- In the case of two assets (𝑎,𝑏) with market return 𝜌 ~ 1, where 𝑎 (𝑏) are allocated long (short) according to a signal 𝑠 𝐿 (𝑠 𝑆 ).
- The PnL correlation is a combination of the market correlation together with the signal overlap.
𝜌(𝑃𝐿 𝑎 ,𝑃𝐿 𝑏 ) ~ 𝑐𝑜𝑛𝑠𝑡 ∙𝜌(𝑟 𝑎 ,𝑟𝑏 )∙𝜌(𝑠 𝐿,𝑠 𝑆 )
- 𝜌(𝑠 𝐿 ,𝑠 𝑆 )= 0: if the 𝑠 𝐿 signals are always generated on different days than 𝑠 𝑆 , the two PnL streams are complementary but without any hedging benefit w.r.t. their combined risk.
- 𝜌(𝑠 𝐿 ,𝑠𝑆 ) ≠ 0: if the 𝑠 𝐿 and 𝑠 𝑆 signals can occur on the same days, hedging will reduce their combined risk with a potential benefit w.r.t. their risk adjusted performance.
- This scenario applies to (high 𝜌 ) inter-commodity assets, such as WTI vs RBOB, however, can also be applied to intra-commodity assets, such as WTI Jul vs WTI Dec.
- The possibility of reducing the portfolio risk is one reason for generating AiLA allocations for individual commodity contracts.