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TRANSCRIPT
Are Commodities In a Bubble?
IE: 441
Industry sponsor: Dr. Wilson YaleFaculty Supervisor: Dr. Auriéle Thiele
Team 2
Jiexia Ding
Allen Wong
Yuning Ye
IE:441 Final Report Team 2
Executive Summary
Rapid rises in food prices in late 2006 to early 2008 have caused social unrest and economic
instability around the world. Since the boom in the agricultural sector coincided with the bust in
the housing markets, this led some to wonder whether speculation caused a bubble in food
prices. Our paper seeks to shed some light on whether speculative bubbles were present in some
agricultural commodities during this time period. We begin by explaining the different
definitions of what a bubble is in the academic literature as well as the bubble definition we have
chosen to frame our discussion. We then present a survey on the most common explanations for
the run up in food prices during this time and how the evidence seem to suggest that speculation
could strongly explain the price explosion seen in the agricultural sector. Following this, we
briefly explain the paper we have chosen to replicate and provide reasons for why we have
chosen this paper over other papers. We lay out the model we have used in detail and provide an
analysis on the data that we have collected. Since food and energy often appears to be closely
related, we decided to include natural gas and crude oil in our advanced analysis. As part of our
advanced analysis, we also decided to split our original data into two time horizons to see
whether we could derive any new insights. Due to some problems with the implementation of
our model, we decided to use part of the model we could implement and supported the rest of our
advanced analysis with what we found in the literature.
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Contents
1. Literature Review 3
1.1 Fundamental value 3
1.2 What is a Bubble? 4
1.3 Historical Context 5
1.4 Commodity sector we are most interested and two common explanations for price increase6
1.5 Direct and Indirect tests and paper we will replicate 8
2. Paper replication 10
2.1 Deriving the regression model 10
2.2 Deriving the inputs 14
3. Results/Analysis 17
4. Advanced Analysis 22
5. Conclusion 24
List of TablesTable 1 Summary of statistics for agriculture 17
Table 2 (our calculations of parameters) 19
Table 3 (authors’ calculations of parameters) 19
Table 4 Two Regression model coefficients 21
Table 5 Summary of statistics for energy 22
Table 6 Calculations of energy parameters 22
List of FiguresFigure 1, Agriculture spot price and net convenience yield 27
Figure 2, Agriculture fundamental price and absolute bubble measure 30
Figure 3, Energy spot price and net convenience yield 33
Figure 4, Energy fundamental price and absolute bubble measure 30
Figure 5, All commodities (1989 to 2001) 35
Figure 6, All commodities (2001 to 2013) 38
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1. Literature Review
The topic of our research is whether there is a commodity bubble in the market. In this
literature review, we first briefly discuss what we mean by fundamental value. Defining
fundamental value is crucial since that will provide the rule by which we measure whether there
is a bubble or not. We follow that up with a brief discussion of the different definitions of
bubbles. We then provide some historical context as to why researchers think there is a bubble in
the commodity market as a whole. Since agriculture was the subject of many research articles we
have reviewed, we narrowed our focus to this category. We examined the two most common
explanations for the agricultural commodity boom in 2008: increase in demand from emerging
markets and increase in oil prices. We then provide a discussion on two broad classes of tests
that are used in the literature to detect bubbles. Based on our understanding of the limitations and
advantages of these tests, we conclude with the mention/description of the paper that we will
replicate.
1.1 Fundamental value
Before defining a financial bubble, it is necessary to briefly discuss what fundamental
value means. In Malkiel’s seminal book “A random walk down Wall Street” (1973), the author
outlines two methods that financial assets are priced. One method is known as the “firm-
foundation” theory while the second method is known as the “greater-fool” theory. The “firm-
foundation” theory takes the view that an analysis of a firm’s balance sheet, growth prospects
and expected dividend will allow an investor to calculate the fair value of a financial asset. On
the other hand, the “greater-fool” theory adopts the view that a financial asset’s intrinsic value is
based on what other investors are willing to pay for it (Malkiel, 1973). Since the first definition
is widely used in the literature and lends itself to rigorous debate, we will adopt the first
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definition when discussing fundamental value in this paper.
1.2 What is a bubble?
A search in the literature for what a financial bubble is reveals a wide array of definitions.
Some definitions of bubbles rely on complex mathematical models and these include
deterministic bubbles and near random walk bubbles. Other definitions of bubbles, such as
speculative bubble, mainly rely on using fundamental value to explain what a bubble is. For
example, Stiglitz (1990) defined an asset price bubble as “If the reason that the price is high
today is only because investors believe that the selling price will be high tomorrow-when
“fundamental” factors do not seem to justify such a price-then a bubble exists” (Stiglitz, 1990).
In essence, a bubble is when the value of a financial asset exceeds its fundamental value by a
significant amount. We will adopt this definition of bubble in this paper.
1.3 Historical Context
The recent rise in commodity prices in 2008 has stirred a heated debate on the causes of
the price boom. A few articles have tried to explain the commodity boom through a number of
factors. For instance, Baffes and Haniotis (2010) suggest that “the recent price boom was fueled
by numerous factors, including low past investment in extractive commodities, weak dollar,
fiscal expansion and lax monetary policy in many countries and investment fund activity.” Most
of the articles in the literature have tried to localize the debate by examining one or two factors
that might have caused the price boom. Perhaps the most controversial discussion centers on
whether financial investors and speculative activities were the main drivers for the price peak. As
Liu and Tang have noted (2010), commodities have only caught the attention of investors in the
recent decade; “Prior to the 1990s, the Prudent Investor rule prohibited pension plans from
buying commodities futures contracts.” Since then, interest in this asset class has only grown
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after Gorton and Rouwenhorst (2006) showed that commodities had little co-movements with
stocks and Erb and Harvey (2006) showed that commodities have little co-movements with each
other. Due to the diversification benefits and the collapsed of the equity market in 2000, many
institutions came to view commodities as a new asset class (Tang and Xiong, 2010). These
institutions, such as pension funds and sovereign wealth funds, would mainly obtain exposures to
commodities through index funds. The two most widely used funds are the Dow Jones-AIG and
S&P Goldman Sachs Commodity Index. It is particularly noteworthy to discuss how investors
have come to behave in this new asset class. Perhaps the strongest evidence for institutional
investors’ enthusiasm for this asset class has been the fact that on a net basis, investments have
flowed mostly into funds rather than out (Haniotis, 2010). Moreover, it appears that unlike
traditional speculators, investors are indiscriminate with regard to the range of commodity
futures they take a position in. As Masters’ testimony (2009) revealed, investors actually take
position across the entire range of commodity futures. It should also be noted that since these
investors invest mainly in the index as a whole, they typically view commodity, stocks and
bonds from a strategic portfolio allocation perspective (Barberis and Schleifer, 2003). As a
result, these index investors tend to move in and out of a given commodity index at the same
time (Barberis and Schleifer, 2003).
1.4 Commodity sector we are most interested and two common explanations for price
increase
When examining the commodity asset class as a whole, we encountered some difficulties.
The commodity asset class is generally divided into five sectors: energy, industrial metals,
precious metals, agriculture and livestock. Each sector is attached to a wide number of economic
forces that may or may not have overlap with the other sector. To get a better handle on the
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situation, we decided to closely examine on the sector that has gotten the most coverage in the
literature, which is agriculture. Some researchers have tried to explain the increase in agricultural
commodities through an increase in demand from emerging economies. For example, von Braun
(2008) has argued that as income level has increased in China and India, consumers in these
countries have moved away from traditional food staples towards meat and dairy products.
However, the data for this argument has not been very convincing. Baffes and Haniotis (2010),
have presented data showing that for most grains used for feed, there has actually been a lag in
demand both for China and India from 1997 to 2008. In addition, Heady and Fan (2008) have
offered two counter arguments. One argument is that both India and China are self-sufficient in
terms of food and this also includes agricultural commodities for which prices have been rising.
The second, even more compelling argument is based on that fact that China has actually
decreased its import of wheat and rice in recent years while India’s import of wheat is negligible
and has generally been an exporter or rice. However, this analysis has also been complicated by
countries’ export policies. As Mitchell noted (2008), Argentina, India, Kazakhstan, Pakistan,
Ukraine, Russia and Vietnam have imposed either export restrictions or export bans on a number
of grain exports to control domestic price increases. Gutierrez (2013) has commented that on the
same days that India and Thailand announced export bans on rough rice, CBOT prices for this
commodity showed signs of price explosions. Rapid price increases for rice followed shortly
after in 2008. Despite negligible change in production or stocks, rice prices increased about three
fold from January to April of 2008 (Mitchell, 2008). This led Mitchell to reason that the rapid
rise in wheat prices in 2007 must have led countries to question whether global grain supplies
were adequate for demand. This in turn caused several countries to impose export bans on rice
and other countries to increase imports of rice (Mitchell, 2008). Not only was there a price
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increase in rice and wheat, but there were also price increase in soybeans, sugar, corn and other
agricultural commodities (Mitchell, 2008). None of the literature we have examined suggested
that export bans played a role for the price increase in these commodities. Thus, although export
bans may explain the price increase for rice and grain products, other explanations are needed to
explain the price increase for the other agricultural commodities. For that we turn to the second
most common explanation for the commodity price boom: increases in oil prices.
One of the similarities of the 2008 commodity price boom compared to the commodity
price boom of 1973 was how the two commodity booms coincided with the oil price booms
during the same time. Another similarity is the excess liquidity that was introduced into the
global financial system during the two periods (Gilbert, 2010). The first similarity has led some
researchers to suspect that the price transfer mechanism between oil and commodities as
explained by Hanson et al. (1993) was at work; higher oil prices caused higher input prices
which caused higher agricultural prices (Hanson et al., 1993). As intuitive as this explanation
sounds, a number of papers published in the past few years have called this explanation into
question. Gilbert (2010) has argued that agriculture is not energy intensive. Citing research by
Baffes (2007) and Mitchell (2008), Gilbert placed the pass-through estimates of oil prices to
agriculture prices between 15-20%. Moreover, Nazlioglu and Soytas (2011) did not find world
oil prices to Granger cause prices of soybeans, cotton, and wheat from 2006 to 2010. This
finding is also consistent with the findings of Mutuc et al. (2010) that cotton prices are largely
not responsive to oil price shocks. Baffes and Haniotis (2010), however, have discovered two
important findings. Their first finding is that most commodities (including agriculture) do
respond strongly to energy prices. Their second finding is that the link between energy prices and
most commodities (including agriculture) have strengthened in recent years. Difference in
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econometric models used, time periods, and other model specifications could explain why the
first finding of Baffes and Haniotis differ from that of other authors. With regard to the second
finding, perhaps this is further evidence of the “financialization of commodities” that Tang and
Xiong (2010) have written about. It is also worth noting that a surprising argument has emerged
recently that establishes an indirect link from oil prices to commodity prices. Harri et al. (2009)
argued that oil prices can influence commodity prices through exchange rates. Since in many
parts of the world oil is priced in U.S. dollars, when the price of oil changes, this makes it either
more or less expensive for foreign countries based on their local exchange rates. This in turn will
influence how much agricultural commodities foreign countries are willing to import/export
which in turn will contribute to the overall agricultural supplies in the foreign countries.
1.5 Direct and Indirect tests and paper we will replicate
Having examined the two most common explanations for the price increase in
agricultural commodities, we now discuss how the presence of bubbles is detected. In the
literature, two classes of tests are often employed to detect whether bubbles exist or not and these
are direct tests and indirect tests. Although both classes of tests use a wide array of statistical
techniques to explore the relationship between fundamental values and observed prices, there are
substantial differences between the two types of tests. Indirect tests apply statistical tests on a
data set without first specifying what kind of bubble (e.g., near random walk bubbles,
periodically collapsing bubbles, etc) it seeks to uncover (Liu et al., 2013). In contrast, direct tests
can be used to examine whether a data set is consistent with a specific type of bubble (Liu et al.,
2013). Moreover, indirect tests have been found to be rather fragile in a certain class of rational
bubbles. In his classic work, Evans (1991) found in simulations that indirect tests such as unit-
root tests, cointegration tests, and autocorrelation patterns were unable to detect periodically
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collapsing bubbles. Since it is unclear whether periodically collapsing bubbles exist in the
market, we have decided to avoid replicating papers that made use of the direct tests. In addition
to the kinds of tests one should be cognizant of when applying to a data set, one should also be
mindful of the assumptions one applies to the data set. For example, some econometric models
assume that the underlying data are covariance stationary. However, Pagan and Schwert (1990)
research on monthly stock returns from 1835 to 1987 showed a dramatic increase in the variance
after 1930. An explanation could be that financial innovation such as stock index arbitrage could
affect the variance of returns (Phillips and Loretan, 1990). Since some financial innovations are
here to stay, that means changes in variance can be irreversible. Bearing many of these
considerations in mind, we decided on a paper that used the direct test and made the least amount
of assumptions in terms of constant variances in the data set. The paper we decided to replicate is
“Testing for speculative bubbles in agricultural commodity prices: a regime switching approach”
by Liu et al. (2013).
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2. Paper replication
As noted in the literature review, we decided to replicate the model in “Testing for
speculative bubbles in agricultural commodity prices: a regime switching approach.” The authors
conducted empirical analysis on six agricultural commodities: corn, cotton, rough rice (hereafter
rice), soybeans, sugar, and wheat. The authors obtained daily data for the period from January
1989 to December 2011 through Bloomberg. Although data as early as the 1960’s are available,
the authors restricted their analysis to the above mentioned time frame since prices before 1989
may have been contaminated through government interventions, such as commodity storage
programs and price support. We also obtained daily data through Bloomberg but collected our
data from January 1989 to December 2013. The following Preliminary analysis will be organized
as follow: we first derive the regression model used in the paper, we then explain the inputs that
are used for the model, and finally we end with the results we obtained.
2. 1 Deriving the regression model
Citing the work of Blanchard and Watson (1982) the authors assume that if there is a
rational bubble, it moves between two states: a surviving state S and a collapsing state C. The
expected value of the rational bubble for this next time period is
Et [Bt+1 ]=(1−q ) Et [Bt+1∨C ]+q Et [Bt+1∨S ] (1)
It should be noted that in the collapsing state C, the authors allow for either a partial or a full
collapse of the bubble. This is captured by the following equation
Et [Bt+1∨C ]=g(bt)P t (2)
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where g(·) is a continuous function with the restrictions that g(0)=0 and 0≤ ∂g(b t)/∂bt≤1. It
should also be noted that the q’s from two equations above are time varying probabilities. The
time varying probability of entering a surviving state is specified as
q t+1≡m (b t ) ,∂m (b t )
∂∨bt∨¿<0¿ (3)
The term ¿bt∨¿ means that it is possible to have either positive or negative bubbles. We can use
the above equations to derive the expected size of the bubble in the surviving state as
Et [Bt+1∨S ]=(1+R)Bt
m(bt)−( 1−m(b t)
m(bt)g (bt )Pt) (4)
We can then solve the expected gross returns Rt+1for the surviving state and the collapsing state
as
Et [R t+1∨S ]=1−m(b t)m(bt)
[ (1+R )bt−g (bt )] (5)
Et [R t+1∨C ]=g (bt )−(1+R)bt (6)
If we take first order Taylor expansion of the above two equations around an arbitrary point b0
we get
Et [R t+1∨S ]=βS0+βS 1
b t (7)
Et [R t+1∨C ]=βC0+βC1
bt (8)
βS1andβC1
are equal to:
βS1≡− 1
m¿¿ (9)
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βC1≡∂ g(bt)∂b t
¿b t=b0−(1+R) (10)
Since we assume the following from the beginning:
0≤ ∂g(b t)/∂bt≤1 (11)
∂m (b t )∂|bt|
<0 (12)
R≥0 (13)
These assumptions mean that βS1should be positive and βC1should be negative, or more generally
βS1>βC1
. This makes intuitive sense since it states that the expected returns in a surviving
(collapsing) state will grow larger as the size of the bubble becomes larger (smaller). The sign
restrictions on these two terms also serve as a way to test whether there is a rational bubble or
not; if rational bubbles exist in the data, βS1 must be positive and βC1must be negative. Thus, if
βS1is found to be negative and βC1
is found to be positive, rational bubbles can be ruled out. In
order to forceq t+1to be between 0 and 1, the authors set
q t+1=Φ( βq 0+ βq 1
∗|b t|) (14)
whereΦ ( βq 0)is the probability of entering the surviving state given the current bubble size is 0.
βq1is the probability of a bubble entering the surviving state when the absolute size of the bubble
increases. The assumptions of the model also forceβq1 to be negative.
Finally, the authors replaced the following expected returns
Et [R t+1∨S ]=βS0+βS 1
b t (15)
Et [R t+1∨C ]=βC0+βC1
bt (16)
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with realized values and an error term to obtain the two regime switching regression model:
RS ,t+1=βS 0+ βS1
b t+εS , t+1 (17)
RC , t+1=βC0+βC1
bt+εC ,t+1 (18)
P (S )=q t+1=Φ (βq0+ βq1
∗|b t|) (19)
where
ε i ,t+1 N (0 , σ i ) , i=S ,C (20)
To obtain the parameter estimates, ε i ,t+1 was assumed to be normally distributed and the authors
used the following maximized the log-likelihood function:
L=∑t=1
N
ln {qt+1 Φ (RS ,t+1−βS 0−βS1
bt ¿ /σS¿¿ σS )+(1−qt+1)Φ (RC ,t+1−βC0−βC1
bt ¿ /σC¿¿σC )} (21)
Note that σ S represents the standard deviation of the unexpected gross return in the surviving
state and σ C represents the standard deviation of the unexpected gross return in the collapsing
state.
2.2 Deriving the inputs
There are two inputs that are used for the regime switching regression model and they are
the relative bubble term b t= Bt/Pt and the daily gross returns. We obtained the daily gross returns
from the Federal Reserve website.Btis the absolute bubble term and Pt is the spot price of the
commodity. The absolute bubble term is obtained by subtracting the theoretical fundamental
value of the commodity from the spot price of the commodity. The most popular method used
for calculating the fundamental value of an asset is to use the present value model. However, this
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is somewhat of a challenge for commodities since commodities do not pay dividends. To
overcome this problem, the authors of our paper argue that the convenience yield derived from
holding a commodity is similar to dividends from stocks. The intuition is that holding a
commodity allows the firm to not only minimize costs from unexpected supply/demand
fluctuations but also to smooth production. Thus, holding a commodity provides benefits and the
authors used the marginal net convenience yield (net of storage and insurance costs) as the
dividend equivalent in the present value model.
Although the net convenience yield cannot be observed directly (it is a latent variable),
we can infer its value from the following formula
F tT=Pt exp [ (it−γt ) (T−t ) ] (22)
This formula must hold under no-arbitrage condition. F tTis the futures price quoted at time t with
a maturity at time T, it and γt are the interest rate and net convenience yield at time t,
respectively. Using the above formula would require using a series of spot prices that matches
the futures contract in terms of product grade and location. As this would be practically difficult,
the authors used the following two equations to infer the spot price
γt=ln ( F tT2
F tT1 ) 1
T 1−T 2+it (23)
Pt=F t
T1
exp ¿¿ (24)
whereF tT1andF t
T2 represent maturity of the nearest and second nearest contract, respectively. From
these two equations, we can use them to calculate the net convenience yield, which is
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y t=γ t Pt (25)
However, this provides us with the current dividend. In order to obtain future dividends, the
authors used the following adapted Gordon model
Pt=c+β y t+εt (26)
Thus, the fundamental value of a commodity is made up of a constant part (c) plus a price
multiple of the current dividend (β y t ¿ added to an error term (ε t ¿. If no bubbles exist, we would
expect the term ε t to be a stationary process. The authors obtained a consistent estimator of β by
running the following regression
∆ Pt=α+β ∆ y t+ε t (27)
This allows us to back calculate what c is by the following
c=E [P t− β y t ] (28)
Using only the consistent estimators, the fundamental value is found to be
Pt¿=c+ β y t (29)
This formula states that aside from the constant term, the fundamental value can be described by
the net convenience yield. Thus, anything above the convenience yield is deemed to be a bubble
term. To account for the fact that net convenience yield will vary based on storage levels which
in turn is based on the seasons, the authors applied a seasonal adjustment to both the inferred
spot prices and the net convenience yield. The following is the seasonal component
st=μ+∑k=1
K
wk cos (ω∗k∗t )+∑k=1
K
δ k sin(ω∗k∗t) (30)
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μ ,wk ,δ k are the coefficients to be estimated. ωstands for the frequency express in terms of
radians per unit of time, that is, 2π/p where p is a measure of periodicity whose value is 250 for
daily data.
3. Results/Analysis
We obtained data for the nearest and second nearest maturing commodity contract through
Bloomberg. We also obtained daily federal rates through the Federal Reserve website. Using the
equations from the previous section, we were able to calculate the inferred spot prices and the net
convenience yields. We then calculated the seasonal components and subtracted this value from
the inferred spot prices and the net convenience yields to obtain their respective adjusted values.
Refer to Table 1 for a summary of these data.
Table 1: Summary of statistics
Commodity unit
Variable parameter
s
First nearby future
Second nearby future
Inferred spot price
Net convenience
yield
Daily gross returns(%)
Wheat (cents/bu)
Min.224.0000 237.7500 221.5209 -1.0220 -0.2197
Mean 408.8453 416.5139 404.2657 -0.1308 0.0003Max. 1280.0000 1282.5000 1296.0245 3.1696 0.3045SD 159.5227 163.4028 157.3404 0.2993 0.0206Var.coeff. 0.3902 0.3923 0.3892 -2.2886 0.7974
Corn (cents/bu)
Min.174.7500 182.5000 168.8806 -3.3002 -1.0000
Mean 323.6253 327.6631 321.0162 -0.0320 0.0001Max. 831.2500 838.7500 846.3294 47.1479 0.1350SD 152.4022 148.4302 155.5720 1.0893 0.0217Var.coeff. 0.4709 0.4530 0.4846 -34.0875 302.3847
Soybeans (cents/bu)
Min.410.0000 410.0000 410.0000 -6.2351 -0.2695
Mean 767.4338 766.4613 770.0776 -1.8833 0.0001
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Max. 1658.0000 1649.0000 1665.8787 4.0040 0.2920SD 245.8281 244.2168 249.0915 1.5807 0.0176Var.coeff. 0.3203 0.3186 0.3235 -0.8393 243.8675
Rice (cents/cwt)
Min.3.4300 3.6350 3.3526 -0.0204 -0.2278
Mean 8.9857 9.1206 8.8919 0.0000 0.0003Max. 24.4600 24.8200 24.2442 0.0504 0.3486SD 3.4219 3.4124 3.4396 0.0058 0.0196Var.coeff. 0.3808 0.3741 0.3868 -239.3153 60.5794
Sugar (cents/lb)
Min.4.5000 4.0800 4.1399 -0.1801 -0.3007
Mean 11.5616 11.4653 11.7608 -0.0355 0.0005Max. 35.3100 32.7600 40.6710 0.0237 0.1883SD 5.3052 5.0386 5.8344 0.0390 0.0266Var.coeff. 0.4589 0.4395 0.4961 -1.0979 53.1559
Cotton (cents/lb)
Min.28.5200 30.2200 27.5995 -0.1320 -0.2720
Mean 67.2510 67.5631 67.0471 0.0038 0.0003Max. 215.1500 214.1400 218.1758 0.5255 0.1471SD 23.1796 20.9404 24.5875 0.0542 0.0193Var.coeff. 0.3447 0.3099 0.3667 14.3131 71.6338
Although, we conducted our analysis on a slightly different timeline than the authors, we would
expect the values presented in Table 1 to not differ significantly from the authors’. Indeed, our
values matched very closely with those of the authors’. We then calculated the fundamental
values as well as the bubble terms. To calculate the fundamental values, we calculated the
seasonally adjusted inferred spot prices and seasonally adjusted net convenience yield. Similar to
the authors, we used log inferred spot prices and applied a GLS estimator. Running this
estimator, we obtained the values for c and β. With the net convenience yield, this allowed us to
calculate the fundamental values (equation 29). Refer to Table 2 for the c, β and values. For
comparison with the authors’ results, we have included their results in Table 3.
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Table 2: (our calculations of parameters)
Commodity Parameter
Wheat Corn Soybeans Rice Sugar Cotton
5.86996 5.601663 6.271845 2.182094 2.090664 4.186758 -.7473232 -.4769436 -.164805 14.13659 -8.489745 2.755116
0.308417 0.074476 0.747747 0.055203 0.795927 0.344417Note: Significant at 5% level.
Table 3: (authors’ calculations of parameters)
Commodity Parameter
Wheat Corn Soybeans Rice Sugar Cotton
5.952298 5.626228 6.515155 2.121116 2.350699 4.155014 0.129672 0.131630 0.048498 5.561309 7.604924 0.758869
2R 0.199828 0.128489 0.223106 0.254617 0.309727 0.222531Note: Significant at 1% level.
We find that for the c values, our results are fairly close with those of the authors’. There were
significant differences between our β compared to the authors’. Interestingly, our 2R values for
wheat, soybean, sugar and cotton were all higher than those of the authors’. It’s unclear whether
there are systematic or unsystematic errors in our corn and rice analysis. Nonetheless, our highest
2R value was only 34.44% (cotton). In other words, changes in net convenience yields could at
best explain a fraction of the changes in the spot price. This suggests that we should expect to see
some bubble periods for our commodities. We turn first to a plot of each commodity’s inferred
spot price with their net convenience yield. Since the underlying assumption of our model is that
the price of each commodity is the present value of their discounted net convenience yields, we
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should observe a close relationship between the spot price and net convenience yields.
Deviations between the two over time could indicate the presence of a bubble. Refer to Figure 1.
We find that our graphs for wheat, rice and cotton match closely with that of the authors’.
Interestingly, we see cyclical data appearing in the soybean graph. Since the seasonal effect
calculation contains sine and cosine functions, we suspect that error in this calculation led to the
cyclical appearance in the soybean graph. For corn, we suspect that there is a calculation error in
the net convenience yield and perhaps in the seasonal adjustment calculation. For sugar, the
graph of the spot price matches closely with that of the authors’ while the net convenience yield
differed. It appears that the inferred spot price and net convenience yield for wheat started to
diverge from around 2007 and has persisted till today. Thus, the data seem to suggest that a
wheat bubble may have started in 2007 and is continuing till today. It should also be noted how
close the net convenience yield follows the spot price for rough rice and even more so for cotton.
Thus, it appears unlikely that there was a bubble in either of these two commodities. We now
turn to a plot of each commodity’s fundamental price with their associated absolute bubble term
to see if there is a direct relationship between the two. Refer to Figure 2.
Although our wheat graph did not match as close with that of the authors’, there are
strong resemblances in certain parts between the two graphs, such as the peak absolute bubble
measures in 1996 and 2008, that leads us to think the difference is not significant. Since the net
convenience yield for wheat diverged around 2008 and we again see a peak in the wheat bubble
term in Figure 2, there appears to be strong evidence that a wheat bubble did occur during this
time. Comparing our graphs with that of the authors, we find there are close matches with the
rice and cotton graphs. For rice in particular, there appears to be a pronounced peak in 2008
although we did not observe a divergence between the rice inferred spot price and net
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convenience yield in Figure 1. For soybean, there appears to be brief periods of bubble in the
time interval that we examined, although the absolute bubble measures do not appear to be too
significant. For corn and sugar, it’s unclear to us why there are such large deviations exhibited on
our graph compared to the authors’. The regime test would allow us to have greater confidence
in determining whether a bubble occurred in any of the commodities. We conducted a regime
test for all of the commodities. Below, we present the result for one of our commodities. Refer to
Table 4.
Table 4: Two Regime model coefficients
Coefficient Cotton
βq0 6253.04746328634
βq1 6253.04746328634
βS0 -1369.22379235809
βS1 -1369.22347397123
βC 0 383.104112167015
βC 1 383.104112167015
σ S 43658.3678598195
σ C 3836.34180306155
Since we obtained nonsensical results (our Beta coefficients are in the thousands whereas the
maximum number from the authors’ were single digit value) running the maximum log
likelihood function, we concluded that we must have erred in our calculation. We obtained
similar nonsensical results for the other commodities. We have reached out to the authors with
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regard to the results of our calculations. Unfortunately, we were not able to obtain an explanation
as to where the source of the problem is coming from. As such, for the remainder of the paper,
we will only present analysis for part of the model we were able to derive meaningful results.
Since energy is just as important as agriculture, we decided to conduct our
analysis in this sector as well. We performed analyses on both crude oil and natural gas using the
same methodology and also obtained our data for these commodities from Bloomberg. For these
two commodities, we collected data from January 1989 to December 2013. Refer to Table 5 for a
summary of the statistics.
Table 5: Summary of statistics for energy
Commodity unit
Variable parameter
s
First nearby future
Second nearby future
Inferred spot price
Net convenience
yield
Daily gross returns(%)
Crude oil (dollars/barrel)
Min.
10.72 11.02 9.905546 -0.1567011 -1Mean 43.69959 43.80288 43.57049 0.001689 0.005799Max. 145.29 145.86 144.371 0.4149199 0.3424312SD 30.496 30.73325 30.14761 0.0191382 0.0335918Var.coeff. 0.697856 0.701626 0.691927 11.3108 57.92688
Natural gas(dollars/million Btu)
Min.
1.046 1.099999 0.8842089 -0.0338358 -1Mean 3.97064 4.05874 3.871461 -0.001285 0.0010789Max. 15.378 15.427 15.31029 0.1802634 0.6137714SD 2.431633 2.488 2.391608 0.0054699 0.0488079Var.coeff. 0.6124032 0.6129981 0.6177533 -4.256731 45.238576
Similar to before, we conducted a GLS estimator to obtain the parameter values of c, β and ,
which would allow us to calculate our fundamental values for these commodities. Refer to Table
6 for the results we obtained from our GLS estimator.
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IE:441 Final Report Team 2
Table 6: Calculations of energy parameters
Commodity Parameter
Crude Oil Natural Gas
3.778778 1.339977-6.968313 -9.37006
0.03981 0.006575Note: Significant at 5% level.
Interestingly, the R2 of the regressions of spot prices on convenience yields for both
crude oil and natural gas were very low. In fact, the R2 was lowest for Natural Gas compared to
any of our commodities. This suggests that changes in spot prices explain very little of the
variability in the fundamental values. We decided to also graph the relationship between the
inferred spot price and the net convenience yield for these two commodities in order to better see
their co-movements (or lack thereof). Refer to Figure 3.
Since changes in the spot prices explain very little of the changes in fundamental values,
we decided to see if the absolute bubble term would help explain prices over time. Refer to
Figure 4. From Figure 4, it appears that there were a few periods where crude oil was in a
bubble territory and they were: between 1991 to 1996, late 1996 to 2000, 2007 to 2009 and 2011
to today. For natural gas, it appears that we experienced a bubble in this commodity from 2004
to 2006 and from 2007 to 2009.
4. Advanced Analysis
We decided to split our data into two time horizons (1989 to 2001 and 2001 to 2013) to
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IE:441 Final Report Team 2
determine if looking at a smaller time interval will allow us to draw any new insights. To make
the analysis tractable and because the absolute bubble measure provide us with a more direct
relationship with the fundamental price, we decided to examine only the fundamental price and
absolute bubble measure between the two time horizons. Refer to Figure 5 for all the
commodities in the 1989 to 2001 time window.
There are two main conclusions we can derive from these graphs. Examining at a smaller
time interval reveals a lot more bubble periods for all commodities. The second conclusion is
that there appears to be strong co-movements between the absolute bubble term in both corn and
crude oil. However, we have strong suspicion that there may be error in our corn analysis. There
are two reasons for this suspicion. The first reason is because the graph for corn looks very
different from graphs of the other commodities. Whereas the graphs for other commodities
appear to be more “smooth”, there appears to be a lot of noise in the graph for corn. The second
reason is because of the corn inferred spot price to net convenience yield graph. Here, it also
appears that there is a lot of “noise” for the net convenience yield. In contrast, due to the
smoothness of the graph for crude oil, we do have some confidence that our analysis accurately
represents the underlying data. Compared to the overall timeframe for crude oil in Figure 4, there
appears to be a stronger relationship between the fundamental price and the absolute bubble term
in this shorter timeframe. Refer to Figure 6 for all of the commodities in our second timeframe.
Similar to before, examining at a smaller time interval reveals some bubble periods for all
commodities. Of particular interest to us, there appears to be a bubble for the following
commodities between the 2007 to 2009 period: wheat, corn, rice, sugar, crude oil and natural gas.
Since we experienced difficulty running our regression, we decided to delve back into the
literature to explore if others have found evidence for rational bubbles in these commodities
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IE:441 Final Report Team 2
during this period. In fact, we discovered a paper that was somewhat similar to our regime
switching model. Similar to our paper, Gutierrez (2011) incorporated the net convenience yield
into his present value model to derive the fundamental values for both wheat and rough rice.
Also in a similar vein, Gutierrez separated the timeline of a bubble between a surviving state and
a collapsing state. Utilizing a bootstrapping methodology coupled with a Monte Carlo
simulation, Gutierrez found wheat prices peaked in September 27, 2007 and prices collapsed on
March 27, 2008, pg. 13. This coincides somewhat well with our wheat graph in Figure 6. For
rough rice, Gutierrez found prices peaked on April 23, 2008 and prices collapsed on May 28,
2008 pg. 13. This also matches very well with our rough rice graph from Figure 6.
Unfortunately, we were not able to find a model similar to ours in the literature that examined
corn, sugar, crude oil or natural gas.
5. Conclusion
Although we were not able to apply our data to the regime switching model, we
were able to apply part of the authors’ model to derive some inferences about the agricultural and
energy commodities that we examined. To reiterate, our analysis seem to suggest that wheat and
rough rice were briefly in bubble territories from 2007 to 2008. This is further supported by
Gutierrez’s findings, whose model has very similar features as our model. However, we retain a
certain amount of skepticism of our analysis since our authors did not find bubble processes
taking place for either of these commodities. Furthermore, as our literature review has
demonstrated, the field is fraught with many definitions for the bubble term. Thus, further
research needs to be conducted to determine what kinds of bubbles can exist in the market as
well as to determine the type of bubble is or has taken place.
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IE:441 Final Report Team 2
Figure 1: Agriculture spot price and net convenience yield
Spot price (left axis) and net convenience yield (right axis)
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
200
400
600
800
1000
1200
1400
-2
-1
0
1
2
3
4
wheat spot price wheat net convenience yield
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
20112011
20122013
0
100
200
300
400
500
600
700
800
900
-4
-2
0
2
corn spot price corn net convenience yield
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IE:441 Final Report Team 2
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
20102011
0
200
400
600
800
1000
1200
1400
1600
1800
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
soybean spot price soybean net convenience yield
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
5
10
15
20
25
30
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
rice spot price rice net convenience yield
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IE:441 Final Report Team 2
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
5
10
15
20
25
30
35
40
45
-0.2
-0.15
-0.1
-0.05
0
0.05
sugar spot price supar net convenience yield
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
20112011
0.0000
50.0000
100.0000
150.0000
200.0000
250.0000
-0.2000
-0.1000
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
cotton spot price cotton net convenience yield
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IE:441 Final Report Team 2
Figure 2: Agriculture fundamental price and absolute bubble measure
Fundamental price (left axis) and absolute bubble measure (right axis)
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
100
200
300
400
500
600
700
800
900
0
200
400
600
800
1000
1200
wheat fundamental price wheat absolute bubble measure
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
20112011
20122013
0
200
400
600
800
1000
1200
0
100
200
300
400
500
600
700
800
corn fundamental price corn absolute bubble measure
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IE:441 Final Report Team 2
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
20112011
20122013
0
200
400
600
800
1000
1200
1400
1600
0
200
400
600
800
1000
1200
soybean fundamental price soybean absolute bubble measure
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
rice fundamental price rice absolute bubble measure
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IE:441 Final Report Team 2
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
20102011
0
5
10
15
20
25
30
35
40
0
2
4
6
8
10
12
sugar fundamental price sugar absolute bubble measure
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
20112011
0.0000
50.0000
100.0000
150.0000
200.0000
250.0000
300.0000
0
20
40
60
80
100
120
140
160
cotton fundamental price cotton absolute bubble measure
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IE:441 Final Report Team 2
Figure 3: Energy spot price and net convenience yield
Spot price (left axis and net convenience yield (right axis)
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20130
20
40
60
80
100
120
140
160
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
crude oil spot price crude oil net convenience yield
19901991
19921993
19941995
19961997
19981999
20002001
20022003
20042005
20062007
20082009
20102011
20122013
0
2
4
6
8
10
12
14
16
18
-0.05
0
0.05
0.1
0.15
0.2
natural gas spot price natural gas net convenience yield
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IE:441 Final Report Team 2
Figure 4: Energy fundamental price and absolute bubble measure
Fundamental price (left axis) and absolute bubble measure (right axis)
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20130
20
40
60
80
100
120
140
0
20
40
60
80
100
120
140
crude oil fundamental price crude oil absolute bubble measure
19901991
19911992
19931994
19951996
19961997
19981999
20002001
20012002
20032004
20052006
20062007
20082009
20102011
20112012
20130
1
2
3
4
5
6
0
2
4
6
8
10
12
14
natural gas fundamental price natural gas absolute bubble measure
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IE:441 Final Report Team 2
Figure 5: All commodities (1989 to 2001)
Fundamental price (left axis) and absolute bubble measure (right axis)
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
20102011
0
50
100
150
200
250
300
350
400
450
500
0
100
200
300
400
500
600
700
800
wheat fundamental price wheat absolute bubble measure
19891989
19901990
19911991
19921992
19931993
19941994
19951995
19961996
19971997
19981998
19991999
20002000
0
200
400
600
800
1000
1200
0
100
200
300
400
500
600
700
800
corn fundamental price corn absolute bubble measure
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IE:441 Final Report Team 2
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
20112011
20122013
0
100
200
300
400
500
600
700
800
0
100
200
300
400
500
600
soybean fundamental price soybean absolute bubble measure
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
2
4
6
8
10
12
14
16
0
1
2
3
4
5
6
rice fundamental price rice absolute bubble measure
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IE:441 Final Report Team 2
19891989
19901991
19921993
19941994
19951996
19971998
19991999
20002001
20022003
20042004
20052006
20072008
20092009
201020110
2
4
6
8
10
12
0
1
2
3
4
5
6
7
8
9
10
sugar fundamental price sugar absolute bubble measure
19891989
19901991
19921993
19941995
19961997
19981999
20002000
20012002
20032004
20052006
20072008
20092010
201120110.0000
50.0000
100.0000
150.0000
200.0000
250.0000
0
10
20
30
40
50
60
70
80
90
100
cotton fundamental price cotton absolute bubble measure
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IE:441 Final Report Team 2
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010
10
20
30
40
50
60
70
0
5
10
15
20
25
30
35
40
45
50
crude oil fundamental price crude oil absolute bubble term
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 20020
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0
1
2
3
4
5
6
7
8
9
10
natural gas fundamental price natural gas absolute bubble measure
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IE:441 Final Report Team 2
Figure 6: All commodities (2001 to 2013)
Fundamental price (left axis) and absolute bubble measure (right axis)
20002001
20012002
20022003
20032003
20042004
20052005
20062006
20062007
20072008
20082008
20092009
20102010
20112011
20110
100
200
300
400
500
600
700
800
900
0
200
400
600
800
1000
1200
wheat fundamental price wheat absolute bubble measure
20012001
20012002
20022003
20032003
20042004
20052005
20062006
20062007
20072008
20082008
20092009
20102010
20112011
20110
100
200
300
400
500
600
0
50
100
150
200
250
300
350
400
450
500
corn fundamental price corn absolute bubble measure
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IE:441 Final Report Team 2
20012001
20022002
20032003
20042004
20052005
20062006
20072007
20082008
20092009
20102010
20112011
20122012
20130
200
400
600
800
1000
1200
1400
1600
0
200
400
600
800
1000
1200
soybean fundamental price soybean absolute bubble measure
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
rice fundamental price rice absolute bubble measure
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20012001
20012002
20022003
20032003
20042004
20052005
20062006
20062007
20072008
20082008
20092009
20102010
20112011
20110
5
10
15
20
25
30
35
40
0
2
4
6
8
10
12
sugar fundamental price sugar absolute bubble measure
20002003
20012001
20022002
20032004
20042005
20052006
20062007
20072008
20082009
20092010
20102011
20110.0000
50.0000
100.0000
150.0000
200.0000
250.0000
300.0000
0
20
40
60
80
100
120
140
160
cotton fundamental price cotton absolute bubble measure
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2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130
20
40
60
80
100
120
140
0
20
40
60
80
100
120
140
crude oil fundamental price crude oil absolute bubble measure
20022002
2003
20032004
2004
2004
20052005
20062006
2006
20072007
20082008
20092009
20092010
20102011
2011
20112012
2012
201320130
1
2
3
4
5
6
0
2
4
6
8
10
12
14
natural gas fundamental price natural gas absolute bubble measure
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IE:441 Final Report Team 2
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