Literature review

An extensive body of literature has examined whether futures prices are unbiased and provide accurate forecasts of cash prices in agricultural markets. However, most studies have primarily focused on the lack of convergence between futures and cash prices in grain markets (e.g., Aulerich, Fishe, and Harris, Reference Aulerich, Fishe and Harris2011; Garcia, Irwin, and Smith Reference Garcia, Irwin and Smith2015; Goswami, Adjemian, and Karali, Reference Goswami, Adjemian and Karali2022; Irwin et al., Reference Irwin, Garcia, Good and Kunda2008; Li and Chavas, Reference Li and Chavas2023). Specifically, previous research has analyzed corn, soybean, and wheat markets, attempting to explain the lack of convergence through delivery instruments and storage rates. Garcia, Irwin, and Smith (Reference Garcia, Irwin and Smith2015) found that grain futures expired up to 35% above cash prices in most periods between 2005 and 2010. They attributed this non-convergence to instances in which the market price of physical grain storage exceeded the maximum storage rate allowed on delivery instruments. Li and Chavas (Reference Li and Chavas2023) examined the co-dependence between futures and spot prices in corn and soybean markets using a quantile vector autoregression-copula approach, noting that futures prices tend to stabilize as nearby contracts approach maturity.

Relatively few studies have examined convergence in livestock futures markets, particularly lean hog futures. Some related work has instead focused more broadly on basis behavior in these markets. Liu et al. (Reference Liu, Brorsen, Oellermann and Farris1994) analyzed the forecastability of the live cattle basis during the month preceding contract delivery, noting that pricing noise during the delivery period complicates accurate basis forecasting. Frank et al. (Reference Frank, Gómez, Kunda and Garcia2008) examined basis behavior in lean hog futures following the transition to cash settlement in 1997, observing a wider and more volatile basis. However, they found no significant increase in ex-ante basis risk. Trujillo-Barrera, Garcia, and Mallory (Reference Trujillo-Barrera, Garcia and Mallory2018) assessed ex-ante density forecasts for lean hog futures and identified short-term deviations from convergence during periods of market volatility. More recently, He, Serra, and Garcia (Reference He, Serra and Garcia2021) investigated liquidity resilience in lean hog futures during price shocks, noting that although liquidity replenished after shocks, deviations from convergence became more pronounced during volatile periods. In a related study, Bina, Schroeder, and Tonsor (Reference Bina, Schroeder and Tonsor2022) examined how feeder cattle basis risk has changed over time, highlighting significant variation across regions and marketing periods, and identifying key factors contributing to this variability. They found that basis risk increased notably during the 2014–2015 cattle market volatility but has since returned to earlier levels.

Another branch of literature has examined the impact of Livestock Mandatory Price Reporting (LMR), which was implemented in 2001, on US hog markets.Footnote ² Franken, Parcell, and Tonsor (Reference Franken, Parcell and Tonsor2011) found that the Iowa-Southern Minnesota hog market leads terminal markets, attributing this to the thinning of hog cash markets. Mathews et al. (Reference Mathews, Brorsen, Hahn, Arnade and Dohlman2015) observed that while futures markets played a key role during the LMR period, cash markets held a small yet significant role in convergence dynamics. However, their diminished share in overall transactions raised concerns about the reliability of cash prices. Bekkerman and Tejeda (Reference Bekkerman and Tejeda2017) noted that only few studies have examined how thinning cash markets impact futures price convergence, despite the recognition that active cash markets are essential for the effectiveness of futures markets.

Overall, previous studies provide valuable insights into the dynamics of hog markets and the role of futures markets in relation to cash prices. Some studies have examined livestock futures and LMR; however, only a few have investigated convergence bias in hog markets or empirically demonstrated its link to thinning cash markets. While market structures continue to evolve with the rise of contracts and internal transfers, negotiated cash markets remain a crucial reference for futures settlement. This highlights the need for further investigation into convergence dynamics in lean hog markets, particularly to understand the implications of reduced negotiated cash market activity.

Empirical approach

Given the assumptions of rational expectations and risk-neutral market participants, futures prices should equal expected future spot prices, with deviations arising only from unforeseen shocks. Under these conditions, the spot price at delivery should equal the futures price plus a zero-mean error term (Working, Reference Working1949). Although Working’s model was developed for storable commodities, its insight – that futures prices reflect market expectations – remains broadly relevant. Futures markets for non-storable commodities such as livestock can also reflect expectations about supply and demand conditions (Leuthold, Reference Leuthold1979; Naik and Leuthold, Reference Naik and Leuthold1988). Given that, we estimate the following regression to test the unbiasedness hypothesis:

(1) $$ C_{t} = \alpha + \beta F_{t} + \epsilon _{t}, $$

where C _t represents the cash price at time t, F _t is the nearby futures price, and ϵ _t denotes the error term. If the futures price serves as an unbiased predictor of the future spot price, the regression coefficients for the intercept and the futures price should not be statistically different from zero and one, respectively (Chevallier, Reference Chevallier2010).

We use the nearest expiring futures contract in a daily continuous time series, rolling over to the next active contract upon expiration.Footnote ³ For cash prices, we consider negotiated and SPMF prices, which are used to calculate the CME Lean Hog Index. Following common practice in the futures market literature, we apply a logarithmic transformation to the prices to stabilize variance and allow for a proportional interpretation of price changes.

To gain further insights into the bias and predictability of futures prices near expiration, we examine the alignment of futures prices with spot prices at expiration (see Figure 3). Specifically, we define the absolute difference between daily futures prices near expiration and spot prices at expiration (|F _{t − i}−C _t|), where F _{t − i} represents futures prices i day(s) prior to expiration for each contract month, and C _t represents cash prices at expiration.Footnote ⁴ In other words, we use the same cash price at expiration (C _t) and vary the futures price (F _{t − i}) for each day leading up to expiration (i days prior). This approach allows us to examine convergence dynamics by plotting the absolute difference between futures prices and cash prices against the number of days to expiration. The magnitude of this difference reflects the deviation between futures and cash prices, helping us visually assess whether futures prices converge predictably as a futures contract nears expiration. It is worth noting that predictability of the basis is critical in evaluating the effectiveness of the futures as a risk management tool. For this measure, we collected futures prices near expiration (0 to 50 days before expiration) for all contract months from February 2002 to April 2022.Footnote ⁵ The data were sourced from the Commodity Research Bureau (CRB Infotech CD). If futures prices do not closely align with spot prices at expiration, this may indicate potential bias or weaker predictability in the basis.

We then examine whether the thinness of cash markets has contributed to the convergence of lean hog futures and cash prices. To address this, we consider the share of negotiated volume purchased through the cash or spot market by a packer from a producer. USDA’s LMR provides daily volume by purchase types: 1) Negotiated; 2) Swine/Pork Market Formula; 3) Other Market Formula; 4) Other Purchase Agreement; 5) Negotiated Formula; 6) Packer Sold; and 7) Packer Owned. We define the share of negotiated volume from the seven aforementioned purchase types. The equation is given as follows:

(2) $$\begin{equation} \begin{aligned}\left | \textit {Basis}_{t} \right | &= \beta _{0} + \beta _{1} \textit {NegShare}_{t} + \beta _{2} \textit {Volume}_{t} + \beta _{3} \textit {Corn}_{t} + \beta _{4} \textit {Volatility}_{t} +\beta _{5} \textit {VIX}_{t} + \beta _{6} \textit {Month}_{i, t} \\[4pt]&\,\,\,\,\,\,\,+ \beta _{7} \textit {Year}_{j, t} + \beta _{8} \textit {NegShare}_{t} \times \textit {Year}_{j, t}+ \epsilon _{t}\end{aligned}\end{equation}$$

where |Basis| is the absolute value of the basis, defined as negotiated prices minus nearby futures prices in logarithms. In this regression, we consider three negotiated prices: National, Western Cornbelt, and Iowa/Southern Minnesota. NegShare is the share of volume purchased via the negotiated cash market out of seven purchase types discussed above. Volume represents the daily trading volume for lean hog futures contracts in thousands of units. Corn represents futures prices (in logarithms) for corn, a primary feed for hog production. For corn futures, we use data provided by Bloomberg, referencing the same time points as those used for Lean Hog Futures in our analysis. Volatility measures the risk associated with lean hog futures price moves, calculated from the standard deviation of day-to-day logarithmic historical price changes over the 60 most recent trading days. VIX represents the CBOE Volatility Index (VIX), which measures market expectations of future volatility based on options prices of the S&P 500 index. This variable captures overall market volatility and investor sentiment. Month _i and Year _j are included as monthly and yearly fixed effects. Eleven binary variables for months are included from January to November to capture any potential seasonality. Likewise, twenty-three binary variables are included for quoted years, each representing a year from 2001 to 2023. December and 2024 serve as the reference points (omitted indicators) for the monthly and yearly fixed effects, respectively. Lastly, NegShare × Year _j represents the interaction term between the negotiated share and yearly fixed effects. The coefficient β ₁ is of particular interest to evaluate the impact of the thinning of cash markets on the convergence.

Empirical results

Our analysis focuses on daily lean hog futures and cash prices from August 1, 2001, to September 6, 2024. As noted, final futures prices are cash-settled based on the CME Lean Hog Index, which is a two-day weighted average of prices and volumes from Negotiated, Negotiated Formula, and Swine/Pork Market Formula (SPMF) transactions. We collected Negotiated and SPMF prices from the USDA Agricultural Marketing Service (AMS) Datamart, which provides historical mandatory reporting data since 2001. We also collected CME Lean Hog futures, their trading volume, corn futures, the Lean Hog Index, the volatility measure of lean hog futures, and the VIX from the Bloomberg Terminal.Footnote ⁶ The CME hog futures contracts began in 1966, listed as live contracts, with a 30,000-pound unit and deliverable grade of USDA No.1, 2, and 3 barrows and gilts. In 1997, the contract was updated to a lean basis, with a 40,000-pound unit, which corresponds to the quantity of meat produced from around 200 hogs.

Figure 2 presents the time series plot for nearby futures, negotiated prices, and their basis. In the early periods, the basis fluctuated relatively close to zero. However, it has experienced substantial variation over the past decade, with nearby futures often greatly exceeding negotiated prices. It is worth noting that the implementation of Livestock Mandatory Reporting (LMR) for wholesale pork in 2013 may have contributed to the observed increase in basis variation. This coincided with a growing interest in using the cutout value for pricing, which likely influenced both the negotiated cash market and futures market dynamics. Another notable point is the substantial basis observed in 2020. This may partly result from the impact of COVID-19, which created a substantial price gap between negotiated and other prices. During the pandemic, negotiated prices were the most affected compared to prices derived from the futures market or those determined by formula (Meyer and Goodwin, Reference Meyer and Goodwin2021). Moreover, many pork processing plants temporarily closed or reduced operations, leading to an oversupply of hogs at the farm level and a shortage of pork at the retail level. Interestingly, even after the COVID period, we still observe concerning basis levels, as they exhibit higher fluctuations compared to historical levels.

Figure 2. Futures, negotiated, and basis (Aug. 1, 2001–Sep. 6, 2024).

Table 1 presents the regression results of Equation (1), which examines the convergence of nearby futures and cash prices.Footnote ⁷ The analysis considers three cash price series: the CME Lean Hog Index, negotiated, and SPMF prices. Prior to the analysis, we conducted the Augmented Dickey-Fuller unit root tests for the price series in Equation (1), confirming that all the logarithmic price series are stationary at levels.Footnote ⁸ To assess whether futures prices serve as unbiased predictors of future spot prices, we test the joint null hypothesis that α=0 and β=1. As presented in Table 1, the F-statistics indicate significant deviations from the theoretical values across all series. The most significant bias is observed in negotiated prices, with regression estimates for the intercept and slope of −0.38 and 1.08, respectively.

Table 1. Convergence of futures and cash prices: C _t = α + βF _t

Notes: Negotiated refers to negotiated prices, SPMF represents the Swine or Pork Market Formula, and Index refers to the CME Lean Hog Index. The F-tests are performed to test the joint hypothesis that α = 0 and β = 1. All standard errors are adjusted using the Newey-West method to account for heteroscedasticity and autocorrelation.

** and ^*** indicate statistical significance at the 5% and 1% levels, respectively.

This bias may reflect the negotiated market functioning as a residual market for lower-quality hogs, potentially contributing to biased estimates. It could also indicate structural issues within the negotiated cash market. Franken and Parcell (Reference Franken and Parcell2012) observed a decline in hog quality in cash markets as transactional volumes decreased, suggesting that reduced negotiated transactions diminish the representativeness of cash prices. They emphasize the need to maintain sufficient cash market activity for accurate price discovery, as many contracts reference these prices. Butcher and Schulz (Reference Butcher and Schulz2021) found that the declining volume of negotiated trades has increased price variability, reducing their effectiveness for price discovery. Furthermore, SPMF prices have increasingly incorporated pork cutout values – estimated to account for approximately 50% in 2022 (Meyer and Schulz, Reference Meyer and Schulz2024) – which have shown a weakening correlation with negotiated prices.

It is also worth noting that SPMF and Index prices exhibit smaller bias estimates compared to negotiated cash prices. This is reasonable, given that lean hog futures are cash-settled and designed to converge with the CME Lean Hog Index. As noted, the Index is a weighted average of values transacted through Negotiated, Negotiated Formula, and SPMF prices. With SPMF currently accounting for over 90% of the Index, it closely aligns with SPMF prices, which likely explains their smaller bias estimates.Footnote ⁹

Figure 3 graphically presents the alignment of expiring futures (up to 50 days prior to expiration) with negotiated and SPMF prices at expiration. As noted above, futures at expiration are expected to serve as unbiased predictors of future spot prices. Therefore, futures and cash prices are not expected to differ significantly as expiration approaches. We confirm results consistent with the regression findings. Specifically, futures prices align closely with SPMF prices across all contract months. Even 40 days before expiration, all contracts exhibit values within a 10% difference, except for the May contract. This deviation is reasonable, given that the May hog futures contract was newly introduced in 2001 and remains thinly traded compared to other contract months (Carter and Mohapatra, Reference Carter and Mohapatra2008). Notably, we observe larger differences with negotiated prices near expiration. Futures prices often expire up to 5% above negotiated prices in many contract months. More interestingly, these differences frequently exceed 10%, even 20 days prior to expiration, raising concerns about bias and weaker predictability in the basis associated with negotiated prices.

Figure 3. Convergence of futures to SPMF and to negotiated prices (Feb. 2002–Apr. 2022).

Table 2 presents the regression results of Equation (2).Footnote ¹⁰ Notably, we find a negative and statistically significant coefficient for the negotiated share (NegShare) in the regression using national prices, indicating that a higher share of negotiated transactions is associated with a smaller absolute basis.Footnote ¹¹ This may indicate that greater negotiated market activity is associated with improved convergence between futures and cash prices. Conversely, a decline in the share of negotiated volume may increase the absolute basis, potentially contributing to non-convergence. While similarly negative estimates are observed for the IA/MN and Western Cornbelt series, these coefficients are not statistically significant. Nonetheless, the consistency in sign across regions is noteworthy and aligns with expectations, given that IA/MN is a subset of the Western Cornbelt, which in turn is a subset of the National market.

Table 2. Regression results

Notes: The model includes yearly fixed effects and interaction terms between the negotiated share and yearly fixed effects. These are not presented here but are available in Table A4 of the Appendix. December and 2024 serve as the reference points (omitted indicators) for the monthly and yearly fixed effects. Corn represents futures corn prices in logarithmic form. Volatility is a measure of the risk associated with price movements of lean hog futures. All standard errors are adjusted using the Newey-West method to account for heteroscedasticity and autocorrelation.

*, **, and ^*** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

The estimates for trading volume are statistically significant and positive yet close to zero, indicating that the influence of trading activity in lean hog futures on convergence is somewhat limited over the periods considered. Corn prices show a negative relationship with the absolute basis, suggesting that as corn prices rise–a key input in hog production–the gap between futures and cash prices narrows. Conversely, positive and statistically significant estimates for lean hog futures volatility are observed, suggesting that higher hog futures volatility leads to greater divergence between futures and cash prices. This finding aligns with conventional wisdom that, with greater uncertainty in futures prices, a wider basis is expected. On the other hand, the estimates for the VIX are close to zero, suggesting that overall market volatility has a limited impact on price discovery in lean hog markets. This implies that broader market conditions, as measured by the VIX, do not significantly affect the convergence process in the lean hog market. Therefore, hog markets are more influenced by their own dynamics than by broader market fluctuations.