# Correlation Between Physical Prices & Futures: The Key To Optimal Hedging

*This analysis illustrates how to measure the correlation between physical commodities cash & futures prices in order to design optimal hedging strategies. **Reading time: 8 minutes*

Correlation analysis is critical to many aspects of finance and trading – whether the Capital Asset Pricing Model (CAPM), Value at Risk (VaR) models, or trading strategies such as statistical arbitrage, the correlation between assets underpins many trading and risk models.

In physical commodities trading, understanding the correlation between physical prices and related futures prices is key to optimal hedging.

Similarly, basis trading – or pricing physical contracts at a fixed level above or below a particular futures contract – is a primary pricing mechanism for many agriculture products.

Whether optionally hedging physical positions – that is, hedging fixed-price physicals contracts – or pricing contracts on an explicit basis, correlation analysis between physical and futures prices is in fact a fundamental aspect of commodities trading.

However, how do we measure the correlation between two-time series? Or two assets, such as a physical commodities contract and a futures contract for a related product? And what are some of the challenges in doing so?

### Measuring Correlation

While there are many ways to measure the relation between two-time series, the Pearson correlation coefficient is its most common statistic. The Pearson correlation coefficient measures the degree of the linear relationship between two variables. Its values range between

- -1 (perfect negative correlation)
- 1 (perfect positive correlation)

Zero correlation implies no relationship between variables.

For example, a simple visual comparison of Free on Board (FOB) Indonesian Palm Oil physical prices and Bursa Malaysia Palm Oil futures shows that the two assets are closely related over time. Directional movements, whether short term or longer trends are largely mirrored by the other asset.

Source: AgFlow

Indeed, the Pearson correlation over the period from 2017 to May of 2020 is 0.77, indicating that daily returns for physical Indonesian Palm Oil and Malaysian Palm futures exhibit a relatively strong and positive correlation. In other words, if the cash prices of Indonesia Palm Oil increase on any particular day, the prices of Bursa Malaysia Palm Oil futures have likely increased as well, as one would expect.

Many physical commodities exhibit similarly strong positive correlations with related futures markets, for logical reasons. If a closely related futures market was uncorrelated, at a general sense, to the underlying physical commodity, the futures market would have little *raison d’être *

French Milling Wheat 11% protein FOB, for example, demonstrated a Pearson correlation of 0.84 with the ICE UK Feed Wheat futures contract during the period of 2017 to May 2020, and 0.71 with Euronext French Milling Wheat contract.

Source: AgFlow

### The Instability of Estimates

Any statistical estimate, such as the Pearson correlation coefficient, comes with a degree of uncertainty, but often that uncertainty is ignored. This is incredibly dangerous in financial markets.

After all, a statistical estimate is precisely that – an “estimate”; and comes with some degree of uncertainty.

More importantly, time-series statistics or estimates are often, if not always, non-stationary. That is, the nature of the statistical properties of time series, and hence markets changes over time. As a result, a single point statistic such as Pearson correlation does not necessarily capture the current market correlation.

To highlight this point, it is helpful to provide rolling statistical estimates. For example, below we measure rolling Pearson correlation estimates over 120, 90, and 30-day look-back windows.

While the Pearson correlation coefficient between FOB Indonesian Palm Oil physical prices and Bursa Malaysia Palm Oil is 0.77, we notice that the rolling estimate is unstable – over any 120, 90, or 30 day period the correlation is often dramatically different than the single point value estimated over the full period since 2017. Considering a 30-day rolling window, for example, June 2017, August 2018, March 2019, and August 2019 experienced a negative correlation.

In other words, to say that “the correlation between FOB Indonesian Palm Oil physical prices and Bursa Malaysia Palm Oil is 0.77”, while technically accurate, fails to capture the reality of an unstable and uncertain relationship between the assets.

Source: AgFlow

Source: AgFlow

When we take the Pearson correlation of a data set or any statistic, we do not know the real correlation – we have estimated the correlation as best as possible from the data. Furthermore, this real correlation we are attempting to estimate also changes over time. As a result, any correlation estimate can be, and generally is, incorrect. This is true of any parameter we estimate.

To better understand what is happening, we need to determine how good our estimate is by looking at its stability, standard error or standard deviation, and confidence intervals.

Further curves for Indonesia FOB Palm Oil, French FOB Milling Wheat 11%, and Brazil FOB Corn.

Source: AgFlow

### Correlation and Risk Management in Physical Commodities Trading

As per Investopedia’s very apt definition: a hedge ratio compares the value of a position protected through the use of a hedge with the size of the entire position itself, or, similarly, a comparison of the value of futures contracts purchased or sold to the value of the cash commodity being hedged.

In financial theory, the minimum variance hedge ratio, or optimal hedge ratio, is fundamental to determining the optimal number of futures contracts to purchase or sell to hedge a particular physical commodities position.

The minimum hedge ratio, in turn, is calculated as the product of the correlation coefficient between the changes in the spot and futures prices and the ratio of the standard deviation of the changes in the spot price to the standard deviation of the futures price.

However, as we have seen, the correlation between a physical commodity and related futures contracts is not stable over time.

As a result of uncertainty and instability of the real correlation of the assets, whether now or in the future, this hypothetical hedge ratio, like correlation or other statistical measures, can only be estimated and is generally not a perfect measure of the real correlation.

### Instantaneous Phase Synchrony

Instantaneous Phase Synchrony is helpful when working with time-series data that exhibit oscillating properties. As the analysis of rolling window Pearson correlations demonstrates, the relationship between physical commodities prices and related futures prices, broadly speaking, follows a clear oscillating pattern. Even assets with high correlation witness time-varying Pearson coefficients that often oscillate significantly over time.

The benefit of applying instantaneous phase synchrony, in addition to Pearson correlation analysis, is that this approach allows a great way to compute moment-to-moment synchrony between two signals without arbitrarily deciding the window size as done in rolling window correlations.

Technically speaking, instantaneous phase synchrony measures the phase similarities between two signals, or time series, at each time point. The phrase refers to the angle of the signal when it is resonating between 0 and 360 degrees, or -Pi to Pi degrees.

Source: Medium

When two signals line up in phase their angular difference becomes zero. The angles can be calculated through the Hilbert transform of the signal, which splits the signal into its phase and power. We can say two points in sync when these are moving up or down together, thus the phase synchrony is 1.

While certainly more mathematically technical than Pearson correlation analysis, understanding the relationship between physical commodities prices and related futures contracts using instantaneous phase synchrony allows commodities traders and risk managers another tool to understand the co-movement of physical and related futures prices.

For example, applying both rolling correlation analysis and instantaneous phase synchrony to FOB Brazil soybean prices and CME and Dalian soybean futures allows us to confirm, and hence have more confidence, in our estimate of co-movement.

A 30-day rolling correlation study demonstrates that while FOB Brazil soybean prices are generally more correlated to CME soybean futures prices, during 2017 or 2019, FOB Brazilian soybean prices demonstrated more co-movement with Dalian soybean futures prices in 2018.

Source: AgFlow

Source: AgFlow

Source: AgFlow

Source: AgFlow

However – Pearson correlation analysis is a best estimate. Applying instantaneous phase synchrony allows for a second, independent, analysis of co-movement that can improve our confidence of what the real correlation is and how it is evolving over time.

Just as 30 day rolling correlation indicates, applying instantaneous phase synchrony highlights a breakdown of FOB Brazil soybean price correlation with CME soybean futures around Summer 2018 while the correlation with Dalian soybean futures remains relatively in line with historical norms.

Source: AgFlow

Source: AgFlow

By using both rolling Pearson correlation estimates and instantaneous phase synchrony, we are thus able to have confidence in our understanding of asset co-movement and hedging or trading decisions based on this analysis.

Conversely, instantaneous phase synchrony analysis can cast doubt on the accuracy of a rolling Pearson correlation estimate.

For example, in Q4 2019 a 30-day rolling correlation estimate of FOB Argentina soybean oil prices and CME soybean oil futures prices show a significant breakdown in historical estimates. During the period, Argentina’s physical soybean oil prices showed a mere 0.14 correlation with CME futures prices and a strong 0.79 correlation with Dalian futures.

Source: AgFlow

### Conclusion

Understanding the co-movement, or correlation, of physical commodities prices and related futures prices is fundamental to both trading and risk management.

However, any statistical measure or parameter is merely a best estimate of the real value of the measure or parameter using available data. Furthermore, in the case of non-stationary time series, the real value of statistical measures and parameters vary over time, often markedly so.

To better understand asset price co-movement, it is often helpful to use rolling window Pearson correlation estimates. One challenge with this approach, however, is that rolling window correlation estimates depend on an arbitrarily decided look-back window – in the case of this study, 120, 90, and 30-day windows.

Meanwhile, instantaneous phase synchrony analysis is gaining popularity mainly because it offers a single time-point resolution of co-movement in oscillating time-series data while avoiding arbitrary decisions inherent in rolling correlation analysis.

In many cases, then, it is helpful for traders and risk managers to apply both techniques to gain confidence in their estimates of co-movement, or to question short term breaks in historical price relationships.