· Web vieweconometric 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

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.

1


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

2


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

3


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

4


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

5


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

6


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

7


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

8


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).

9


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)

10


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)

11


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

13


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

14


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)

15


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


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

16


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


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.

17


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

18


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

19


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

20


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.

21


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

22


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

23


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.

24


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

25


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

26


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

27


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

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400

500

600

700

800

900

0

200

400

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800

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wheat fundamental price wheat absolute bubble measure

19891989

19901991

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19941995

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20032004

20052006

20072008

20092010

20112011

20122013

0

200

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1200

0

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corn fundamental price corn absolute bubble measure

28


19891989

19901991

19921993

19941995

19961997

19981999

20002000

20012002

20032004

20052006

20072008

20092010

20112011

20122013

0

200

400

600

800

1000

1200

1400

1600

0

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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

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14

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18

20

0

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rice fundamental price rice absolute bubble measure

29


19891989

19901991

19921993

19941994

19951996

19971998

19991999

20002001

20022003

20042004

20052006

20072008

20092009

20102011

0

5

10

15

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30

35

40

0

2

4

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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

30


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

31


Figure 4: Energy fundamental price and absolute bubble measure


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

32


Figure 5: All commodities (1989 to 2001)


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

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800


19891989

19901990

19911991

19921992

19931993

19941994

19951995

19961996

19971997

19981998

19991999

20002000

0

200

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800

1000

1200

0

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33


19891989

19901991

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20012002

20032004

20052006

20072008

20092010

20112011

20122013

0

100

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300

400

500

600

700

800

0

100

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300

400

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600


19891989

19901991

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20042004

20052006

20072008

20092009

201020110

2

4

6

8

10

12

14

16

0

1

2

3

4

5

6


34


19891989

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19921993

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19971998

19991999

20002001

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20042004

20052006

20072008

20092009

201020110

2

4

6

8

10

12

0

1

2

3

4

5

6

7

8

9

10


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


35


1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 20010

10

20

30

40

50

60

70

0

5

10

15

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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


36


Figure 6: All commodities (2001 to 2013)


20002001

20012002

20022003

20032003

20042004

20052005

20062006

20062007

20072008

20082008

20092009

20102010

20112011

20110

100

200

300

400

500

600

700

800

900

0

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400

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1200


20012001

20012002

20022003

20032003

20042004

20052005

20062006

20062007

20072008

20082008

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20102010

20112011

20110

100

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300

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500

600

0

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37


20012001

20022002

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20042004

20052005

20062006

20072007

20082008

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20102010

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20122012

20130

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2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110

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38


20012001

20012002

20022003

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20042004

20052005

20062006

20062007

20072008

20082008

20092009

20102010

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20110

5

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25

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0

2

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12


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

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39


2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 20130

20

40

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120

140

0

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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


40


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Documents

· Web vieweconometric 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