Questions:

- The weights are generated for all AiLA strategies daily using the relevant portfolio construction methodologies according to the portfolio configurations.
- What is the historical risk associated with the portfolio on a given date ?

Approach:

- Three different approaches are used to calculate the daily returns where the fundamental approach for the analysis remains same –
- Applying the weights to the historical returns of the individual assets/ front month contracts.
- Aggregating the returns at Commodity, Sector and Portfolio levels
- Calculating various Risk Metrics to evaluate the historical risk of the portfolio on that given date.

- Three AiLA strategies of different configurations/underlying assets are considered for the analysis - AiLA-S015 (Long Only), AiLA-S030 (Long Short) and AiLA-S108 (Long Short based on BCOM assets excluding Agricultural sector commodities).

**Figure 1 :** Weight Allocations on 2024-06-26 for AiLA-S015 (Long Only)

**Figure 2 :** Weight Allocations on 2024-06-26 for AiLA-S030 (Long Short)

- Three different methods are used to calculate the daily returns which are further aggregated at Commodity, Sector and Portfolio levels for the historical risk evaluation.
- First method is a Standard approach (method A) where the assets’ weights are multiplied with the respective historical assets’ returns to obtain a return series for each asset which are further aggregated at commodity level
- However, the standard approach does not consider the seasonality into consideration – for example, a front month contract with an allocation at a point of time may not be the front month at a different point of time.
- To avoid the seasonality issue, the individual assets’ weights are aggregated at the commodity level (as displayed in the Figure 1 and 2) and individually multiplied with both the commodity’s front month return (method B) and the equal weighted return of all the individual contracts traded in the portfolio under that commodity (method C).
- By allocating to the front month and equally among all the traded contracts, both the high volatility and the average volatility scenarios are considered making the analysis more robust.

**Figure 3 :** Returns Distribution of AiLA-S030 strategy using Method A

**Figure 4 :** Returns Distribution of AiLA-S108 strategy using Method A

- The Commodity returns are aggregated at Sector and Portfolio levels and the portfolio level returns distributions are illustrated in the Figures 3, 4, 5, 6 for various portfolios.
- Distribution metrics such as Mean, Median, Standard Deviation, Skewness, Kurtosis and Risk metrics such as Daily Value at Risk (VaR) are calculated to understand the portfolio returns risk profile and return distribution (displayed in Table 1).
- Daily VaR at 95% Confidence level for AiLA-S015 strategy is calculated as -0.99%, which explains that there is 5% probability or approximately 13 trading days in a year that the weight allocation under consideration could generate a portfolio return less than or equal to -0.99%.
- As mentioned in the Table 1, returns generated using Method A and Method C have a similar risk profile and are less risky than the returns generated using Method B, where the entire weight is allocated to the front month which is typically more volatile than the other contracts.
- Excluding the outliers (all days with absolute returns greater than 1.5%), the Kurtosis and Skewness can be seen to vary significantly indicating the distribution and risk of the portfolio returns without considering the extreme cases.

**Figure 5 :** Returns Distribution of AiLA-S015 strategy using Method A

**Figure 6 :** Returns Distribution without outliers of AiLA-S015 strategy using Method A

- Different approaches are used to calculate the returns to account for seasonality and volatility of the commodities contracts.
- Returns distribution and risk metrics are calculated based on the above calculated returns to evaluate the historical risk of the weights on a given date for a portfolio configuration.
- Returns generated from Method A and Method C have better risk profile than the returns generated from Method B, which explains the diversification advantages of allocating across different points on the curve rather than allocating only to the front month contract.
- However, in this analysis, Method B provides a perspective of what could be the worst-case scenario if all the traded contracts of a commodity are as volatile as the front month contract.
- Distribution and Risk metrics calculated excluding the returns outliers helps understand if the negative skew of the portfolio is due to the extreme cases of the returns or if its due to the portfolio’s true ability to generate the negative skew returns.
- Examining the dates with the lowest five returns listed in Table 2 helps to understand the historical minimum return that the strategy would have recorded if these weights had been allocated.

Metric | AiLA-S015 | AiLA-S015 (No Outliers) | ||||

Method A | Method B | Method C | Method A | Method B | Method C | |

Mean | 0.020% | 0.016% | 0.020% | 0.027% | 0.024% | 0.028% |
---|---|---|---|---|---|---|

Median | 0.022% | 0.015% | 0.021% | 0.023% | 0.016% | 0.022% |

Std. Deviation | 0.625% | 0.725% | 0.615% | 0.526% | 0.584% | 0.521% |

Skewness | -0.23 | -0.24 | -0.26 | -0.05 | -0.03 | -0.05 |

Kurtosis | 3.20 | 3.04 | 3.17 | 0.11 | -0.17 | 0.11 |

Daily Var 90% | -0.70% | -0.85% | -0.69% | -0.66% | -0.75% | -0.64% |

Daily Var 95% | -0.99% | -1.14% | -0.97% | -0.88% | -0.99% | -0.87% |

Daily Var 99% | -1.69% | -1.94% | -1.66% | -1.24% | -1.34% | -1.24% |

**Table 1 :**
Risk and Distribution metrics of AiLA-S015 strategy’s return using Method A, B, C based on 2024-06-26 weights

Method | Day 1 | Day 2 | Day 3 | Day 4 | Day 5 |

A | -4.12% 2008-10-10 |
-3.76% 2008-09-29 |
-3.75% 2008-10-06 |
-3.61% 2020-03-09 |
-3.61% 2020-04-21 |
---|---|---|---|---|---|

B | -5.14% 2020-04-21 |
-4.45% 2022-03-09 |
-4.39% 2020-03-09 |
-4.38% 2008-10-10 |
-3.98% 2008-10-06 |

C | -3.99% 2008-10-10 |
-3.78% 2020-03-09 |
-3.66% 2008-09-29 |
-3.60% 2008-10-06 |
-3.33% 2009-03-02 |

**Table 2 :**
Dates with the lowest 5 returns calculated using Method A, B, C for AiLA-S015 based on 2024-06-26 weights