Questions:

- The return distribution from AiLA products often demonstrate a positive skew.
- This could relate to several aspects of the AiLA strategy methodology, one being the allocation investment period.
- Can we observe any relationships between the return skewness and the investment period used to construct the asset allocation strategy?

Approach:

- Distinguish between daily returns and returns compounded over an investment period.
- Pool returns from many assets and winsorize at about 5 standard deviations to reduce uncertainty and impact from outliers.
- Investigate asset return skew, conditional on investment periods used to design asset allocation strategy.

All skew results are based on the Fisher-Pearson coefficient G1 from [SciPy]. [SciPy]: E. Jones et al., Open Source Scientific Tools for Python (2001), http://www.scipy.org

- AiLA asset returns refer to the (%) returns obtained by being long or short a single asset, e.g. the CME Corn Dec22 futures contract, according to the AiLA allocation signals generated for that asset.
- We distinguish between daily asset returns vs returns compounded over a period, since different potential sources of skew could affect the results differently, e.g.
- Skew generated by the AiLA upstream modelling might have similar impact on the two return types.
- Whereas the risk/reward targets implying asymmetric allocation exits, might introduce a skew primarily affecting the compounded returns.

- Here the compounded returns are obtained over the actual period a given allocation was held, i.e. period can vary for each return.
- It should be noted that compounded returns can obtain a positive skew purely from the compounding [Farago22]. However, due to the modest volatility as well as investment periods covered in this study, these contributions to the skew are estimated to be significantly smaller than the effects observed.

[Farago22]: A.Farago and E.Hjalmarsson, Long-Horizon Stock Returns Are Positively Skewed, Review of Finance (2022) 1–44.

- The AiLA asset allocations are typically produced with different intended investment periods for different assets.
- The (213) different assets used were therefore binned in to three equally large sets of assets with investment periods (IP) of,
- Short: IP <= 9 days
- Medium: 9 < IP <= 21 Days
- Long: 21 < IP

- For the compounded returns, the return period can be shorter than the IP, however, is usually of the same order.
- From the return distributions of the three bins it is observed that,
- The daily returns show a negligible amount of positive skew for all three bins.
- The compounded returns indicate a noticeable positive skew, in contrast to the daily returns, for all three bins.
- The compounded returns also show the most positive skew for the two bins comprising assets with the longest investment periods.

- The return distribution associated with the AiLA products often show a positive skew.
- Several aspects could impact the contribution to such a return skew, where one is the investment period used when producing the AiLA asset allocation strategies.
- Therefore, an investigation was made, at an AiLA asset return level, of any relations between a positive skew and the investment period associated with the different assets.
- The results indicated no significant skew of the daily asset returns.
- However, the returns compounded over the respective allocation period showed an increasing amount of positive skew with an increasing investment period.
- This can be expected, for example, due to the asymmetric risk/reward targets involved in the strategies.
- Related to the skew observed at portfolio level it is possible that effects in addition to those observed at asset level are relevant, e.g. successfully predicting correlated events like the 2020 crash across many assets could possibly increase these effects at portfolio level.