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Price Discovery, Volatility Spillovers and Adequacy of Speculation in Cheese Spot and

Futures Markets

Marin BozicUniversity of Minnesota-Twin Cities

NDSU Seminar, 10/28/2011

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Motivation: Volatility in Dairy Sector

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Moti

vatio

n: H

ow to

Mod

el A

gric

ultu

ral P

rices

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Moti

vatio

n: H

ow to

Mod

el S

pecu

lativ

e In

fluen

ce?

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Volatility in the Dairy Sector: Why?

S

D

D′

Quantity

Price

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Volatility in the Dairy Sector: Why?

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Dealing with High Volatility

Price Support ProgramsMilk Income Loss Contract

Catastrophic Insurance (LGM-Dairy)Market-based instruments: Dairy Futures & Options, OTCs

Herd Termination ProgramsSocial InsuranceSupply Management

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Purpose of this paper

• Where does the new information about prices originate?

• Are there volatility spillovers between dairy markets?

• Did speculators contribute to rising volatility in the market?

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Pricing Milk in the U.S. : 1. Government

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Spot market trades daily for 15 minutes each morning.No cash market for dry whey or milk.

Pricing Milk in the U.S. : 2. CME Cash Market

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Thin Slicing

- Markets are very thin- USDA reports results of daily trading as well as weekly average- Prices for cheese used as benchmark in setting prices in direct

transactions across the nation

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Pricing Milk in the U.S. : 3. CME Futures Market

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Class III Milk Futures: Comparing mid-October liquidity 2000-2011

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Functions of the futures market: Price Discovery

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Questions of interest

• How do futures and cash market for cheese interact?– Price discovery– Volatility spillovers

• Impact of speculation on dairy futures

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A typical modeling approach

• Test if cash and futures are stationary– If yes: VAR– If no: Co-integration

• Volatility spillovers:– If high-frequency: realized volatility/VAR– If low-frequency: GARCH

• Effects of speculation– If high-frequency: additional regressor in VAR– If low-frequency: BEKK-X, EGARCH-X

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VAR vs. co-integration

1 11 11 12

21 222 1 2

...t t t

t t t

f fc c

1 1 11 11 12

21 222 1 1 2

...t t t t

t t t t

f f fc c c

αβ'

Case 1: Variables of interest are stationary (no persistent shocks)Instruction: Build a vector autoregressive model

Case 2: Variables are non-stationary (some shocks are persistent)Instruction: Build a co-integration model

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Data limitations

• Cash market is thin– Closing price may indicate unfilled bid/uncovered

offer– No cash market for manufacturing grade milk or

dry whey• Futures market– Cheese futures market did not exist until 07/2010– Data on speculative positions available only

weekly

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Implied Cheese Futures

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Implied vs. observed cheese futures

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Creating Nearby Futures Price Series

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Unit root tests of cheese cash and futures time series

1. Augmented Dickey-Fuller (Said and Dickey, 1984)

Null: : (unit root present; no drift)2. Phillips-Perron (1988):

Null: alpha=0, rh 1

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Unit Root Tests Results: Cash Cheese

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Unit Root Tests Results: Cheese Futures

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Devil is in the details: accounting for past lagged differenced futures

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Unit Root Tests Results: Cheese Futures

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Making sense of unit root results: 1. Economic Theory• Cash price analysis based on production

theory– Perfect competition: zero long-run economic

profit for the marginal producerProfit margin will be a mean-reverting time series

– If long-run industry average cost curve is flatPermanent shifts in demand temporary shifts to

cash pricesPermanent changes in input prices structural

changeIf supply is inelastic in short run high persistency

of shocks– If long-run AC curve is sloped

Permanent shifts in demand permanent shocks to cash price series

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Making sense of unit root results: 1. Economic Theory

• Futures price analysis based on finance theoryEfficient market

prices in a single contract will be martingales if the marginal risk premium is zero;

submartingales (downward biased) if marginal risk premium is positive

Supermartingales (upward biased) if marginal risk premium is negative

- In any case: efficient futures prices will be non-stationary, i.e. all shocks to futures prices are permanent

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Making sense of unit root results: 2. Time Series Modeling Exercise

• What if there was a market in which cash price was indeed second-order stationary• If there was a futures contract designed to

cash-settle against such a spot price, what would be the characteristics of that time series?

• For simplicity, assume no marginal risk premium

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Making sense of unit root results: 2. Time Series Modeling Exercise

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Making sense of unit root results: 2. Time Series Modeling Exercise - Results

1. Martingale Property within each contract

2. Nearby series not a martingale

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Making sense of unit root results: 2. Time Series Modeling Exercise -What would Unit Root Tests Show?

Cash Prices: 1) Null would likely be rejected

Futures prices: 2) for a single contract, null would likely not be

rejected3) Null more likely to be rejected for n-th than for n+1

nearby series4) More obs. between rollover periods null less

likely to be rejected (reducing data frequency increases likelihood of

rejecting the null)

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Unit Root Tests: Conclusions

• Cash Cheese is mean reverting• Nearby cheese futures are nonlinear– Unit-root processes within each contract– Mean-reverting at contract rollover

Next: How to model this?

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Modeling information flows

Causality in mean

Second-order causality (causality in variance)

~ 0,t tN Hε

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Second order non-causality

• Granger non-causality: knowing the futures price does not help us predict cash (and vice versa).

• Second-order non-causality: knowing the futures price history may or may not help you predict the cash price level, but it does not influence the magnitude of cash price forecast conditional variance

• Non-causality in variance: Granger non-causality and second-order non-causality combined

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GARCH-BEKK and second-order non-causality

~ 0,t tN Hε

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Adding speculators• The key problem is how to preserve positive

definiteness of conditional variance matrix• Adding another term?

• Sign of the impact of additional regressor is restricted to be positive but we must have flexibility!

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GARCH-MEX

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GARCH-MEX

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Measuring “Adequacy” of Speculation

• Based on Working (1960) – “Working’s T”• The idea is that when hedgers are net long,

long speculative position is not really ‘necessary’. But if it is there, it may “grease up” the market, or may be indicative of excessive speculation if T is too high.

So, if

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Measuring “Adequacy” of Speculation

• Likewise, if hedgers are net short, then only long speculative positions are needed to balance the market. Having long speculators may help, but too much of it may be “excessive”.

So, if

• Key assumption: how to treat unreportables.

S LH H 1 S

S L

STH H

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Results: Information flows in mean

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Results: Information flows in mean

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Results: Information flows in mean

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Results: Information flows in mean

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Results: Information flows in mean

• Conclusion: Using daily close prices at either daily or weekly frequency, using either nominal or log prices, and either control for heteroskedasticity or not – we always find that adjustment to spread between cash and futures is done in the cash market

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Results: volatility spillovers

In a model where only GARCH-BEKK is added to error-correction model for mean, we find bi-directional volatility spillovers.

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Results: Speculative Influence

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Conclusions

• Not likely that speculators increased volatility in dairy futures; if anything, speculative presence seems to be below what is deemed required for liquid market.

• GARCH-MEX has a potential for allowing flexible functional form, but restriction on correlation coefficient may flip the sign (and reduce the likelihood)

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