Faculty of Business and Law School of Accounting, Economics and Finance

Financial Econometrics Series

SWP 2013/02

An analysis of commodity markets: What gain

for investors?

P.K. Narayan, S. Narayan, S. Sharma

The working papers are a series of manuscripts in their draft form. Please do not quote without obtaining the author’s consent as these works are in their draft form. The views expressed in this paper are those of the author and not necessarily endorsed by the School or IBISWorld Pty Ltd.

An analysis of commodity markets: What gain for investors?

Paresh Kumar Narayana*, Seema Narayanb and Susan Sunila Sharmaa

aSchool of Accounting, Economics and Finance, Deakin University, Melbourne, Australia

bSchool of Economics, Finance and Marketing, RMIT University, Melbourne, Australia

Abstract

In this paper we study whether the commodity futures market predicts the commodity spot market. Using historical daily data on four commodities—oil, gold, platinum, and silver—we find that they do. We then show how investors can use this information on the futures market to devise trading strategies and make profits. In particular, dynamic trading strategies based on a mean-variance investor framework produce somewhat different results compared with those based on technical trading rules. Dynamic trading strategies suggest that all commodities are profitable and profits are dependent on structural breaks. The most recent global financial crisis marked a period in which commodity profits were the weakest.

JEL Classification: C22; G11; G17

Keywords: Commodity Futures; Commodity Spot; Trading Strategies; Profits

*Corresponding author. Tel.: +61 3 9244 6180; fax: +61 3 9244 6034. E-mail addresses: paresh.narayan@deakin.edu.au (P. Narayan), seema.narayan@rmit.edu.au (S. Narayan), s.sharma@deakin.edu.au (S. Sharma).

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1. Introduction

Our focus on commodity futures and spot markets is motivated by the fact that commodity

markets—gold and oil in particular—have been at the forefront of financial and economic

news over the last half-decade. Oil and gold prices have risen persistently over the last five

years. Oil prices, for instance, peaked at over US$140 per barrel, after reaching the US$100

per barrel mark for the first time in 2008. So much was the influence of oil price rise that

when it reached US$100 per barrel mark it created a psychological barrier for investors in the

US market (Narayan and Narayan, 2013). By comparison, gold prices have also risen sharply

over the last decade. Gold prices have quadrupled over the 2001 to 2010 period; a detailed

analysis can be found in Baur and McDermott (2010). As noted in Baur and McDermott

(2010), gold prices tend to react positively to negative market shocks, which is a behavior

inconsistent with other asset classes. With respect to oil prices, Narayan and Sharma (2011)

show that all sectors on the New York Stock Exchange respond significantly to oil price

shocks. It follows that the relevance of oil and gold prices to the functioning of financial

markets has been well documented by the literature.

The commodity futures market is even more relevant because, as explained by French (1986),

it serves two social functions. The first function is that the futures market facilitates the

transfer of commodity price risk. Risk transfer refers to hedgers using futures contracts to

shift price risk to others (Garbade and Silber, 1983). The second function is that futures

prices forecast spot prices. In other words, investors can use futures prices for pricing cash

market transactions (Working, 1953). The subject of the current paper is based on the second

function of the futures market with respect to four commodities, namely, crude oil, gold,

silver, and platinum. We test whether the commodity futures market predicts the commodity

spot market. This line of research is nothing new, however. Several studies (see, inter alia,

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Coppola, 2008) examine evidence of commodity spot price predictability using the

commodity futures price. That there is a motivating theory behind this predictability

relationship has facilitated a significant interest in this topic. The key limitation of this

literature, however, is on the economic implications and significance of the role of the

commodity futures market. In this regard, two questions remain unanswered. The first

question is: if the commodity futures market predicts the commodity spot market, as shown

by Coppola (2008) for instance, can investors devise profitable trading strategies? The second

question is: can different trading rules, such as the simple moving average technical trading

rules, range break trading rules, and the dynamic trading strategies based on a mean-variance

investor framework, produce statistically significant profits across all four commodities? In

other words, are profits, if they exist, in these four commodity markets robust? These

questions are relevant for investors. Deciding whether or not the futures market predicts the

spot market is only the first step in informing investors. Equally importantly, how such

knowledge from the futures market can be used to devise profitable trading strategies is

equally, if not significantly more, interesting. Subsequently, this is our contribution to this

literature.

Our results provide three main messages. First, we find that commodity futures returns do

predict commodity spot returns. We observe that these results hold in both linear and non-

linear models and in models that account for structural breaks. Thus, we find robust evidence

that the commodity futures market predicts the commodity spot market. Second, we observe

that the simple moving average technical trading rule and trading range break rule-based

strategies consistently produce statistically significant profits in three of the four markets—

with the exception of the platinum market. We also note that profits, like predictability, are

influenced by structural breaks in the data. Finally, we devise dynamic trading strategies

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based on a mean-variance investor framework. We find that regardless of whether or not we

allow for short-sales, profits from the oil, gold, and silver markets are statistically significant.

Platinum remains the only market where investors do not make statistically significant

profits.

The rest of the paper is organized as follows. In Section 2, we discuss the theory that

motivates our research question and explain the estimation approach. In Section 3, we discuss

the results and in the final section we provide the concluding remarks.

2. Motivating theory and estimation approach

2.1. Motivating theory

As explained in substantial detail by Kaldor (1939), the relationship between spot and futures

prices is driven by three things: interest rates, convenience yields, and warehousing costs.

There are at least two reasons why one can expect the commodity futures market to alter the

information reflected in spot prices. First, as argued by Cox (1976), organized futures trading

attracts an additional set of traders to a commodity’s market. Speculators are key market

players. Cox (1976: 1217) notes the role of speculators eloquently: “When these speculators

have either a net long or short position in the futures market, hedgers (firms that deal in

physical commodity) have a corresponding net short or long position which causes the

amount of stock held for later consumption to be different than it would have been in the

absence of futures trading”. Second, because transaction costs in the futures market are

relatively low, it provides an incentive for speculators to close out their positions with an off-

setting sale or purchase of futures contracts at the expense of accepting delivery of and

selling the physical commodity (Cox, 1976). Trading in the futures market is completely

centralized. Compared to dispersed trading and private negotiations, investors are able to

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trade and communicate their information—such as identifying potential traders, searching for

best bid or offer, and negotiating a contract—in the futures market relatively cheaply (see

Hayek, 1945).

The empirical framework that binds the relationship between the price of an index futures

contract and the price level of the underlying spot index is motivated by the work of Stoll and

Whaley (1990), and has the following mathematical form:

( )( ) ( )

where is the index futures price at time , is the index spot price at time , is the

net cost of carrying the underlying stocks in the index—that is the rate of interest cost less

the rate at which dividend yield accrues to the stock index portfolio holder , and is the

expiration date of the futures contract, so is the time remaining in the futures contract

life. Stoll and Whaley (1990) show that the instantaneous rate of price appreciation in the

stock index equals the net cost of carrying the stock portfolio plus the instantaneous relative

price change of the futures contract. This relationship is depicted as follows:

( )

( )

where is the spot price index return computed as

( ⁄ ) , and is the

futures price index return computed as ( ⁄ ) .

2.2. Estimation approach

Based on Equation (2), our predictive regression model is of the following form:

( )

The variables are as previously defined; the error term is characterized by a zero mean and

variance . Equation (3), assuming that ( ) and ( ) , can be

expressed as follows:

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( )

Following Rapach and Wohar (2006), we allow for a structural break in both the intercept

and slope coefficients of the predictive regression model. This dual structural break treatment

is relevant as both the predictive slope and the intercept affect the conditional expected

return. Rapach and Wohar (2006: 4-5)1 show that the predictive regression model with a

structural break has the following form:

, ( )

(

) , ( )

Where (

) and ( ). The structural break model in matrix notation takes

the following form:

( )

Here (

) , ( ) and ( ). Rapach and Wohar (2006)

show that when the structural break date, , is known, one can simply apply the familiar

Chow (1960) structural break test. The Chow test amounts to testing the null hypothesis that

against the alternative hypothesis that there is a structural break ( ). The Chow

test has been extended by Andrews (1993) in the case of an unknown structural break date.

Specifically, Andrews (1993) considers test statistic. This requires a sample trimming

factor (say ), which we set to 15%. The statistic is nonstandard and trimming factor

dependent. We examine the null hypothesis of no structural break by comparing this test

statistic with the asymptotic critical values reported in Andrews (1993). When the null

hypothesis is rejected, Andrews recommends estimating the break data as:

[ ( ) ] ( ) ( )

So far we have just focused on the possibility of a single structural break. There is no reason

to believe that the regression model does not contain multiple structural breaks. Bai and

1 The model was estimated using the GAUSS codes available from David Rapach’s website.

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Perron (1998) propose a test that allows us to extract multiple (as much as five) structural

breaks. Bai and Perron (1998) propose a multiple linear regression model with breaks and

( ), which takes the following form:

( )

For , is the vector of regression coefficients in the regime. The -

partition ( ) denotes regime-specific break dates, which are explicitly treated as

unknown in Equation (10). The Bai and Perron (1998) procedure estimates the unknown

regression coefficients by least squares. For each -partition ( ), the least squares

estimates of are generated by minimizing the sum of squared residuals (SSR):

( ) ∑ ∑ (

)

( )

The break dates are computed as follows. Assume that the regression coefficient estimates are

denoted by ({ }), where ( ). Substituting this into Equation (10),

we have:

( ) ( ) ( )

A suite of tests are available from Bai and Perron (1998) to first determine the existence of

one or more structural breaks in a series and, then, assuming that there are one or more

breaks, ascertain their location. To determine the existence of one or more structural breaks,

Bai and Perron (1998) propose the ( ) F-statistic and double maximum tests. The

( ) F-statistic, where represents the upper bound on the possible number of breaks,

considers the null hypothesis of no structural breaks ( ) against the alternative

hypothesis that there are breaks. This involves searching for all possible break dates

and minimizing the difference between the restricted and unrestricted sum of squares over all

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the potential breaks. The double maximum test examines the null hypothesis of no structural

breaks ( ) against the alternative hypothesis of at least one through to structural

breaks. There are two forms of the double maximum test, which Bai and Perron (1998) call

and . The statistic is the maximum value of the ( ) F-

statistic, while the statistic weights the individual statistics so as to equalize the p-

values across values of .

Bai and Perron (1998) also suggest a sequential ( ⁄ ) procedure to determine the

optimal number and location of structural breaks, if the null hypothesis of no structural break

is rejected by the double maximum test. The sequential procedure considers the null

hypothesis of breaks against the alternative hypothesis of ( ) breaks. For the model

with breaks, the estimated break dates, depicted as , are obtained by global

minimization of the sum of squared residuals. The null hypothesis is rejected in favor of a

model with ( ) breaks, provided that the overall minimum value of the sum of squared

residuals is sufficiently smaller than the sum of squared residuals from the break model.

Bai and Perron (1998) provide appropriate critical values.

An initial trimming region must be specified before implementing the Bai and Perron (1998)

procedure to ensure that there are reasonable degrees of freedom to calculate an initial error

sum of squares. The trimming region provides the maximum possible number of breaks and

minimum regime size. We follow the Bai and Perron recommendation and use a trimming

region of 15%. We allow the system to search for a maximum of five breaks, which is the

largest permissible number according to the Bai and Perron procedure.

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3. Results

In this section we present two sets of results. The first set of results demonstrates the

predictive ability of commodity futures returns. Here, we test whether commodity spot

returns can be predicted using commodity futures returns. To achieve this goal, we use a wide

range of predictability tests. The second set of results relates to a test of economic

significance. Two issues are investigated here. First we compare mean returns from two types

of trading strategies. The first strategy is based on the widely-applied moving average and

range break technical trading rules. The second strategy is based on a spot price return

predictive model, where we specifically test the economic significance of commodity futures

prices in devising trading strategies in the commodity spot market. To achieve this goal, we

devise a dynamic trading strategy based on a quadratic utility function depicting a mean-

variance investor. The key objective is to compare the returns from technical trading rules

based exclusively on spot price with the returns from a spot price forecasting model that uses

futures returns as a predictor. The key implication behind this exercise is that it will provide

an investor with information on whether profits from commodity spot markets are robust.

3.1. Results on predictability

Our data set consists of spot and futures prices of four commodities: oil, gold, silver, and

platinum. We choose these four commodities because they together constitute around 75% of

total trading volume of the commodity market. We have daily data. The time span varies

from commodity to commodity, and is dictated by data availability. For gold and silver, we

have a total of 11,649 observations spanning the period 1/01/1980 to 11/22/2011; for oil

price, we have 10,418 observations spanning the period 5/16/1983 to 11/22/2011; and for

platinum, we have data for the period 1/06/987 to 11/22/2011, totalling 9,087 observations.

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All data were downloaded from BLOOMBERG. All spot and futures price data are converted

into return form, as explained previously. A plot of the data is presented in Figure 1.

INSERT FIGURE 1

Selected descriptive statistics of the returns series for each of the four commodities are

presented in Table 1. Two observations are worth noting here. First, as expected, all returns

series are stationary, which is corroborated by the plots in Figure 1. This ensures that our

predictive regression model will be free from the issue of predictor persistency—an issue

which has been the subject of significant concern in the literature (see Lewellen, 2004;

Westerlund and Narayan, 2012). Second, the oil market is the most volatile, followed by

silver, while the gold market is the least volatile. Similarly, disparities in returns across

markets are noted, implying different opportunities for making profits—something which

forms the main contribution of this paper, and we explore it in detail later in this section.

INSERT TABLE 1

The results from the predictive regression model, based on Equation (3), are reported in Table

2. The results are organized as follows. The predictive regression model is run for each of the

four commodities—gold, oil, platinum, and silver—and results are reported column-wise.

Row 2 reports the coefficient on the intercept and its t-statistic; row reports the coefficient on

the predictor (futures return) variable and its t-statistic examining the null hypothesis of no

predictability; row 4 contains the regression models R-squared; the next row contains the

statistic and its p-value generated using a 15% trimming factor. The statistic

examines the null hypothesis of no structural change against the one-sided (upper-tail)

alternative hypothesis of a structural break. The estimated break date is reported in the last

row.

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There are three key results here. First, we find strong evidence of predictability. The null

hypothesis that futures return does not predict spot return is rejected at the 1% level in all

four commodity markets. This implies that futures return is a useful predictor of spot return,

and investors can, potentially, utilize this information in devising profitable trading strategies.

INSERT TABLE 2

Second, we discover a relatively small R-squared. This is nothing surprising and, in fact, is

typical of the return predictability literature (see Welch and Goyal, 2008; Campbell and

Thompson, 2008). Campbell and Thompson (2008), in particular, show that significant

economic gains can be made by investors even when the R-squared is small. The economic

gain aspect of commodity spot market is a subject we will investigate later.

Finally, the results from the structural change test reveal strong evidence of a structural

change in three of the four commodity markets. The null hypothesis of no structural change is

rejected at the 5% level or better for the gold, oil and silver markets; the exception is the

platinum market for which we are unable to reject the null. Overall, there is clear evidence

that structural change is a feature of the predictive regression model we have estimated so far.

One limitation, however, is that we have restricted the number of structural changes to one

when, in fact, there may be multiple structural changes. We explore the possibility of

multiple structural changes by using the Bai and Perron (1998) test as explained earlier. The

results for each of the four regression models are reported column-wise in Table 3, and are

organized as follows. The and the statistics, reported in rows 2 and 3,

respectively, examine the null hypothesis of zero breaks against the alternative hypothesis of

an unknown number of breaks given an upper bound (maximum) of five breaks. The results

seem to suggest strongly that there is at least one structural break in each of the four

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predictive regression models. The and the tests both reject the null of zero

breaks at the 1% level. The results from the test help us identify exactly how many

breaks there are in each of the predictive regression models. Across all four models, we

discover evidence of two structural breaks, implying three regimes.2

INSERT TABLE 3

Next, we utilize this information and form three regimes for each commodity market. The

idea is to re-estimate the predictive regression model over each of the three regimes and

gauge whether structural breaks have disturbed the predictive ability of commodity futures

returns. The results are reported in Table 4.

INSERT TABLE 4

We notice that for the gold market the null of no predictability is rejected in all three regimes.

However, while the null that gold futures returns do not predict gold spot returns is rejected at

the 1% level in the first two regimes, it is weakly rejected (at the 10% level) in the third

regime. This implies that the predictive ability of the gold futures returns has somewhat

declined due to the structural break. Moreover, we notice that the R-squared of the predictive

regression model declined from around 0.15 in regime 1 to 0.002 in regime 3. This, again,

highlights the fact that the relevance of gold futures returns in predicting gold spot returns has

weakened following structural breaks. A similar trend in the results is found for the oil

market. However, for the oil predictive regression model we notice that, in regime 3, the sign

on predictability has changed from positive to negative. This regime actually coincides with

the oil price hike and the global financial crisis. A similar result is observed for the silver

market, with predictability found in only regimes 1 and 2. For platinum, on the other hand,

there is no predictability in regime 1, but regimes 2 and 3 reveal strong evidence of

2 The break dates are generally associated with market events such as demand and supply of commodities, political instability including wars, and macroeconomic news. A detailed analysis of this topic is provided in the Working Paper version of this paper. Details are available upon request.

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predictability. The main implication of this regime-wise test for predictability of the

commodity spot returns is that structural breaks do influence the predictive ability of the

commodity futures returns. Thus, in devising any trading strategies, one must account for

possible structural changes.3

3.2. Robustness test: Is return predictability data frequency dependent?

In this section, we seek to test whether our results on return predictability of the commodity

spot market are robust to different data frequencies. It should be made clear that we are not

testing the robustness of the structural break. The structural break dates are likely to be

different as we have two different data frequencies. In the return predictability literature,

apart from daily data, monthly data are commonly used. In this section, consistent with this

literature, we repeat our predictability tests based on monthly data. As with daily data, we

have different start and end dates for each of the four commodities.

The results, based on the predictive regression model (Equation 3), are reported in Table 5.

We notice that except for the gold market, we reject the null hypothesis of no return

predictability. This suggests that based on monthly frequency, commodity futures returns

3 We also estimate all results using the commodity futures returns as the dependent variable and spot returns as the predictor variable. We also perform all structural break tests on the commodity futures returns. These results are not included here as the subject of our investigation is the commodity spot market consistent with theory. However, all results are available upon request. In brief, we summarise the main findings from our analysis here. First, the null hypothesis of no predictability (that is, spot returns do not predict futures returns) is rejected at the 1% level for gold and platinum and at the 5% level for oil. There is no evidence of predictability for silver. Second, the null of no structural change is rejected for gold, platinum, and silver at the 5% level or better, with no evidence of a structural break for oil. However, when we allow for multiple structural breaks in commodity futures returns, two structural breaks are found for gold, oil, and platinum, and one structural break for silver. Third, using these structural breaks we create three regimes for gold, oil, and platinum, and two regimes for silver. We find that predictability is regime-dependent in that in the second regime all commodity spot returns predict commodity futures returns while relatively weak evidence of predictability is found in regimes 1 and 3.

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predict commodity spot returns with the exception of gold. When we test for the null

hypothesis of no structural change, we reject the null in only two (gold and silver) of the four

markets. The R-squared are all positive, suggestive of the information content in futures

prices. However, compared with daily data where we discovered return predictability in all

four markets, monthly data only reveal predictability in three of the four markets. This

suggests that greater evidence of spot return predictability is found with high frequency data.

INSERT TABLE 5

We also test for structural changes in the predictive regression model based on the Bai and

Perron (1998) test. We find that for the oil predictive model there are two structural changes,

leading to three regimes, and for gold, platinum and silver there is only one structural change,

leading to two regimes. These results are not reported here to conserve space, but are

available from the authors upon request. The regime-wise results on predictability by

commodity are reported in Table 6. The results, as in the case of daily data, suggest that

commodity spot returns are regime-dependent. This implies that structural breaks have

influenced the predictive information contained in commodity futures returns. In summary,

the null hypothesis of no predictability is rejected in regime 2 but not in regime 1 for gold,

silver, and platinum, while for the oil market the null is rejected in regimes 1 and 3 only.

INSERT TABLE 6

A second way we wish to test the robustness of our results is to apply a non-linear predictive

regression model. So far in our analysis, we have assumed that the predictive regression

model is linear. A related branch of the literature has shown that financial variables do tend to

behave in a non-linear manner. We apply a version of the ESTAR model considered by

Rapach and Wohar (2005), who propose the following data-generating process to capture the

non-linear dynamics in the predictor variable under the null hypothesis of no predictability4:

4 The model was estimated using GAUSS codes available from David Rapach’s website.

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( )

{ [ (

) ]}( ) ( )

Here, and are the mean of the spot and futures returns and the disturbance terms are

independently and identically distributed. We follow Rapach and Wohar (2005) and (a)

estimate the process by non-linear least squares, (b) re-sample the residuals in order to

generate a pseudo-sample of observations for commodity spot returns and futures returns,

matching the sample size we began with, (c) extract t-statistics for , and (d) create an

empirical distribution of t-statistics for . The results based on both daily and monthly data

are reported in Table 7.

INSERT TABLE 7

Based on daily data, the null of no predictability is rejected in all four non-linear predictive

regression models; at the 1% level in the case of gold, platinum and silver, and at the 5%

level in the case of oil. At the monthly frequency, we discover relatively less evidence of

predictability. We reject the null hypothesis of no predictability at the 10% level only for two

commodities—oil and platinum. These results are generally consistent with those obtained

from the linear predictive regression model.

It follows that the main implication here is that regardless of whether one uses linear or non-

linear models, greater evidence of predictability is found with high frequency data. This is not

surprising because information content increases with an increase in data frequency. Our

results here merely reflect this.

3.3. Trading strategies

There is limited work on the economic significance of commodity spot return predictability.

Equally significantly, none of the studies examines the predictive power of commodity

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futures returns. All works focus on the profitability of the commodity futures market directly.

On this, there are a number of interesting and appealing studies. The most recent contribution

on this subject is from Szakmary et al. (2010). They examine the performance of trend-

following strategies in 28 commodity futures markets, and unravel evidence of significant

profits from a range of trading rules. Miffre and Rallis (2007) examine the profitability of 13

agricultural futures using momentum and contrarian trading strategies. They find evidence of

significant profits in these futures markets. Wang and Yu (2004) find that short-term

contrarian strategies lead to abnormal returns on commodity futures. And, in perhaps one of

the most comprehensive analyses of profitability of futures markets, significant evidence of

profitability in commodity futures is documented by Marshall et al. (2008) and Fuertes et al.

(2010).

Our research question is different from the literature that documents strong evidence of

profitability in commodity futures markets. Based on our earlier finding that commodity

futures return predicts commodity spot return, we ask whether investors can devise trading

strategies to profit from the commodity spot market. Then, following the large body of

literature cited above which has used technical trading rules, we also estimate profits from

moving average (MA) technical trading rules and trading range break rules. We then compare

whether the profitability of the commodity spot market, based on a forecasting model that

uses the commodity futures return as a predictor, is different from simple technical trading

rules. This means that our focus on profitability is not on the commodity futures market;

rather, it is on the commodity spot market—a market about which relatively less is known

when it comes to profitability (or otherwise) of trading strategies.

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3.3.1. Moving average technical trading rules

A trend-determining technique, such as the crossing of two MA of prices, identifies trend

changes which have implications for investment positions. According to the MA rule, for

instance, buy (sell) signals are extracted when the short-term moving average exceeds (is less

than) the long-term MA by a specified percentage. Thus, the MA rule is to go long in a cross-

rate if the short-term MA is equal to or greater than the long-term MA. Conversely, a short

position is established if the short-term MA is less than the long-term MA. To see this

relationship formally, let us: (a) define the short term and long term of the MA as and

days, respectively; and (b) let be an indicator of the trading position on day .

if (∑

) (∑

),

= 0 otherwise.

As in Ratner and Leal (1999), we use a number of specifications for and ; in particular, we

set and and and . Following Szakmary and Mathur (1997) and

Lee and Mathur (1996a,b), we allow a transaction cost of 0.1% each time a long or short

position is established, and the adjusted returns, or profits , are computed as follows:

( ⁄ ) ( )( ⁄ ) | | ( )

The first two terms on the right-hand side of the equation represent raw returns, either when

an investor takes a long position or a short position in the market. The final term in the

equation accounts for transaction costs (1%) that are paid whenever a new position is

established in the market.

The results from the MA technical trading rules are reported in Table 8. Results are presented

for each of the different short and long periods by commodities and are organized into two

panels: Panel A does not impose any restrictions on price movements, while results in Panel

B are based on a price band of 1%. Two observations are worth making. The first aspect of

17

the result is with respect to the relative profitability of the commodities across the different

trading rules. Based on results without a price band, we notice that the oil and silver spot

markets offer investors the highest daily returns, platinum returns are ranked third, while the

lowest return is recorded for gold.

INSERT TABLE 8

Second, we notice that when we allow for a price movement of 1%, the MA(5,150) and

MA(2,200) offer statistically insignificant returns. Trading rules with shorter short and long

days offer statistically significant returns. Based on the MA(1,50) and MA(1,150) rules, we

notice that investors gain higher returns from the oil spot market, followed by the silver and

gold/platinum spot markets. And, when we average the returns across the four trading rules,

returns from the oil and silver spot markets turn out to be 0.07% and 0.04%, respectively, and

these are the only markets that offer statistically significant returns.

In summary, we unravel three things about the profitability of the commodity spot markets:

(a) oil and silver are the most dominant commodities in terms of offering the highest returns

to investors, depending on whether or not we allow for a 1% price band; (b) all trading rules

offer significant returns when no price band is imposed, and, when a price band is imposed,

only lower short-term MA and long-term MA rules offer statistically significant profits; and

(c) platinum and, in particular, gold spot markets offer limited opportunities for profits.

One of our feature results on spot return predictability is the role of structural changes. Recall

that structural changes had influenced spot return predictability. There is no reason to believe

that structural changes do not affect profitability from the MA technical trading rules. We test

for this possibility. Using structural break dates obtained from the Bai and Perron (1998) test,

as reported in the previous section, we estimate profits in the different regimes for each of the

18

four commodities. The use of structural breaks to sub-sample data for empirical analysis is

not uncommon; see, inter alia, Pastor and Stambaugh (2001) and Rapach and Wohar (2006).

We report the results in Table 9. Our main findings are as follows. In the case without a 1%

price band, we find that the oil spot market is the most profitable in regimes 2 and 3. In the

first regime—that is, before any structural breaks, silver was the most significant commodity.

We also notice that, clearly, profits are regime-dependent in the sense that for oil and

platinum, profits have increased from regime 1 to regime 3, while in the case of gold and

silver, profits have declined over time.

INSERT TABLE 9

By comparison, when a 1% price band is allowed, relatively less evidence of profitability in

the commodity markets is found. Profits from the oil market are statistically significant in

only two of the three regimes. While profits from oil are significant in regimes 1 and 2, they

become insignificant in regime 3. Similarly, profits from the silver market are only

significant in regimes 1 and 3. Finally, we notice that profits from the gold and platinum

markets are statistically insignificant in all regimes. Our results on profitability are, generally,

consistent with the evidence on predictability.

3.3.2. Summary

The results from the MA technical trading rules reveal two main messages for investors in the

commodity spot market. The first message is that technical trading rules lead to statistically

significant profits in the oil and silver spot markets. Thus, these commodities turn out to be

the most profitable amongst the four commodities considered. Profits from the gold and

platinum markets are, generally, statistically insignificant and, where they are significant,

they are much less so than those obtained from the oil and silver markets.

19

The second message relates to the relevance of structural changes in influencing profits from

the MA technical trading rules in commodity spot markets. We find that profits do change

from one regime to another, reflecting the relevance of structural breaks.

3.3.3. Trading range break rule

In this section, we apply an additional trading strategy—the trading range break rule (TRBR).

The idea here is to test the robustness of the results obtained from the MA technical trading

rule in the previous section. The TRBR is implemented as follows:

(a) compare the current price ( ) to the recent maximum ( ) and minimum price

( );

(b) TRBR emits a buy signal when by at least a pre-specified band—we consider

a 1% price band;

(c) TRBR emits a sell signal when by at least a pre-specified band—we consider

a 1% price band;

(d) As in Brock et al. (1992), we consider recent minimums and maximums over the prior 50,

150, and 200 days and evaluate trading rules with bands of 0% and 1%.

The results from the TRBR are reported in Table 10. Panel A contains profits when minimum

and maximum days of 50, 150, and 200 are considered without a price band, while Panel B

contains results with a 1% price band. We again notice, consistent with results obtained from

the MA trading rule, that the oil spot market offers investors the highest (and statistically

significant) profits from 50 days and 150 days trading rules, regardless of whether or not we

impose a price band. The second best market turns out to be silver. When the technical

trading rule over 200 days is considered, profits from the oil spot market are statistically

insignificant, however. A 200-day trading rule leads to highest profits from the silver spot

20

market when no price band is imposed, and when a 1% price band is imposed the profits are

highest from the platinum market. In sum, the evidence that the oil and silver spot markets

are most profitable holds in at least two of the three cases.

INSERT TABLE 10

3.3.4. Is the trend in profits similar for commodity futures?

While our focus in this paper is on the profitability of commodity spot market, as one referee

of this journal suggested, there is nothing that stops us from examining the profitability of

commodity futures market. Doing so, will evince whether or not profitability of commodity

futures like commodity spot is consistent across different trading rules and technical trading

methods and whether or not profitability is sub-sample (structural break) dependent. To

address the first issue we simply generate results based on a 1% price band and report results

in panels A and C of Table 11. The moving average strategies suggest that on average only

oil and silver futures are profitable while the range break trading rules suggest that all

commodity futures are profitable consistent with earlier results. To address the second issue,

we run the structural break predictability test using commodity futures returns as the

dependent variable and commodity spot returns as the predictor. Using the resulting structural

break dates from the Bai and Perron test we divide the sample into sub-samples and compute

the profits using the same trading rules as before for each of the sub-samples. In panel B we

only report the average profits for each of the sub-samples. We observe that profits are sub-

sample dependent and same as those obtained for the commodity spot markets, consistent

with the descriptive statistics provided in Table 1.5

INSERT TABLE 11

5 Detailed results are available from the corresponding author upon request.

21

3.3.5. Trading strategies for a mean-variance investor

One limitation of the technical trading rules considered so far is that they do not account for

volatility of commodity returns and investor preference for risk. Several studies (Rapach et

al. 2010; Campbell and Thompson, 2008; Marquering and Verbeek, 2004; Westerlund and

Narayan, 2012) show that these factors matter for not only investor profits but also for

investor utility. Motivated by these studies, we consider a mean-variance investor

characterized by a quadratic utility function of the following form:

{ }

{

} ( )

Such that, given a portfolio of for the risky asset, the utility simply becomes:

{ }

{ } ( )

where is the commodity spot return, is the risk-free rate of return, is the

rolling variance of the risky asset, is the risk aversion factor, and is the investor’s

portfolio weight in period t+1, computed as follows:

{ }

{ }

( )

The portfolio weight is positively related to expected excess return on the commodity spot

return, and conditional variance—a measure of risk—is negatively related to the portfolio

weight. In other words, an investor will invest more in the commodity if predicted excess

return is increasing, and will be equally discouraged from investing in a risky asset if its

variance is rising over time. The risk aversion factor, , is set to 6, which represents a

medium level of risk position for an investor typically considered by the empirical studies.

Since commodity markets are characterized by short-selling, we allow for limited short-

22

selling and borrowing at the risk-free rate by restricting the weight to lie between -0.5 to 1.5.6

The expected excess return is based on a predictive regression model of the form represented

by Equation (3), except now the dependent variable is the excess commodity spot return. For

each of the regimes, we choose an in-sample period that includes 50% of the observations in

our sample, estimate the structural break predictive regression model, and use the coefficients

to forecast excess commodity spot returns for 50% of the out-of-sample period. Following

Welch and Goyal (2008), we also consider a short in-sample period (30% of observations)

and a long in-sample period (65% of observations). We find little difference in the results;

detailed results are available upon request.

The results are summarized in Table 12. For the purpose of comparing profits with our earlier

trading strategies, one needs to consider results that take into account transaction costs, which

we set to 0.1%. We also compute all results without transaction costs. We do not report these

results but they are available upon request. There are three main features of the results. First,

we find that profits with transaction costs in all four markets are generally lower than without

transaction costs.

INSERT TABLE 12

Second, in terms of rankings of commodities, the silver spot market is the most profitable,

followed by gold, platinum and oil. These rankings barely change when we consider

profitability in the three regimes. Moreover, regime-wise profits reveal that for all four

commodities, profits have declined from regime 1 (before any structural break) to regime 3

(the period marked by the global financial crisis). In fact, in regime 3, profits from all

6 In detailed results, unreported here, we undertake the following analysis: (a) we allow unlimited short-selling; (b) we allow for borrowing only by setting the weight to lie between 0 to 1.5; and (c) we allow for no short-selling and borrowing by setting the weight to 0 to 1. In summary, and as expected, we find that profits from unlimited short-selling are the largest. This is true for all four commodities. Detailed results are available upon request.

23

commodities are the lowest. We also notice that whereas for the oil and gold markets profits

were maximized in regime 1, for platinum and silver the profits were maximized in regime 2.

The main implication of these findings is that, consistent with our previous findings, profits

are regime-dependent and, therefore, structural breaks in commodity markets matter for

analyzing profitability.

Finally, profits from all four commodities are statistically significant. The results for platinum

are opposite to those found from MA technical trading rules. Moreover, with MA and TRBR

profits are trading rule dependent. This implies that dynamic trading strategies based on a

mean-variance investor framework by allowing for commodity market variance and risk

preference are an important consideration in modeling profits. While our study connects with

both technical trading rule based profits and the utility maximisation-based profits, we wish

to emphasise that the preference for utility-based measures of profitability are generally

preferred for the following reasons. First, the utility based approach maximizes expected

returns for a given level of risk and for given set of investment constraints. Technical trading

strategies, on the other hand, do not take into account the risk and investor preference.

Second, technical trading rules merely aim to predict the future prices based on past market

data. However, as Fama (1965) argues, if prices are characterised by a random walk then the

technical trading strategies should not add any value in predicting the future stock prices.

Third, technical analysis lacks a theoretical motivation. In particular, the fact that the

selection of trading rules is ad hoc has not gone down well with researchers as this opens the

possibility for data mining. Sullivan et al. (1999) find that the superior performance of

technical rules disappears once the effect of data snooping is taken into account7

7 In an equally interesting piece of research, Dewachter and Lyrio (2006) assess the value of technical trading rules for rational risk averse investors. They find that the opportunity cost of

24

3.3.6. A real-time structural break trading strategy model

One referee of this journal suggested that, since the investors do not know a priori the regime

in which they are, a valuable contribution will be to have a forecast model that produces

structural breaks which the investors take into account in devising their trading strategies in a

real time manner. We agree. The advantage of such a model is that it simply avoids the need

to group investors into different regimes. One disadvantage of our previous analysis was we

assumed that the investor knows the break dates and using these break dates decides on

which regime she is in.

We now follow Rapach et al. (2010) and estimate a forecasting model in real time using a

recursive expanding window for forecasting in the presence of a structural break. More

specifically, we do the following. We estimate the in-sample predictive regression model

with a structural break (Equation 5) for the period t0 to t and forecast returns for the time

period t+1. We then re-estimate the predictive regression model over the period t0 to t+1 and

obtain forecasts for t+2. We repeat this process of generating forecasts until all data are

exhausted. Because it is a recursive predictive regression model and because at every stage

(expanding predictive regression window) the model accounts for a structural break it means

that at each stage (daily, given we use daily data) we are including all information (including

any structural break) that would have been available to the investor at the time. This is same

as saying that we are mimicking real-time trading where the investor is not only accounting

for information contained in the futures market but also in the structural break. Because the

model is updated every day (since we are using daily data), if a break occurs, the model will

using technical trading rules tends to be very high and that the irrationality of technical trader is an important component of the total opportunity cost of using technical trading rules.

25

produce this break. If the model indeed finds the break then forecasts generated will take into

account this break.

We generate profits, assuming a mean-variance investor utility function as before, from

forecasts generated from this structural break predictive regression model. The results are

reported in Table 13. As before, we allow for transactions costs and different risk aversion

parameters. We find that investors can make statistically significant profits from all

commodities.

INSERT TABLE 13

4. Concluding remarks

In this paper we show the relevance of commodity futures in predicting commodity spot

returns. We show, using both linear (with and without structural breaks) and non-linear

models, that commodity futures return predicts commodity spot return in the case of the oil,

gold, and silver markets. We then use a wide range of trading strategies to show that investors

can make profits in the commodity markets. Most interestingly, using MA technical trading

rules and range break trading rules, we show that profits from the oil spot market are the

highest, followed by silver. Relatively less profit is obtained from investing in the gold and

platinum spot markets.

We also consider dynamic trading strategies for a mean-variance investor. Using commodity

futures returns, which showed evidence of predictive ability, we forecast commodity spot

returns. We then show that by using commodity futures returns as a predictor, investors can

still generate statistically significant profits in all four markets. Our results from dynamic

trading strategies are somewhat different from those under MA technical trading rules and

26

range break trading rules. First, dynamic trading strategies suggest that all four commodities

are profitable, while MA technical trading rules on average suggest that platinum and gold

are unprofitable markets. Second, we find that the ranking of the most profitable market is

different when considered regime-wise. Finally, both technical trading rules and dynamic

trading strategies reveal that profits are regime-dependent. In other words, structural breaks

matter, and all commodity profits were the lowest in the regime characterized by the recent

global financial crisis.

27

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31

Figure 1: A plot of spot and futures returns

This figure plots the commodity spot and futures returns. We have four commodities—oil, gold, platinum, and silver. The sample period differs by commodity and is dictated by data availability. For oil, daily data are for the period 5/16/1983 to 11/22/2011; for gold and silver, daily data are for the period 1/01/1980 to 11/22/2011; and for platinum, daily data are for the period 1/06/1987 to 11/22/2011. Thus, we have no less than 10,418 observations for oil, 9,087 observations for platinum, and 11,649 observations for gold and silver.

-30

-20

-10

0

10

20

30

1980 1985 1990 1995 2000 2005 2010

SILVER_SPOT

-30

-20

-10

0

10

20

30

1980 1985 1990 1995 2000 2005 2010

SILVER_FUTURES

-15

-10

-5

0

5

10

1980 1985 1990 1995 2000 2005 2010

PLATINUM_SPOT

-30

-20

-10

0

10

20

1980 1985 1990 1995 2000 2005 2010

PLATINUM_FUTURES

-60

-40

-20

0

20

40

1980 1985 1990 1995 2000 2005 2010

OIL_SPOT

-50

-40

-30

-20

-10

0

10

20

1980 1985 1990 1995 2000 2005 2010

OIL_FUTURES

-15

-10

-5

0

5

10

15

1980 1985 1990 1995 2000 2005 2010

GOLD_SPOT

-15

-10

-5

0

5

10

1980 1985 1990 1995 2000 2005 2010

GOLD_FUTURES

32

Table 1: Descriptive statistics Variables ADF Mean SD

-109.56 0.0159 0.8409

-115.61 0.0159 0.8367

-104.25 0.0185 2.0274

-101.48 0.0197 1.9805

-107.32 0.0199 1.5344

-114.95 0.0193 1.5182

-71.393 0.0131 1.2005

-94.141 0.0131 1.1243

In this table selected descriptive statistics are reported for both commodity spot and futures returns. Column 2 reports the ADF test, which examines the null hypothesis of unit root against the alternative that the return series is stationary. The test is implemented for a model with an intercept but no trend. The optimal lag length for the lagged first difference of the dependent variable used to control for serial correlation in the model is chosen using the Schwarz Information Criteria. The mean returns and standard deviations are reported in columns 3 and 4, respectively.

33

Table 2: Results from the predictive regression model based on daily data

Gold Oil Platinum Silver

0.0075

(0.7940) 0.0120

(0.6247) 0.0124

(1.0519) -0.0014

(-0.0910) 0.2156***

(22.8936) 0.1091*** (5.6509)

0.0653*** (5.5497)

0.4691*** (28.8302)

0.0431 0.003 0.0033 0.0666 474.72***

(0.000) 38.7302**

(0.03) 8.9161 (0.54)

917.31*** (0.000)

Break date 8/05/1993 9/07/1988 3/09/1995 11/24/1993

In this table, results from the structural break predictive regression model are reported for each of the four commodities. Row 2 contains the coefficient on the intercept term, followed by its t-statistic in parenthesis; row 3 contains the coefficient on the predictor variable, followed by its t-statistic in parenthesis used to test the null hypothesis of no predictability; the R-squared appears in row 4; row 5 contains the statistic—used to examine the null hypothesis of no structural change— and its p-value, reported in parenthesis, generated using a 15% trimming factor, respectively; and, the estimated break date is reported in the last row. ***denotes statistical significance at the 1% level.

34

Table 3: The Bai and Perron test for multiple structural breaks based on daily data

Gold Oil Platinum Silver 473.98*** 45.5336*** 20.8906*** 910.60*** -1% 473.98*** 45.5336*** 26.4271*** 910.60*** ( | ) 473.9873*** 45.5336*** 10.6137* 910.60*** ( | ) 17.3261*** 15.7167*** 28.1931*** 25.7765*** ( | ) 17.3261*** 6.0778 3.977 5.1694 ( | ) 12.0229 7.0671 2.9652 3.6498 ( | ) -- -- 1.2762 -- This table reports the structural test results based on the Bai and Perron (1998) procedure. Two forms of the double maximum test— and —are reported in rows 2 and 3, respectively. The statistic is the maximum value of the ( ) F-statistic, while the statistic weights the individual statistics so as to equalize the p-values across values of . Rows 4 to 8 report the sequential ( ⁄ ) procedure to determine the optimal number and location of structural breaks, if the null hypothesis of no structural break is rejected by the double maximum test. The sequential procedure considers the null hypothesis of breaks against the alternative hypothesis of ( ) breaks. For the model with breaks, the estimated break dates, depicted as , are obtained by global minimization of the sum of squared residuals. The null hypothesis is rejected in favor of a model with ( ) breaks, provided that the overall minimum value of the sum of squared residuals is sufficiently smaller than the sum of squared residuals from the break model. Bai and Perron (1998) provide appropriate critical values. *(***) denote statistical significance at the 10% and 1% levels, respectively.

35

Table 4: Predictive regression model results for different regimes based on daily data

Predictor Regime 1 Regime 2 Regime 3

End point End point End point

Gold -0.01349 [-0.4451]

0.4138*** [20.185] 0.1479

6/16/1986 [ 6/27/1985, 5/18/1988]

0.0023 [0.1668]

0.3052*** [16.235]

0.0912

8/5/1993 [4/29/1993, 11/15/1993]

-0.0117 [-0.9834]

0.036317* [1.9845] 0.0017

6/4/2001 [8/19/1998, 7/11/2002]

Oil -0.0329 [-0.8157]

0.3936*** [8.6130] 0.0368

9/7/1988 [8/7/1987 , 8/29/1989]

0.0191 [0.7862]

0.1112*** [4.5023] 0.0030

1/11/2007 [4/3/2005 , 5/5/2009 ]

0.0433 [0.8990]

-0.0801* [-1.9226] 0.0020 11/22/2011

Platinum -0.0043 [-0.2449]

0.0091 [0.4601] 0.0000

3/9/1995 [7/2/1994, 9/7/1995]

0.0039 [0.1622]

0.2292*** [7.8789] 0.0329

3/2/2000 [4/24/1999 ,2/7/2001]

0.0274 [1.4353]

0.0519*** [3.0754] 0.0022 11/22/2011

Silver -0.0342 [-0.8072]

0.8749*** [28.044] 0.2142

11/21/1987 [7/5/1987, 4/1/1989]

-0.0056 [-0.2838]

1.0940*** [36.346] 0.3761

11/24/1993 [11/3/1993, 12/3/1993]

0.0303 [1.5547]

-0.0421 [-0.9548] 0.0006 11/22/2011

This table reports results from the predictive regression based on different regimes. Under each regime, the results are organized as follows: in the first column, we report the intercept term and its t-statistics in square brackets; in column 2, we report the coefficient on predictability with its t-statistics in squared brackets; the R-squared appears in the third column, while the end point appears in the final column. *(***) denote statistical significance at the 10% and 1% levels, respectively.

36

Table 5: Results from the predictive regression model based on monthly data—a robustness test

Gold Oil Platinum Silver

0.274

(1.0631) 0.3390

(0.5716) 0.0124

(1.0519) -0.0014

(-0.0910) -0.2978

(-1.1541) 1.2789** (2.1485)

0.0653*** (5.5497)

0.4691*** (28.8302)

0.0035 0.0134 0.0033 0.0666 15.734**

(0.02) 6.8823 (0.5)

8.9161 (0.54)

917.31*** (0.000)

Break date 3/30/2001 9/28/1990 3/09/1995 11/24/1993 In this table, results from the structural break predictive regression model are reported for each of the four commodities. Row 2 contains the coefficient on the intercept term, followed by its t-statistic in parenthesis; row 3 contains the coefficient on the predictor variable, followed by its t-statistic in parenthesis used to test the null hypothesis of no predictability; the R-squared appears in row 4; row 5 contains the statistic—used to examine the null hypothesis of no structural change— and its p-value, reported in parenthesis, generated using a 15% trimming factor, respectively; and the estimated break date is reported in the last row. **(***) denote statistical significance at the 5% and 1% levels, respectively.

37

Table 6: Predictive regression model results for different regimes based on monthly data – a robustness test

Predictor

Regime 1 Regime 2 Regime 3 End point End point End point

Gold -0.3706

[-1.2014]

-0.1816 [-0.5707] 0.0012

3/30/2001 [6/30/1997, 2/27/2004]

1.7601*** [3.8768]

-0.9531** [-2.2164] 0.0372 10/31/2011

- - - -

Oil 0.3907 [0.3025]

3.6858*** [3.0426] 0.09618

9/28/1990 [9/30/1987, 2/28/1994]

0.1004 [0.1262]

-1.3390 [-1.6034] 0.01473

1/31/2005 [8/30/2002, 8/29/2008]

0.8191 [0.7905]

3.3316*** [3.2430] 0.11492 10/31/2011

Platinum -0.2877 [-0.7119]

-0.4645 [-0.9618] 0.0062

6/30/1999 [ 6/30/1995, 11/29/2002]

0.7675 [1.4079]

1.6519*** [3.4566] 0.0747 10/31/2011

- - - -

Silver -2.9643 [-1.3743]

0.2663 [0.1939] 0.0006

2/28/1985 [4/29/1983, 11/30/1994]

0.6115 [1.3925]

-1.0086* [-1.9467] 0.0117 10/31/2011

- - - -

This table reports results from the predictive regression based on different regimes. Under each regime, the results are organized as follows: in the first column, we report the intercept term and its t-statistics in square brackets; in column 2, we report the coefficient on predictability with its t-statistics in squared brackets; the R-squared appears in the third column, while the end point appears in the final column. * (***) ** denote statistical significance at the 10%, 1%, and 5% levels, respectively.

38

Table 7: A non-linear predictive regression model—a robustness test

Commodity Panel A: Daily data Panel B: Monthly data

-stat p-value -stat p-value

Gold -0.2597*** -8.1240 0.0000 0.0036 0.0517 0.5000 Oil -0.1314** -2.0655 0.0180 -0.1338* -1.3724 0.0900 Platinum -0.0536*** -2.8650 0.0100 -0.1562* -1.5696 0.0900 Silver -0.2994*** -9.2579 0.0000 -0.0520 -0.8041 0.1700

This table reports results from a non-linear predictive regression model based on a version of the ESTAR model considered by Rapach and Wohar (2005). They propose the following data-generating process to capture the non-linear dynamics in the predictor variable under the null hypothesis of no predictability:

{ [ (

) ]} (

) Here, and are the mean of the spot and futures returns and the disturbance terms are independently and identically distributed. We follow Rapach and Wohar (2005) and: (a) estimate the process by non-linear least squares; (b) re-sample the residuals in order to generate a pseudo-sample of observations for commodity spot returns and futures returns, matching the sample size we began with; (c) the computed t-statistics are extracted for ; and (d) we repeat this process 500 times leading to an empirical distribution of t-statistics for and the p-values used to test the null hypothesis of no predictability are generated. The results are reported for both daily (Panel A) and monthly data (Panel B). * (**) (***) denote statistical significance at the 10%, 5%, and 1% levels, respectively.

39

Table 8: MA technical trading rule profits

Panel A: Without price band MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average Oil 0.3209***

(16.7034) 0.1806*** (9.1589)

0.0527*** (2.6626)

0.0836*** (4.2265)

0.1595*** (8.1879)

Gold 0.1496*** (16.9390)

0.0919*** (10.3977)

0.0167* (1.8805)

0.0406*** (4.5900)

0.0747*** (8.4518)

Silver 0.2574*** (16.9524)

0.1613*** (10.6180)

0.1613*** (10.5660)

0.0658*** (4.3034)

0.1615*** (10.6099)

Platinum 0.1762*** (15.1354)

0.1059*** (8.9990)

0.0329*** (2.7814)

0.0494*** (4.1575)

0.0911*** (4.2988)

Panel A: With 1% price band MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average Oil 0.1411***

(7.2662) 0.1159*** (4.5606)

0.0153 (0.7395)

0.0137 (0.6675)

0.0715*** (3.3085)

Gold 0.0274*** (3.0688)

0.0186** (2.0908)

-0.0157 (-1.7690)

0.0124 (1.4237)

0.0107 (1.2036)

Silver 0.0965*** (6.2850)

0.0566*** (3.7334)

0.0138 (0.9085)

0.0109 (0.7226)

0.0445*** (2.9124)

Platinum 0.0567*** (4.8132)

0.0167 (1.4090)

-0.0068 (-0.5685)

0.0047 (0.3947)

0.0178 (1.5121)

This table reports profits for each of the four commodities based on the moving average (MA) trading rule technique. The MA rule generates buy (sell) signals when the short-term MA exceeds (is less than) the long-term MA by a specified percentage. The MA rule is to go long in a cross-rate if the short-term MA is equal to or greater than the long-term MA. Conversely, a short position is established if the short-term MA is less than the long-term MA. To see this relationship formally, let us: (a) define the short term and long term of the MA as and days, respectively; and (b) let be an indicator of the trading position of day . if (∑

) (∑

),

= 0 otherwise. We use a number of specifications for and ; in particular, we set and and and . We allow transaction costs of 0.1% each time a long or short position is established, and the adjusted returns, or profits , are computed as follows: ( ⁄ ) ( )( ⁄ ) | | The first two terms of the right-hand side of the equation represent raw returns, either when an investor takes a long position or a short position in the market. The final term in the equation accounts for transaction costs that are paid whenever a new position is established in the market. * (**) *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

40

Table 9: Sub-sample MA trading rule Panel A: Without price band Sub-sample 1

MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average

Oil 0.2825*** (6.6924)

0.15189*** (3.2432)

0.0671 (1.4268)

0.0690 (1.4638)

0.1426*** (3.2066)

Gold 0.1994*** (7.1243)

0.1141*** (4.0775)

0.0384 (1.3683)

0.0658*** (2.2926)

0.1044*** (3.7157)

Silver 0.3272*** (8.3483)

0.2131*** (5.4525)

0.0708* (1.8022)

0.1017*** (2.5645)

0.1782*** (4.5419)

Platinum 0.1418*** (8.2020)

0.0887*** (5.1315)

0.0049 (0.2836)

0.0305* (1.7249)

0.0666*** (3.8355)

Sub-sample 2

MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average

Oil 0.3272*** (13.546)

0.1857*** (7.4937)

0.0367 (1.4733)

0.0813*** (3.2636)

0.1577*** (6.4442)

Gold 0.1228*** (8.4035)

0.07650*** (5.1945)

0.0083 (0.5633)

0.0294* (1.9823)

0.0593*** (3.0447)

Silver 0.2012*** (8.1589)

0.1134*** (4.3686)

0.0142 (0.5431)

0.0409 (1.5927)

0.0924*** (3.6658)

Platinum 0.1513*** (6.1120)

0.0935*** (3.5273)

0.0105 (0.3948)

0.0365 (1.2844)

0.07295*** (2.8296)

Sub-sample 3

MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average

Oil 0.3405*** (6.8446)

0.2217*** (4.2014)

0.1089** (2.0550)

0.1273** (2.3927)

0.1996*** (3.8734)

Gold 0.1427*** (13.508)

0.0919*** (8.4911)

0.0126 (1.1572)

0.0380*** (3.4717)

0.0713*** (6.6569)

Silver 0.2457*** (12.664)

0.1577*** (8.0128)

0.0128 (0.6455)

0.0620*** (3.1243)

0.11955*** (6.1115)

Platinum 0.2111*** (11.120)

0.1267*** (6.4737)

0.0596*** (3.0301)

0.0669*** (3.3983)

0.1160*** (6.0056)

Panel B: With 1% price band Sub-sample 1

MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average

Oil 0.1002** (2.3450)

0.1545** (2.5837)

-0.0003 (-0.0048)

0.0989 (1.6516)

0.0883* (1.6439)

Gold 0.0669** (2.3655)

0.0678** (2.4156)

-0.0088 (-0.3136)

0.0537 (1.7974)

0.0449 (1.5662)

Silver 0.1209*** (3.0523)

0.0910** (2.3344)

0.027415 (0.7047)

0.0436 (1.1158)

0.0707* (1.8018)

Platinum 0.0380** (2.1698)

0.0385** (2.2161)

0.0089 (0.5130)

0.0212 (1.1932)

0.0267 (1.5230)

Sub-sample 2

MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average

Oil 0.1654*** (6.7632)

0.0966*** (3.8849)

0.0106 (0.4194)

0.0208 (0.8351)

0.0734*** (2.9757)

Gold 0.0220 (1.4722)

0.0089 (0.5996)

No signal -0.0111 (-0.6846)

0.0066 (0.4624)

41

Silver 0.0383 (1.5256)

0.0367 (1.4226)

No signal 0.0004 (0.0146)

0.0251 (0.9876)

Platinum 0.0606*** (2.4271)

-0.0060 (-0.2229)

No signal -0.0306 (-0.7871)

0.0080 (0.4724)

Sub-sample 3

MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average

Oil 0.06914 (1.2323)

0.1743*** (3.2904)

-0.0044 (-0.0825)

-0.1080*** (-2.0446)

0.0328 (0.5989)

Gold 0.0189* (1.7531)

0.0083 (0.7573)

-0.0565** (-2.2148)

0.0161 (1.0496)

-0.0033 (0.3363)

Silver 0.1044*** (5.3241)

0.0541*** (2.7343)

0.0178 (0.8679)

-0.0001 (-0.0069)

0.0441** (2.2299)

Platinum 0.0693*** (3.6072)

0.0059 (0.3014)

-0.0032 (-0.1299)

0.0084 (0.4230)

0.0201 (1.0504)

This table reports profits for each of the four commodities based on the moving average (MA) trading rule technique. The profits are reported for each of the regimes as identified by structural break tests earlier. Profits are generated for both, with and without a price band. The MA rule generates buy (sell) signals when the short-term MA exceeds (is less than) the long-term MA by a specified percentage. The MA rule is to go long in a cross-rate if the short-term MA is equal to or greater than the long-term MA. Conversely, a short position is established if the short-term MA is less than the long-term MA. To see this relationship formally, let us: (a) define the short term and long term of the MA as and days, respectively; and (b) let be an indicator of the trading position of day . if (∑

) (∑

),

= 0 otherwise. We use a number of specifications for and ; in particular, we set and and and . We allow transaction costs of 0.1% each time a long or short position is established, and the adjusted returns, or profits , are computed as follows: ( ⁄ ) ( )( ⁄ ) | | The first two terms of the right-hand side of the equation represent raw returns, either when an investor takes a long position or a short position in the market. The final term in the equation accounts for transaction costs that are paid whenever a new position is established in the market. * (**) *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

42

Table 10: Profits from trading range break rules

Panel A: Without price band 50 days 150 days 200 days Oil 0.0743***

(3.8291) 0.0417** (2.1226)

0.0227 (1.1491)

Gold 0.0328*** (3.5821)

0.0232** (2.6210)

0.0251*** (2.8353)

Silver 0.0643*** (3.9263)

0.0371** (2.4246)

0.0322** (2.1331)

Platinum 0.0612*** (5.1830)

0.0288** (2.4115)

0.0260** (2.1783)

Panel B: With 1% price band 50 days 150 days 200 days Oil 0.0725***

(3.7033) 0.0453** (2.2531)

0.0209 (1.0388)

Gold 0.0285*** (3.1032)

0.0256*** (2.8890)

0.0235** (2.6506)

Silver 0.0623*** (3.8056)

0.0379** (2.4805)

0.0296* (1.9651)

Platinum 0.0510*** (4.2417)

0.0309** (2.5925)

0.0316** (2.6455)

This table reports profits for each of the four commodities based on the trading range break rule (TRBR). The TRBR is implemented as follows: (a) compare the current price ( ) to the recent maximum ( ) and minimum price ( ); (b) TRBR emits a buy signal when by at least a pre-specified band—we consider a 1% price band; (c) TRBR emits a sell signal when by at least a pre-specified band—we consider a 1% price band; and (d) we consider recent minimums and maximums over the prior 50, 150, and 200 days and evaluate trading rules with bands of 0% and 1%. * (**) *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

43

Table 11: Technical trading rule profits for commodity futures

Panel A: MA rule-based profits with 1% price band MA(1,50) MA(1, 150) MA(5,150) MA(2,200) Average Oil 0.1411***

(7.2662) 0.1159*** (4.5606)

0.0153 (0.7395)

0.0137 (0.6675)

0.0715*** (3.3085)

Gold 0.0274*** (3.0688)

0.0186** (2.0908)

-0.0157 (-1.7690)

0.0124 (1.4237)

0.0107 (1.2036)

Silver 0.0965*** (6.2850)

0.0566*** (3.7334)

0.0138 (0.9085)

0.0109 (0.7226)

0.0445*** (2.9124)

Platinum 0.0567*** (4.8132)

0.0167 (1.4090)

-0.0068 (-0.5685)

0.0047 (0.3947)

0.0178 (1.5121)

Panel B: Average profits across all trading rules for different regimes with 1% price band Sub-sample 1 Sub-sample 2 Sub-sample 3 Oil 0.0883*

(1.6439) 0.0734*** (2.9757)

0.0328 (0.5989)

Gold 0.0449 (1.5662)

0.0066 (0.4624)

-0.0033 (0.3363)

Silver 0.0707* (1.8018)

0.0251 (0.9876)

0.0441** (2.2299)

Platinum 0.0267 (1.5230)

0.0080 (0.4724)

0.0201 (1.0504)

Panel C: Profits from range break trading rules with 1% price band 50 days 150 days 200 days Oil 0.0725***

(3.7033) 0.0453** (2.2531)

0.0209 (1.0388)

Gold 0.0285*** (3.1032)

0.0256*** (2.8890)

0.0235** (2.6506)

Silver 0.0623*** (3.8056)

0.0379** (2.4805)

0.0296* (1.9651)

Platinum 0.0510*** (4.2417)

0.0309** (2.5925)

0.0316** (2.6455)

In this table we report three sets of results for profitability of commodity futures markets. In Panel A we include MA technical trading strategy-based profits. In Panel B, we report regime-wise MA profits. These profits are averaged across all trading rules (same rules as considered for spot market—see notes to Table 9). In the last panel we report profits obtained from the range break trading rules. All profits are estimated using a 1% price band.

44

Table 12: Regime-wise dynamic trading strategies of a mean-variance investor Oil Gold Platinum Silver Regime 1 0.011***

(2.822) 0.062*** (11.00)

0.015*** (121.208)

0.250*** (3.629)

Regime 2 0.010*** (21.897)

0.027*** (16.539)

0.09*** (32.941)

0.324*** (15.146)

Regime 3 0.001*** (15.206)

0.0009*** (74.635)

0.008*** (44.331)

0.009*** (70.641)

This table reports profits from a dynamic trading strategy based on a mean-variance investor framework for which portfolio weights are computed based on equations (16) to (18). The portfolio weight will be higher if excess return is increasing, and will be lower if the variance of the risky asset is rising over time. The risk aversion factor, , is set to 6. Since commodity markets are characterized by short-selling, we allow for limited borrowing and short-selling by restricting the portfolio weight to between -0.5 to 1.5. *** denotes statistical significance at the 1% level.

45

Table 13: Structural break-based profits from a dynamic trading strategy

Markets Risk aversion parameter Oil 0.0149***

(32.2523) 0.0147*** (32.2025

0.0144*** (31.9847)

Gold 0.0087*** (34.9031)

0.0086*** (33.5244)

0.0086*** (34.3783)

Platinum 0.0085*** (43.7461)

0.0083*** (40.8527)

0.0081*** (2.7859)

Silver 0.0062*** (16.6511)

0.0063*** (34.1055)

0.0068*** (31.0397)

This table reports profits from a dynamic trading strategy based on a mean-variance investor framework for which portfolio weights are computed based on equations (16) to (18). The forecasts are generated using a structural break predictive regression model (Equation 5) based on an expanding window. We take the first 50% of the sample and generate the first forecast; then, we take the first 50% plus the observation containing the forecasted return and generate return for the next day. We repeat this process until the end of the sample. Since we use daily data and expanding window, each window of predictive regression model produces a structural break, allowing the investor to update his beliefs (using not only information contain in the commodity futures market but also in the structural break) in forecasting returns for the next day. In this way, we mimic real time trading. Since commodity markets are characterized by short-selling, we allow for limited borrowing and short-selling by restricting the portfolio weight to between -0.5 to 1.5. *** denotes statistical significance at the 1% level.