The Informational Role of Spot Prices and
Inventories
James L. Smith, Rex Thompson, and Thomas Lee
Fondazione Eni Enrico Mattei
May 24, 2013
Objectives
• To clarify the role that spot prices and
inventories play in revealing the expectations of
informed traders to uninformed traders.
• To suggest how fundamental characteristics of
commodities and markets determine the scope
for speculative futures trading, and provide
possible explanations for variations in the level
of speculation across markets and through time.
• To bring theory (rational expectations) closer to
the forefront in the debate over speculation.
Speculative Ratio: Working’s T
2.50
2.25
2.00
1.75
1.50
1.25
CBOT_WHEAT
COCOA
COFFEE
COPPER
CORN
COTTON
CRUDE_OIL
FEEDER_CATTLE
GOLD
HEATING_OIL
KANSAS_WHEAT
LEAN_HOGS
LIVE_CATTLE
NATGAS
SILVER
SOYBEANS
SUGAR
Oct-12
Jul-12
Apr-12
Jan-12
Oct-11
Jul-11
Apr-11
Jan-11
Oct-10
Jul-10
Apr-10
Jan-10
Oct-09
Jul-09
Apr-09
Jan-09
Oct-08
Jul-08
Apr-08
Jan-08
Oct-07
Jul-07
Apr-07
Jan-07
Oct-06
Jul-06
1.00
The Debate over Excessive Speculation
• “Though statistical evidence, accumulated first by the Grain Futures
Administration, long ago afforded proof to the contrary, it is still
rather generally believed that futures markets are primarily
speculative markets. They appear so on superficial observation, as
the earth appears, from such observation, to be flat.”
-- Holbrook Working, 1960
• Interpretation: Speculators provide needed liquidity and are called
to the market by hedgers.
Opposing (Dominant?) View
• “Federal legislation should bar oil speculators entirely from
commodity exchanges in the United States.”
-- Joseph Kennedy II, 2012
• Interpretation: Speculators are an autonomous presence in the
markets and their trading activity is, on balance, harmful to the
economy.
News Flash… in the style of Kennedy
+------------------------------------------------------------------------------+
Natural Gas Bets Surge to Record on March Chill:
Energy Markets: 2013-03-18 12:48:01.326 GMT
(Energy Markets Column news alert: SALT NRGM <GO>.)
By Christine Buurma
March 18 (Bloomberg) -- Hedge funds boosted bets on U.S. natural gas to
the highest level on record amid forecasts of colder-than-normal March weather
that would stoke demand for the heating fuel.
Money managers increased net-long positions, or wagers on rising prices,
by 27 percent in the week ended March 12, according to the Commodity Futures
Trading Commission’s March 15 Commitments of Traders report. Bullish bets climbed
for a fourth week and have jumped 81 percent since Feb. 12.
Producers Tempted to Lock In High Prices?
News Flash… in the style of Working
+------------------------------------------------------------------------------+
Hedging Activity Surges as Gas Prices Regain High Ground:
Energy Markets: 2013-03-18 12:48:01.326 GMT
(Energy Markets Column news alert: SALT NRGM <GO>.)
By Donna Hu Sedit
March 18 (Bloomberg) – Gas producers raised their hedging activity to the
highest level on record as the market price of natural gas surged to levels not
seen since September 2011. The recent increases in the price of gas are
attributed to forecasts of colder-than-normal March weather, which is expected to
force a large drawdown in the massive natural gas inventory levels that have been
hanging over the market.
Money managers, who were compelled to provide the needed liquidity to
cover the producers’ hedging demand, increased their net-long positions by 27
percent in the week ended March 12, according to the Commodity Futures Trading
Commission’s March 15 Commitments of Traders report.
A Third Path: Rational Expectations
• “It is shown how the private and social incentives for the operation of
a futures market depend on how much information spot prices alone
can convey from ‘informed’ to ‘uninformed’ traders.”
-- Sanford Grossman, 1977
• Interpretation: Setting aside the volume of trades needed to
accommodate hedgers, speculative trading (trades between
speculators) arises because differences in beliefs exist regarding
forward prices.
Related Literature
• Complete and perfect markets extinguish differences in
beliefs. Milgrom & Stokey (1982), Tirole (1982).
Interpretation: (Rational traders should not engage in
speculative trading).
• Incomplete markets and transaction costs sustain
differences in beliefs, and therefore speculative trading.
Grossman (1977), Grossman and Stiglitz (1982).
• Speculative trading among informed and rational traders
may destabilize the market. Stein (1987).
Related Literature
• We are aware of no previous studies that examine how
variations in:
– the degree of information revelation,
– alignment of expectations, or
– the scope of futures trading
… are explained by fundamental characteristics of the
commodities and markets involved.
The Model
Q
fixed supply (endowment)
D(Pt, wt)
for t = 1, 2
stochastic demand
“n” informed traders observe w1 and θ (forecast of w2).
correlation (w2,θ) = ρ
“m” uninformed traders observe only P1 and know µ(θ).
Each trader may purchase some inventory now (P1) and
hold for sale next period (P2).
Traders are risk neutral; maximize expected profits.
Our Extensions of Grossman (1977)
• Multiple traders of each type, not 1 of each.
• Robust treatment of inventory costs
(Grossman’s cost function embedded as special case).
• Endogenous entry of informed traders.
• Introduction of “passive traders” who invest regardless of
price (e.g. physically-backed ETFs).
• Comparative statics w.r.t. market fundamentals.
Information Revelation
• P1 reflects the inventory demand of informed traders.
• Inventory demand of informed traders depends on their
forecast of future demand and expectation of future
price. So, P1 reflects their forecast.
• Uninformed traders, seeing P1, are exposed to the
expectations of informed traders.
• But P1 also reflects a contemporary demand shock, so
uninformed traders can’t be sure if a high P1 is due to
informed traders’ optimistic forecast, or simply to a
transient demand shock. Incomplete revelation.
Equilibrium Difference in Beliefs
• Definition: Difference in beliefs regarding expected future price:
∆(w 1, θ) =
• E[∆(w1,θ)] = 0
[
]
[
~
~ ~
E P2 | w 1, θ − E P2 | P1 = P1e
]
(uninformed traders are unbiased)
• DIFF = E[∆(w1,θ)]2 > 0
Comparative Statics
• How fundamentals influence Difference in Beliefs:
–
∂DIFF
∂σ 2
≥
0
volatility of demand shocks
–
∂DIFF
∂c
>
0
inventory cost
–
∂DIFF
∂ρ
>
0
forecast accuracy
–
∂DIFF
∂h
<
0
demand slope
–
∂DIFF
∂m
≥
0
number of uninformed traders
–
∂DIFF
∂n
<
0
number of informed traders
–
∂DIFF
∂n + m
<
0
overall number of traders (holding n/m constant)
Comparative Statics: Market Fundamentals
Comparative Statics: Number of Traders
A New Type of Investor?
“Passive” Investors
• Physically-backed ETF funds, commodity index funds, etc. that
purchase and hold the physical commodity for “diversification”
motive, not based on current price.
3,000
25,000
2,500
20,000
2,000
15,000
1,500
10,000
1,000
5,000
500
0
Apr-06
0
Apr-07
Apr-08
Apr-09
Gold, tons
Apr-10
Apr-11
Apr-12
Silver, tons (right axis)
Impact of Passive Investors
q ~ N(µ q , σ q ) represent quantity of commodity bought by
• Let ~
passive investors in 1st period and held for sale in 2nd period.
• Informed traders observe q, the uninformed know only N(µ q , σ q ) .
• Q is another unobservable that further limits info revelation.
•
∂ DIFF
∂ σq
>
0.
• Conclusion: passive investors increase equilibrium difference in
beliefs between informed and uninformed traders and therefore
increase scope of speculative futures trading.
Impact of Passive Investors
Two Special Cases of Special Interest/Concern
1. If uninformed traders are somehow able to observe w1, then they
can also infer E[w2|θ] and E[P2|w1,θ]. Complete revelation.
2. Even if uninformed traders can’t observe w1 directly, if they know
1st period inventories, they can infer w1. Complete revelation.
• In either case, the informed traders’ expectation is fully revealed.
• DIFF = 0; no speculative trading. 
• But, no private incentive to become informed. 
The Quest for Transparency: A Conundrum
• A price forecast based on all available public data is equivalent to
the “uninformed” price expectation. It is not equivalent to the
forecast of a trader who holds private information.
• The difference between forecasts triggers speculative trading.
• To limit speculation, governments adopt reforms that increase
transparency (inventories, swaps, reserves), which leads to more
complete revelation of private information.
• So, transparency reduces DIFF, but also then reduces the incentive
to gather private information. Although there is more complete
revelation of private information, there is less private information to
reveal.
• The quality of public forecasts ultimately declines.
Some Conclusions
• Commodity characteristics that impede revelation of
information increase scope for futures speculation.
• Spot prices transmit info, but so do inventory levels.
• Government/NGO initiatives to increase market
“transparency” are like attempts to broadcast inventory levels.
• In the extreme, this could lead to full revelation—which
extinguishes the incentive to become informed.
• If governments desire to reduce scope of futures speculation,
they might look to the factors that generate demand for
futures trading, rather than attempting to simply suppress it
via regulation.
Thank You!
Inventory Demand
• Each uninformed trader chooses inventory (I) to max:
E[Πa] = {E[P2|P1] - P1} × I – C(I)
… which gives the “uninformed” inventory demand function:
Ia = Sa(E(P2|P1) – P1)
• Each informed trader chooses inventory (I) to max:
E[Πb] = {E[P2|w1,θ] - P1} × I – C(I)
… which gives the “informed” inventory demand function:
Ib = Sb(E(P2|w1,θ) – P1)
• Total inventory demand: Ι = m × Ia + n × Ib
Rational Expectations Equilibrium
(
)
~ ~
A pair of functions P
that satisfy for all w1, w2, and θ:
1, P2
~
P1
≡
P1e (w 1, θ)
~
P2 ≡ P2e (w 1, w 2 , θ)
( )
=
Q − Ι e (w 1, θ)
( )
=
Ι e (w 1, θ)
D P1e
D P2e
Ιe
=
([
] )
([
] )
~ ~
~
m × Sa E P2 | P1 = P1e − P1e + n × Sb E P2 | w 1, θ − P1e
Linear Version of the Model
1
D t = k + × Pt + w t
h
c × I2
C(I) =
2
MC(I) = c × I
for t = 1 & 2
Revelation of Expectations
The expectation of informed traders regarding future price:
E(P2|w1,θ) = h×(Q-2k) – P1 – y2
… where: y2 = h × w1 + h × E[w2|θ]
Uninformed traders must observe y2 to know the informed traders’
expectation. However, what P1 reveals to them is not y2 but y1:
where: y1
=
n×h − c
n×h
× w1 +
× E[w 2 | θ]
c
c
… which is the wrong linear combination.
Endogenous Entry and Information Acquisition
• Informed traders have profit advantage:
[ (
[ ( )]
( ))]
~
e ~ ~
~ , ~θ − E Π a P
P
=
∆Π ≡ E Π b w
1
1
1 w 1, θ
≥ 0
• Given our specification of demand and cost:
∆Π
=
(
1
× DIFF c, σ 2 , ρ, h, m, n
2c
)
Endogenous Entry and Information Acquisition
• ∆Π
=
(
1
× DIFF c, σ 2 , ρ, h, m, n
2c
)
• Let “z” = cost of becoming informed, then in equilibrium:
(
1
× DIFF c, σ 2 , ρ, h, m, ne
2c
)
≡
z
• Implicit function theorem:
∂ne
> 0
∂σ
∂ne
< 0
∂h
∂ne
> 0
∂ρ
∂ne
= 0
∂m
∂ne
< 0
∂z
∂ne
<> 0
∂c
Recent Variations in ETF Gold and Silver