Project:Sandbox

The S&P Goldman Sachs Commodity Index Total Return (SPGSCITR) stands as a prominent benchmark in understanding the global commodity market beta. This index has been constructed using 24 futures contracts that are exchanged publicly. These contracts are representative of physical commodities that span across five major sectors, namely Energy, Agriculture, Livestock, Industrial Metals, and Precious Metals. A look at the historical data suggests a series of alterations in the weights of various commodities and sectors between 2021 to 2023.

In 2022, Brent Crude Oil, which is exchanged on the Intercontinental Exchange, saw the most significant rise in percentage weight. However, the Energy sector maintained its dominance in terms of weight within the index. The Agriculture sector, driven primarily by Corn and Soybeans, witnessed the largest increase in sector weight. Conversely, the weight of the Precious Metals sector declined, primarily due to a reduction in Gold's weight.

The subsequent year, 2023, observed WTI Crude Oil, a commodity traded on NYMEX, holding the highest weight within the index. Natural Gas, another commodity exchanged on NYMEX, experienced the highest percentage increase in weight. Yet again, the Energy sector retained its position as the most significant sector in terms of weight in the S&P GSCI, with a notable rise in weight percentages of Natural Gas and Heating Oil. On the flip side, the Precious Metals sector saw a dip, mostly due to a reduction in Gold's weight.

To project scenarios for SPGSCITR, a linear regression model has been formulated. This model is a function of the log-difference of the SPGSCITR in relation to the log-difference of the Brent oil price, the difference in the VIX (Volatility Index), the log-difference of AUD (Australian Dollar), and the log-difference of the multiplicative inverse of JPY (Japanese Yen). The equation representing this relationship is:

\[ \text{DLN(SPGSCITR}_t) = \alpha + \beta_1 \times \text{DLN(BRENT}_t) + \beta_2 \times \text{D(VIX}_t) + \beta_3 \times \text{DLN(AUD}_t) + \beta_4 \times \text{DLN(JPY}_t^{-1}) + \epsilon_t \]

The variables are defined as follows:

- \( \text{BRENT}_t \) symbolizes the Brent oil price at time t.

- \( \text{VIX}_t \) stands for the Chicago Board Options Exchange volatility index at time t.

- \( \text{AUD}_t \) represents the exchange rate of AUD to USD at time t.

- \( \text{JPY}_t \) represents the exchange rate of USD to JPY at time t.

- \( \epsilon_t \) is the error term or disturbance at time t.

The logic behind selecting the log-difference transformation is to ensure the stationary nature of the dependent variable. While a level difference transformation was also considered, it was eventually discarded because of concerns related to the potential recurrence of events from the 2007 - 2009 recession.

Brent was included in this model due to its substantial weight (17.19% in 2022) in the S&P GSCI and its significant correlation with the SPGSCITR. The volatility index, VIX, has been included since it's capable of capturing the sharp downturns, particularly during financial crises. As commodities play a pivotal role in international trade, currency exchange rates of major trading nations can be closely tied to global commodity prices. However, from several considered, only the AUD and JPY turned out to be statistically significant for the model.

Considering forecasting:

- In the short-term (covering the first 13 quarters from the last recorded value), forecasts for the SPGSCITR are developed using the regression model.

- For the medium term, which stretches from the 13th quarter to a decade, the baseline scenario prediction is derived from the regression model. However, alternative scenarios make use of a linear interpolation method that smoothens the forecast from the 13th quarter to the 10-year point.

- Over the long term, which commences from the 10-year point and extends to the endpoint of the forecast horizon, all predictions converge to the baseline 10-year projection from the regression model. This assumption stems from the belief that SPGSCITR will maintain stability in the extended run, bringing all scenario predictions to a common value.

\textbf{MRM Assessment:}

At the outset, the model’s foundation on the linear regression technique is both its strength and potential limitation. Linear regression is widely respected for its transparency and ease of interpretation. When modeling financial or economic phenomena, it's crucial to be able to communicate the rationale and implications of a model clearly, and linear regression aids in this endeavor.

However, the assumption that relationships between the dependent variable (SPGSCITR) and the independent variables (like Brent oil price, VIX, AUD, and JPY) are linear might oversimplify the real-world dynamics of the commodity market. Complex financial markets often exhibit non-linear behaviors, especially under extreme market conditions or during financial crises. Thus, relying solely on a linear framework might miss capturing these nuances and potentially lead to inaccurate forecasts during turbulent times.

The model's utilization of the log-difference transformation to achieve stationarity in the dependent variable is commendable. Stationarity is a fundamental prerequisite for many time series forecasting models, ensuring that the properties of the series don't change over time. By ensuring stationarity, the developers have enhanced the model’s reliability and predictive capability.

However, a potential concern is the developers' decision to exclude the level difference transformation based on historical events, such as the 2007-2009 recession. While it's prudent to be cautious about extreme events, it's also essential not to dismiss the possibility of their recurrence entirely. Financial markets can be unpredictable, and past patterns don't guarantee future behaviors.

The selection of independent variables, including Brent, VIX, AUD, and JPY, is rooted in sound logic. For instance, Brent, given its significant weight in the S&P GSCI, is a reasonable choice, and its correlation with SPGSCITR adds to the model's credibility. Similarly, the inclusion of VIX, a measure of market volatility, is pertinent as volatility is often inversely related to commodity prices.

However, the exclusion of other potentially significant exchange rates apart from AUD and JPY could be viewed as a limitation. While these two currencies might have shown statistical significance in the model, the global commodity market is influenced by several major economies. Leaving out currencies like the Euro or the British Pound, which might have indirect effects on commodity prices, could lead to the omission of certain market dynamics.

Lastly, the forecasting approach, while methodical, leans heavily on the assumption of stability in the long run. While this may simplify forecasts and align with some economic theories that markets tend to stabilize over extended periods, it might also be a tad optimistic. As history has shown, long-term stability in financial markets isn't always guaranteed. Assuming that all scenario forecasts will converge to a common value might not account for unforeseen shocks or structural changes in the market.

In conclusion, while the model developed by the developers shows a robust methodology and a logical selection of variables, it's not devoid of limitations. It might benefit from a more comprehensive consideration of potential non-linear relationships and the inclusion of other significant global currencies. Furthermore, long-term forecasting assumptions might benefit from periodic reviews to adapt to changing market dynamics.