3.1. Data

Weekly auction data for all grades of feeder steers and heifers ranging in average weight from 450 to 849 pounds were obtained from the U.S. Department of Agriculture Agricultural Marketing Service (AMS) Weighted Average Reports for 32 auction market locations. These reports summarize weekly feeder cattle auction transactions, aggregating lots sold by sex, frame size, and muscle thickness (e.g., Medium and Large #1–2), 50-pound weight groupings, and cattle sold with quality-related comments. Mitchell, Peel, and Brorsen (Reference Mitchell, Peel and Brorsen2018) used similar AMS data in hedonic modeling of Oklahoma cow auction prices. An estimated 39% of the individual report entries in our feeder cattle data set represent a single lot, or individual transaction, and in other cases represent an aggregation of multiple similar lots.Footnote ³

Cattle identified by an AMS market reporter as having a differentiating characteristic are “commented” in market reports. Comments on cattle are generally associated with either a quality or condition price premium or discount. Commented lots are treated as unique observations in the AMS reports and are reported separately from other feeder cattle sale observations having similar sex, weight, and grade.

Figure 1 depicts the selected market locations. Auction market data go through December 7, 2021; however, the earliest available data vary by market (summarized in Table 1). Twenty-eight of the markets analyzed reside within the CME Feeder Cattle Index 12-State Region and were chosen as they are high-volume feeder cattle markets and provide geographic dispersion. Toppenish, WA (Pacific Northwest), and Montgomery, AL, Lexington, KY, and Thomasville, GA (Southeast) were selected to evaluate basis risk in higher-volume markets outside of the 12-State Region.

Figure 1. Selected feeder cattle market locations used to evaluate basis risk.

Table 1. Summary of selected feeder cattle markets analyzed

Note: [ ] Denotes a market outside of the Feeder Cattle Index 12-State Region.

To reduce impacts of data errors and abnormal transactions, cash prices were calculated as a percentage of the same day’s nearby feeder futures settlement price. Then, separately for each market and sex, observations were omitted where cash price (as a percentage of nearby feeder cattle futures price) was outside the range of ± 2.5 median absolute deviations from the median to remove outliers (Leys et al., Reference Leys, Ley, Klein, Bernard and Licata2013). This procedure resulted in 917,732 observations available for analysis (of 957,741 original observations).Footnote ⁴

Daily settlement prices for the nearby CME Group feeder cattle and corn futures contracts were obtained from Bloomberg (Reference Bloomberg2020a). The nearby futures price was defined as the settlement price of the nearest available contract up to contract expiration, at which point the nearby price rolled forward to the next available contract month. Daily put and call implied volatilities (IV) for nearby at-the-money corn options were likewise obtained (Bloomberg, Reference Bloomberg2020b). An average of the call and put IV was calculated to obtain a single daily IV value. If a call (put) IV was missing, the put (call) IV was used as the daily IV value. Monthly average IV were calculated from the daily values.

3.2. Hedonic Models

Past studies on basis forecasting methods and hedging cattle have implemented historical average basis values to analyze out-of-sample basis prediction errors (e.g., Coffey, Tonsor, and Schroeder, Reference Coffey, Tonsor and Schroeder2018; Tonsor, Dhuyvetter, and Mintert, Reference Tonsor, Dhuyvetter and Mintert2004). Coffey, Tonsor, and Schroeder (Reference Coffey, Tonsor and Schroeder2018) state expected basis is a better predictor if current supply and demand factors are similar to those when the basis prediction was made. Any method of predicting basis will be more accurate if these factors remain similar year-to-year. Additionally, Tonsor, Dhuyvetter, and Mintert (Reference Tonsor, Dhuyvetter and Mintert2004) suggested incorporating current information into basis forecasts to improve basis forecasting accuracy. However, their analysis was constrained to a single feeder cattle cash price series, chosen to hold hedge ratios near 1.0 over the selected time series. Because feeder cattle prices and associated basis vary substantially across cattle characteristics and market conditions, we extend previous work in a more detailed fashion. In particular, we use hedonic modeling of feeder cattle auction data as it allows for an in-depth basis risk analysis across a broader set of cattle types, locations, and market conditions than previous work. By controlling for transaction characteristics, this method results in more informed basis models than traditional time series models using aggregate data.

Our hedonic model includes feeder cattle futures price on the right-hand side, and, as such, prediction errors are the variation in cash price unexplained by feeder cattle futures and other model variables. This unexplained variation in feeder cattle cash price provides a measure of basis risk. Hedonic modeling and detailed feeder cattle auction data allow us to measure basis risk for each observation across numerous cofactors including auction location, year, season, animal sex, weight category, lot size, grade, comments, and varying feed costs, providing a more thorough basis risk assessment than previous studies.

Hedonic pricing models were estimated separately by sex (steer or heifer) and market location for 5-year rolling samples of weekly auction data. Using the coefficients from these models, out-of-sample feeder cattle price predictions were made for the subsequent year. Thus, each observation had an out-of-sample predicted price dependent on (1) observation-specific sex and market location hedonic pricing model coefficients from the previous 5 years and (2) cattle characteristics and market conditions on the day the cattle were sold.

The hedonic pricing model employed is as follows:

(1) \begin{align*}{\rm{PRIC}}{{\rm{E}}_{it}} &= {b_0} + {b_1}{\rm{F}}{{\rm{F}}_t} + {b_2}{{{\rm{F}}{{\rm{F}}_t}} \over {{\rm{W}}{{\rm{T}}_{it}}}} + {b_3}{{{\rm{F}}{{\rm{F}}_t}} \over {{\rm{WTS}}{{\rm{Q}}_{it}}}} + {b_4}{{{\rm{F}}{{\rm{F}}_t}} \over {{\rm{C}}{{\rm{F}}_t}}} + {b_5}{{{\rm{F}}{{\rm{F}}_t}} \over {{\rm{C}}{{\rm{F}}_t}}}{\rm{FIV}}{{\rm{E}}_{it}} + {b_6}{{{\rm{F}}{{\rm{F}}_t}} \over {{\rm{C}}{{\rm{F}}_t}}}{\rm{SI}}{{\rm{X}}_{it}} \\ & + {b_7}{{{\rm{F}}{{\rm{F}}_t}} \over {{\rm{C}}{{\rm{F}}_t}}}{\rm{SEVE}}{{\rm{N}}_{it}} + {b_8}{\rm{H}}{{\rm{D}}_{it}} + {b_9}{\rm{HDS}}{{\rm{Q}}_{it}} + \sum\nolimits_{m = 1}^{11} {{b_{m + 9}}} {\rm{MONT}}{{\rm{H}}_{mt}} \\ & + \sum\nolimits_{g = 1}^{34} {{b_{g + 20}}} {\rm{GRAD}}{{\rm{E}}_{igt}} + {b_{55}}{\rm{COMMPRE}}{{\rm{M}}_{it}} + {b_{56}}{\rm{COMMDIS}}{{\rm{C}}_{it}} + {e_{it}}\end{align*}

where PRICE _it is the weighted average cash price for observation i during auction date t, and e is an error term (variable definitions are provided in Table 2). Hedonic models were estimated using weighted least squares (weighted by number of head) to account for differing number of feeder cattle included in each observation.

Table 2. Description of variables used in hedonic pricing models

Nearby feeder cattle futures prices (FF) are included to account for the effect of futures price on cash price (Schroeder et al., Reference Schroeder, Mintert, Brazle and Grunewald1988), making the random error term reflect basis risk. Average cattle weight in each observation is included to account for changing cash price per pound across animal weight (e.g., Kenyon, Bainbridge, and Ernst, Reference Kenyon, Bainbridge and Ernst1991; Schroeder et al., Reference Schroeder, Mintert, Brazle and Grunewald1988; Zimmerman et al., Reference Zimmerman, Schroeder, Dhuyvetter, Olson, Stokka, Seeger and Grotelueschen2012). Price is expected to decrease at a decreasing rate as animal weight increases. Weight (WT) and weight-squared (WTSQ) are made inverse variables to account for the nonlinear relationship between feeder cattle price and animal weight and to guarantee a downward-sloping relationship at heavier weights. In addition, feeder futures price impact on cash price is conditional on animal weight because lighter-weight cattle prices vary more with futures prices compared to price of cattle meeting futures contract weight specifications. As such, weight and weight-squared variables are interacted with feeder futures.

Nearby corn futures prices are expected to influence the feeder cattle weight-price slide (Dhuyvetter and Schroeder, Reference Dhuyvetter and Schroeder2000). When corn price (and associated cost of gain) decreases, cash price of lighter-weight cattle increases, making lighter cattle more valuable per pound than heavier cattle. Further, corn price may influence how feeder cattle futures prices affect cash prices and this influence could vary by animal weight. For instance, when corn price is high, price of lighter-weight cattle will be more responsive to changes in feeder cattle futures prices compared to cattle meeting futures contract weight specifications. Previous work in live cattle basis modeling (e.g., Leuthold, Reference Leuthold1979; Parcell, Schroeder, and Dhuyvetter, Reference Parcell, Schroeder and Dhuyvetter2000) has included the price of corn. To account for the influence of corn price on cash feeder price and the futures-cash relationship, nearby corn futures price (CF) is included as an inverse variable and is interacted with feeder futures and categorical weight (FIVE, SIX, and SEVEN). Interacting numerous variables with continuous cattle weight variables resulted in collinearity and unstable parameter estimates, necessitating interactions of corn price with categorical, rather than continuous, weight variables.

Additional feeder cattle lot information such as lot size and its square, frame size, muscle score, condition, and fill have been used in past literature (e.g., Kenyon, Bainbridge, and Ernst, Reference Kenyon, Bainbridge and Ernst1991; Schroeder et al., Reference Schroeder, Mintert, Brazle and Grunewald1988; Zimmerman et al., Reference Zimmerman, Schroeder, Dhuyvetter, Olson, Stokka, Seeger and Grotelueschen2012) modeling feeder cattle price and basis. Nonlinear cash price effects of the number of head sold are captured by including headcount (HD) and headcount squared (HDSQ). Categorical variables for month sold (MONTH), grade (GRADE), and commented cattle capture price effects of observation-specific characteristics.Footnote ⁵ Separate categorical variables were created for comments typically associated with a premium (COMMPREM) and comments typically associated with a discount (COMMDISC). Table 3 provides descriptive statistics of data used in the hedonic models. Observations from 2021 are not included in Table 3 as 2021 data were not included in hedonic models (i.e., a 2016–2020 model was the last 5-year rolling sample).

Table 3. Descriptive statistics of variables used in hedonic pricing models, 1992–2020

Note: Observations (Steers) = 449,675; Observations (Heifers) = 417,131; Number of Auction Dates = 6,839.

3.3. Mean Absolute Errors

Out-of-sample price predictions, or basis risk, derived from the hedonic pricing models are used to compute mean absolute errors (MAE), expressed as:

(2) $${\rm{MAE}} = {1 \over n}\sum\nolimits_{i = 1}^n {\left| {{\rm{PRIC}}{{\rm{E}}_{it}} - {\rm{PREDICTIO}}{{\rm{N}}_{it}}} \right|} $$

where n is the number of observations for each market location (l), for each sex (s), during each month (m), for each weight class (w). For notational convenience, subscripts for location, sex, month, and weight class are omitted in equation (2). PREDICTION is each observation’s unique out-of-sample predicted price and the term inside the absolute value bracket is the out-of-sample basis risk value or the difference of each predicted price from the actual cash price. MAE is calculated separately by location (l), sex (s), month (m), and weight class (w), providing a single value of basis risk for feeder cattle with comparable traits.Footnote ⁶

3.4. Explaining MAE

To evaluate how basis risk has changed over time and determine factors associated with those changes, we regress MAE values calculated from equation (2) against selected variables. The model is:

(3) \begin{align*}{\rm{MA}}{{\rm{E}}_{lsmw}} &= {b_0} + {b_1}{\rm{AVGF}}{{\rm{F}}_m} + {b_2}{\rm{AVGC}}{{\rm{F}}_m} + {b_3}{\rm{FH}}{{\rm{V}}_m} + {b_4}{\rm{AVGCI}}{{\rm{V}}_m} \\ & + \sum\nolimits_{l = 1}^{31} {{b_{4 + l}}} {\rm{LOCATIO}}{{\rm{N}}_l} + \sum\nolimits_{y = 1}^{21} {{b_{35 + y}}} {\rm{YEA}}{{\rm{R}}_y} + \sum\nolimits_{m = 1}^{11} {{b_{56 + m}}} {\rm{MONT}}{{\rm{H}}_m} \\ & + {b_{68}}{\rm{FIV}}{{\rm{E}}_w} + {b_{69}}{\rm{SI}}{{\rm{X}}_w} + {b_{70}}{\rm{SEVE}}{{\rm{N}}_w} + {e_{lsmw}}\end{align*}

Monthly average feeder cattle (AVGFF) and corn futures prices (AVGCF) are included to determine how changes in market prices impact feeder cattle basis risk (out-of-sample MAE). Coffey, Tonsor, and Schroeder (Reference Coffey, Tonsor and Schroeder2018) similarly used live steer and corn prices to capture current market conditions in modeling live cattle basis prediction errors. Monthly feeder cattle historical volatility (FHV) and monthly average nearby corn implied volatility (AVGCIV) are included to evaluate effects of market variation on basis risk.Footnote ⁷ Intuitively, greater uncertainty in feeder cattle and corn markets would make it more difficult to predict feeder cattle basis. We are aware of no prior research that has quantified these impacts. Feeder cattle historical volatility was used instead of option implied volatility (as used for corn) to avoid simultaneity with feeder basis risk and because thinly traded feeder cattle option contracts may make implied volatility unreliable. Implied volatility of an option contract is the market’s forecast of future volatility in the underlying asset price (Canina and Figlewski, Reference Canina and Figlewski1993). In this instance, implied volatility is the market’s expectation of future volatility in corn futures priced into option premiums.

Categorical variables are included for market location (LOCATION) to determine how basis risk varies across geographic locations. Categorical year variables (YEAR) are included to evaluate how feeder cattle basis risk has changed over time and to account for changes in contract weight specifications that may have impacted basis risk (e.g., January 2000, January 2005, August 2005, and November 2016 contracts). Categorical month (MONTH) variables allow for seasonality in basis risk. Lastly, categorical weight variables (FIVE, SIX, and SEVEN) are included to measure basis risk across animal weight. Table 4 further describes variables utilized in equation (3) while Table 5 provides descriptive statistics.

Table 4. Description of variables used in MAE models

Table 5. Descriptive statistics of variables used in MAE models, 1997–2021

Note: Observations (Steers) = 27,832; Observations (Heifers) = 27,749.

4.1. Hedonic Pricing Models

Hedonic pricing models were estimated to predict out-of-sample prices for feeder cattle with varying characteristics and market conditions at time of sale, providing a measure of basis risk for each observation. The hedonic framework depicted in equation (1) was applied to each market location and sex and for 5 years of weekly auction data subsequently rolling forward by adding a new year of data and dropping the oldest year. The number of hedonic pricing models estimated for each market location depended on data availability. For example, the first year of available data for Salina, KS, was 1995. Hedonic models for Salina steers and heifers were estimated for time periods of 1995–1999, 1996–2000…2016–2020. A total of 1,250 hedonic models were estimated. Adjusted R-squared values ranged from 0.69 (2006–2010 Roswell heifer model) to 0.99 (2010–2014 Fort Pierre steer model) with a mean of 0.92 and median of 0.94.

Feeder cattle futures coefficients were, as expected, positive and statistically significant (0.05 level) for 92% of the estimated hedonic models. Expectations of the effect of weight on feeder cattle price are generally held based on coefficients for the feeder futures to weight ratio and feeder futures to weight-squared ratio. For 80% of models, lighter-weight animals experienced higher prices, with price decreasing at a decreasing rate with increasing animal weight. Increases in the feeder cattle-to-corn futures ratio result from either increases in feeder futures price or decreases in corn futures price, both of which we expect to result in increased feeder cattle cash prices. As such, we expect a positive relationship between this variable and cash price. Our expectation was generally met, as 53% of models exhibited a positive and statistically significant coefficient for the feeder to corn futures ratio. Interactions of the feeder to corn futures ratio with 450–549 pound, 550–649 pound, and 650–749 pound categorical weights were positive and statistically significant for 37%, 32%, and 23% of models, respectively, meaning that lighter-weight cattle more often had statistically different feeder futures-to-corn futures ratio coefficients than the default 750–849 pound animal. The impact of the feeder-corn futures ratio on cash price was generally greater for lighter-weight cattle. For 64% of models, the magnitude of the categorical weight interaction term coefficient decreased as categorical weight increased.

Expectations of the effect of headcount on feeder cattle price generally held based on coefficients for headcount and headcount squared. Larger headcounts realized higher prices at a declining rate for 55% of hedonic models. Monthly binary variables revealed statistically significant seasonality in the majority of models. Also, commented cattle generally received statistically significant premiums or discounts.

4.2. Basis Variation

Using out-of-sample price prediction errors (basis risk), MAE were calculated for each location, sex, month, and weight class.Footnote ⁸ Equation (3) was then estimated separately for steers and heifers to determine the impact of market conditions and feeder cattle characteristics on MAE values. Results are reported in Table A1. The models explained 43% of the variability in MAE.

Monthly average feeder cattle futures had a negative and statistically significant (0.05 level) impact on MAE for both steers and heifers. A $1 per hundredweight increase in feeder futures resulted in a $0.05 per hundredweight decrease in feeder steer MAE and a $0.10 per hundredweight decrease in feeder heifer MAE. Though previous literature had not used futures prices as a right-hand-side variable in estimating feeder cattle basis risk, Garcia, Leuthold, and Sarhan (Reference Garcia, Leuthold and Sarhan1984) found a positive and statistically significant (0.05 level) impact of the consumer price index on live cattle basis risk for December and June contracts, indicating higher overall prices result in higher basis risk. Monthly average corn futures had a negative and statistically significant (0.05 level) impact on MAE for both steer and heifer models. A 1 cent per bushel increase in corn futures resulted in slightly less than a $0.01 per hundredweight decrease in MAE for both sexes. Previous literature on basis had not implemented corn futures as an independent variable in estimating feeder cattle basis risk. However, Leuthold (Reference Leuthold1979) found an inverse relationship between corn price and live cattle basis for a nearby contract, with a $1 per bushel increase in corn price lowering basis by $1.33 per hundredweight. Similarly, Parcell, Schroeder, and Dhuyvetter (Reference Parcell, Schroeder and Dhuyvetter2000) found a $1 per bushel increase in the nearby corn futures price resulted in $0.75, $0.82, and $0.90 per hundredweight declines in live cattle basis for Colorado, Kansas, and Texas, respectively.

Monthly feeder cattle futures historical volatility had a positive and statistically significant (0.05 level) impact on feeder steer and heifer MAE. A $1 per hundredweight increase in feeder cattle historical volatility was associated with a $0.62 ($0.54) per hundredweight increase in steer (heifer) MAE. Monthly average corn implied volatility had a small, negative impact on both feeder steer and heifer MAE, but was not statistically significant (0.05 level) in either model. This is the first study we are aware of directly estimating the impact of volatility in derivatives markets on feeder cattle basis risk.

The impact and statistical significance of categorical location variables on MAE values varied.Footnote ⁹ Relative to Oklahoma City, steer MAEs were not statistically different (0.05 level) in the Oklahoma Panhandle and Southeast Kansas. Other markets within the Index 12-State Region and into the Pacific Northwest experienced $1–$6 per hundredweight higher steer MAE. Out-of-Index markets to the east (i.e., Lexington and Montgomery) experienced lower steer MAE. For heifers, MAE was generally not statistically different (0.05 level) than Oklahoma City in the southern and western portions of the 12-State Region. Heifer MAE was statistically higher in many northern markets and in the out-of-Index markets, Montgomery and Toppenish.

All categorical year coefficients were statistically different (0.05 level) than the default 2021, with the exception of 2012 for the heifer model. Feeder steer and heifer MAEs gradually increased from 1997 to 2013, elevated sharply to around $16–$22 per hundredweight over the default 2021 in 2014–2015, and then declined post-2015 (Figure 2). MAE for both sex returned to levels experienced in 2011 by 2018, indicated by the magnitude and statistical significance of those coefficients. Steer and heifer MAE in 2021 was between $2.50 and $5.00 per hundredweight higher than levels experienced in 2017–2020.

Figure 2. Feeder steer and heifer MAE model year coefficients (Base = 2021).

Feeder steer and heifer models exhibited seasonality in MAE (Figure 3). Steer MAE was not statistically different (0.05 level) than the January base in February, but was economically and statistically lower in spring, summer, and early fall (declining to $1.94 per hundredweight lower than the January base in September) and higher in December ($0.84 per hundredweight over January). Relative to January, heifer MAE was economically and statistically lower through September (falling as low as $1.85 per hundredweight under the January base in September) and was higher in December ($1.10 per hundredweight over January).

Figure 3. Feeder steer and heifer MAE model month coefficients (Base = January).

All categorical weight variables were statistically significant (0.05 level) for feeder steer and heifer MAE models. Variables for 450–549 pound (FIVE) cattle were higher than the default 750–849 pound animal with coefficients of $2.26 and $0.42 per hundredweight for steers and heifers, respectively. The opposite sign was observed for 550–649 pound (SIX) categorical weight with the steer (heifer) model having a coefficient $1.05 ($1.40) per hundredweight lower than the default 750–849 pound animal. Coefficients were also negative for 650–749 pound (SEVEN) categorical weight with the steer (heifer) model having $1.55 ($1.42) lower MAEs on average relative to 750–849 pound cattle.