance.

(* Given the positive correlation preference studied here, in the rare cases where the constraint cannot be met, the method defaults to only using any available long signals.)