Valuing a Marketing Board’s Price Guarantee and Forward Sales under Geometric Mean Reversion, Currency Risk and Non-Traded Harvest Risk: Evidence from Ghana’s Cocoa Sector
This paper presents a closed-form valuation framework for Ghana's Cocoa Board's price guarantees and forward sales commitments under geometric mean-reverting prices, currency risk, and non-traded harvest risk, revealing that constant-volatility models overstate guarantee values and quantifying the substantial financial reserves required to cover potential over-commitments and statutory price floors.
Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
In the world of global trade, some goods are bought and sold based on promises made long before the product actually exists. Cocoa, the bean that becomes chocolate, is one such commodity. Its price is set on futures markets in London, where traders bet on what the crop will be worth months or even years from now. For a country like Ghana, which relies heavily on cocoa exports, these prices are a matter of national survival. The government acts as the sole buyer and seller of the crop, promising farmers a fixed price for their harvest to ensure their livelihoods, while simultaneously selling large portions of the expected crop to international buyers at prices locked in today. This system creates a delicate balancing act: the government must pay farmers a guaranteed amount, but it only has the money to do so if the crop is large enough and the world price is high enough. If the harvest fails or the price crashes, the government faces a massive financial shortfall.
The challenge for economists and policymakers is figuring out exactly how much risk is hidden in these promises. Traditional methods of calculating this risk often assume that prices move randomly, like a coin toss, where a big jump today is just as likely to be followed by another big jump tomorrow. However, many commodities behave differently; they tend to snap back toward a long-term average after a spike or a drop, much like a stretched rubber band returning to its resting shape. Furthermore, Ghana's situation is complicated by the fact that the country's currency fluctuates against both the US dollar and the British pound, adding a layer of uncertainty that standard models often ignore. Understanding the true cost of these guarantees requires a new way of looking at the math, one that accounts for the rubber-band nature of prices, the volatility of two different exchange rates, and the unpredictable size of the harvest itself.
A recent study by Derrick Delali Atiase of the University of Ghana tackles this complex problem by building a new framework to value the commitments made by Ghana's Cocoa Board. The research focuses on two specific promises: the guarantee that farmers will receive at least 70 percent of the crop's total export value, and the liability created when the board sells more cocoa forward than it actually harvests. By combining a model of how cocoa prices naturally revert to the mean with data on exchange rates and harvest forecasts, the author developed a set of formulas that calculate the fair value of these risks. The study uses decades of historical data on cocoa prices, currency movements, and crop yields to test these formulas against real-world events, specifically looking at the turbulent 2023/24 season and the upcoming 2026/27 season.
The findings reveal that the risks are far more significant than previously understood, but also that the nature of the risk is different from what older models suggest. When the author applied the new model to the 2023/24 season, it showed that the board's over-commitment—selling nearly 787,000 tonnes against a forecast of 800,000 tonnes—was worth about 56 million US dollars before the season began. This was the cost of the risk based on what was known at the time. However, the actual cost that eventually materialized was vastly higher, reaching nearly 269 million US dollars when the model accounted for the combined shock of a poor harvest and a sudden spike in world prices. The study demonstrates that the disaster was not just a bad harvest or a bad price alone, but the dangerous combination of both: when the crop failed, the world price tripled, forcing the board to buy back the missing cocoa at a massive loss.
For the upcoming 2026/27 season, the study calculates that the guarantee to farmers represents a significant financial obligation. The promise to share in rising prices is worth about 5.6 percent of the total producer price, while the promise to hold the price steady if the market falls is worth about 8.5 percent. Perhaps the most striking discovery is that the biggest source of uncertainty is not the price of cocoa itself, but the value of the local currency, the cedi. The research shows that fluctuations in the exchange rate between the cedi and the US dollar account for more than 80 percent of the uncertainty in the final value of the crop. This means that even if the global price of cocoa remains stable, a shift in the currency can drastically change the money the government has to pay out.
The study also corrects a common misconception in how these risks are valued. Many existing models assume that price volatility remains constant, which leads them to overestimate the value of price guarantees. The new research proves that because cocoa prices tend to mean-revert, extreme prices are less likely to persist than a random-walk model would predict. Consequently, valuations that ignore this behavior make the guarantees look more expensive than they truly are. Additionally, the research highlights a counterintuitive danger in forward selling: when a board sells more cocoa than it expects to harvest, a negative relationship between the harvest size and the price actually increases the cost. If the harvest is small, prices tend to rise, forcing the board to cover the shortfall at the highest possible market rates.
To manage these risks, the study offers concrete numbers for how much money should be set aside as a safety net. To cover the price floor guarantee with 99 percent confidence, the Cocoa Board would need a reserve fund of about 1.8 billion Ghanaian cedis for every 100,000 tonnes of forecast crop. This figure is five times larger than the average expected payment, reflecting the need to prepare for rare but severe events. The research concludes that while the board's system of stabilizing prices is vital for farmers, it concentrates immense financial risk in a single institution. By using these new valuation tools, policymakers can better understand the true cost of their commitments, size their reserve funds accurately, and align their currency strategies with their payment obligations, ensuring that the promise made to farmers can be kept even when the market turns.
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