An analysis of commodity markets: What gain for investors?

Journal of Banking & Finance 37 (2013) 3878–3889

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Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf

An analysis of commodity markets: What gain for investors? Paresh Kumar Narayan a,⇑, Seema Narayan b, Susan Sunila Sharma a a b

Centre for Financial Econometrics, School of Accounting, Economics, and Finance, Deakin University, Melbourne, Australia School of Economics, Finance and Marketing, RMIT University, Melbourne, Australia

a r t i c l e

i n f o

Article history: Received 11 July 2012 Accepted 5 July 2013 Available online 12 July 2013 JEL classification: C22 G11 G17

a b s t r a c t 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. Ó 2013 Elsevier B.V. All rights reserved.

Keywords: Commodity futures Commodity spot Trading strategies Profits

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 great was the influence of the oil price rise that when it reached the US$100 per barrel mark, it created a psychological barrier for investors in the US market (Narayan and Narayan, 2013). Gold prices have also risen sharply over the last decade, having quadrupled over the 2001–2010 period; a detailed analysis can be found in Baur and McDermott (2010). As noted in Baur and McDermott (2010), gold prices tend to react positively to negative market shocks, which is a behavior inconsistent with other asset classes. With respect to oil prices, Narayan and Sharma (2011) show that all sectors on the New York Stock Exchange respond significantly to oil price shocks. It follows that the relevance of oil and gold prices to the functioning of financial markets has been well-documented by the literature. The commodity futures market is even more relevant because, as explained by French (1986), it serves two social functions. The ⇑ Corresponding author. Tel.: +61 3 9244 6180; fax: +61 3 9244 6034. E-mail addresses: [email protected] (P.K. Narayan), seema. [email protected] (S. Narayan), [email protected] (S.S. Sharma). 0378-4266/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jbankfin.2013.07.009

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, 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 provoked significant interest in this topic. The key limitations of this literature, however, are the economic implications and the 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, 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

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the spot market is only the first step in informing investors. 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 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

RSt ¼ ðr  dÞ þ RFt ;

ð1Þ

where Ft is the index futures price at time t, St is the index spot price at time t, r  d is the net cost of carrying the underlying stocks in the index—that is, the rate of interest cost r less the rate at which dividend yield accrues to the stock index portfolio holder d, and T is the expiration date of the futures contract, so T  t is the time remaining in the futures contract life. Stoll and Whaley (1990) show

ð2Þ

RSt

where is the spot price index return computed as RSt ¼ lnðSt =St1 Þ  100, and RFt is the futures price index return computed as RFt ¼ ln ðF t =F t1 Þ  100 . 2.2. Estimation approach Based on Eq. (2), our predictive regression model is of the following form:

RSt ¼ b0 þ b1 RFt1 þ et ;

ð3Þ

The variables are as previously defined; the error term is characterized mean and variance r2. Eq. (3), assuming that  by azero 0 F yt1 ¼ 1; Rt1 and b = (b0, b1)0 , can be expressed as follows:

RSt ¼ y0t1 b þ et ;

ð4Þ

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:

RSt ¼ y0t1 b0 þ et ;

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 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:

F t ¼ St eðrdÞðTtÞ ;

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:

t ¼ 1; . . . ; k;

RSt ¼ y0t1 ðb0 þ uÞ þ et ; 0



b00 ; b01

ð5Þ

t ¼ k þ 1; . . . ; T;

ð6Þ



where b ¼ and u = (u0, u1). The structural break model in matrix notation takes the following form:

RSt ¼ Yb0 þ Y 0k u þ e; Here

 0 R ¼ RS1 ; . . . ; RST ; Y ¼ ðy0 ; . . . ; yT1 Þ0 S

ð7Þ and

e = (e1, . . . , eT).

Rapach and Wohar (2006) show that when the structural break date, k, is known, one can simply apply the familiar Chow (1960) structural break test. The Chow test amounts to testing the null hypothesis that u = 0 against the alternative hypothesis that there is a structural break (u – 0). The Chow test has been extended by Andrews (1993) in the case of an unknown structural break date. Specifically, Andrews (1993) considers SupF test statistic. This requires a sample trimming factor (say s), which we set to 15%. The SupF 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:

 0  ^ ¼ argmin ^^ k k2½sT;ð1sÞT ek ek :

ð8Þ

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 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 m breaks and (m + 1 regimes), which takes the following form:

RSt ¼ y0t1 bl þ et ;

t ¼ T l1 þ 1; . . . ; T l :

ð9Þ

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

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For j = 1, . . . , m + 1, bl is the vector of regression coefficients in the jth regime. The m-partition (T1, . . . , Tm) denotes regime-specific break dates, which are explicitly treated as unknown in Eq. (10). The Bai and Perron (1998) procedure estimates the unknown regression coefficients by least squares. For each m-partition (T1, . . . , Tm), the least squares estimates of bl 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 bðfT 1 ; . . . ; T m gÞ, where b ¼ ðb10 ; . . . ; bmþ10 Þ. Substituting this into Eq. (10), we have:

investigated here. First we compare mean returns from two types of trading strategies. The first strategy is based on the widelyapplied 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.

ð Tb 1 ; . . . ; Tb m Þ ¼ arg min ST ðT 1 ; . . . ; T m Þ:

3.1. Results on predictability

SSRT ðT 1 ; . . . ; T m Þ ¼

mþ1 X

Ti  2 X RSt  y0t1 bl :

ð10Þ

i¼1 t¼T i1 þ1

T 1;...; T m

ð11Þ

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 SupFt(L) F-statistic and double maximum tests. The SupFt(L) F-statistic, where L represents the upper bound on the possible number of breaks, considers the null hypothesis of no structural breaks (m = 0) against the alternative hypothesis that there are m = k breaks. This involves searching for all possible break dates and minimizing the difference between the restricted and unrestricted sum of squares over all the potential breaks. The double maximum test examines the null hypothesis of no structural breaks (m = 0) against the alternative hypothesis of at least one, through to m structural breaks. There are two forms of the double maximum test, which Bai and Perron (1998) call UDmax and WDmax. The UDmax statistic is the maximum value of the SupFt(L) F-statistic, while the WDmax statistic weights the individual statistics so as to equalize the p-values across values of m . Bai and Perron (1998) also suggest a sequential SupFt(L + 1/L) 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 L breaks against the alternative hypothesis of (L + 1) breaks. For the model with L breaks, the estimated break b1; . . . ; T b m , are obtained by global minimization dates, depicted as T of the sum of squared residuals. The null hypothesis is rejected in favor of a model with (L + 1) breaks, provided that the overall minimum value of the sum of squared residuals is sufficiently smaller than the sum of squared residuals from the L 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. 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

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/ 1987 to 11/22/2011, totaling 9087 observations. 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 Fig. 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 Fig. 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. The results from the predictive regression model, based on Eq. (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 3 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 SupF statistic and its p-value generated using a 15% trimming factor. The SupF statistic examines the null hypothesis of no structural change against the one-sided (uppertail) alternative hypothesis of a structural break. The estimated break date is reported in the last row. 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. 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

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SILVER_SPOT

SILVER_FUTURES

PLATINUM_SPOT

30

30

10

20

20

5

10

10

0

0

-10

-10

-20

-20

-10

-30 1980 1985 1990 1995 2000 2005 2010

-30 1980 1985 1990 1995 2000 2005 2010

-15 1980 1985 1990 1995 2000 2005 2010

20

PLATINUM_FUTURES

0 -5

OIL_SPOT

40

20 10

10

20

0

0

-10

-10

-20

-20

-20

-40

-30 1980 1985 1990 1995 2000 2005 2010

-60 1980 1985 1990 1995

15

GOLD_SPOT

0

-30 -40 2000 2005 2010

-50 1980 1985 1990 1995 2000 2005 2010

GOLD_FUTURES

10

10

OIL_FUTURES

5

5

0

0 -5

-5 -10

-10

-15 1980 1985 1990 1995 2000 2005 2010

-15 1980 1985 1990 1995 2000 2005 2010

Fig. 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, 9087 observations for platinum, and 11,649 observations for gold and silver.

Table 1 Descriptive statistics. Variables

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

Mean

SD

Goldt

F

109.56

0.0159

0.8409

Goldt

S

115.61

0.0159

0.8367

F Oilt S Oilt

104.25

0.0185

2.0274

101.48

0.0197

1.9805

107.32

0.0199

1.5344

Silv

F er t S er t

0.0193

1.5182

Platinumt

F

71.393

0.0131

1.2005

S

94.141

0.0131

1.1243

Silv

114.95

Platinumt

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.

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

Gold

Oil

Platinum

Silver

^0 b

0.0075

0.0120

0.0124

0.0014

^1 b

(0.7940) 0.2156***

(0.6247) 0.1091***

(1.0519) 0.0653***

(0.0910) 0.4691***

(22.8936) 0.0431 474.72*** (0.000) 8/05/1993

(5.6509) 0.003 38.7302** (0.03) 9/07/1988

(5.5497) 0.0033 8.9161 (0.54) 3/09/1995

(28.8302) 0.0666 917.31*** (0.000) 11/24/1993

R2 SupF Break date

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 SupF 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. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

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

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P.K. Narayan et al. / Journal of Banking & Finance 37 (2013) 3878–3889

Table 3 Bai and Perron test for multiple structural breaks based on daily data. Gold UDmax WDmax-1% SupFT(1|0) SupFT(2|1) SupFT(3|2) SupFT(4|3) SupFT(5|4)

Oil ***

473.98 473.98*** 473.9873*** 17.3261*** 17.3261*** 12.0229 –

Platinum ***

45.5336 45.5336*** 45.5336*** 15.7167*** 6.0778 7.0671 –

***

20.8906 26.4271*** 10.6137* 28.1931*** 3.977 2.9652 1.2762

Silver 910.60*** 910.60*** 910.60*** 25.7765*** 5.1694 3.6498 –

This table reports the structural test results based on the Bai and Perron (1998) procedure. Two forms of the double maximum test—UDmax and WDmax—are reported in rows 2 and 3, respectively. The UDmax statistic is the maximum value of the SupFt(L) F-statistic, while the WDmax statistic weights the individual statistics so as to equalize the p-values across values of m. Rows 4–8 report the sequential SupFt(L + 1/L) 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 L breaks against the alternative hypothesis of (L + 1) breaks. For the model with L breaks, the b1; . . . ; T b m , are obtained by global minimization estimated break dates, depicted as T of the sum of squared residuals. The null hypothesis is rejected in favor of a model with (L + 1) breaks, provided that the overall minimum value of the sum of squared residuals is sufficiently smaller than the sum of squared residuals from the L break model. Bai and Perron (1998) provide appropriate critical values. * Statistical significance at the 10% level. *** Statistical significance at the 1% level.

earlier. The results for each of the four regression models are reported column-wise in Table 3, and are organized as follows. The UDmax and the WDmax 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 predictive regression models. The UDmax and the WDmax tests both reject the null of zero breaks at the 1% level. The results from the SupFt 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 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. 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, and 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 predictability. The main implication of this

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.

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 frequencydependent? 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 (Eq. (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 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 Rsquared are all positive, suggestive of the information content in futures prices. This suggests that greater evidence of spot return predictability is found with high frequency data. 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 regimedependent. 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. 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

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 regimedependent 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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P.K. Narayan et al. / Journal of Banking & Finance 37 (2013) 3878–3889 Table 4 Predictive regression model results for different regimes based on daily data. Predictor

Regime 1 ^0 b

Regime 2 R

^1 b ***

2

Gold

0.01349 [0.4451]

0.4138 [20.185]

0.1479

Oil

0.0329 [0.8157]

0.3936*** [8.6130]

0.0368

Platinum

0.0043 [0.2449]

0.0091 [0.4601]

0.0000

Silver

0.0342 [0.8072]

0.8749*** [28.044]

0.2142

End point 6/16/1986 [6/27/1985, 5/ 18/1988] 9/7/1988 [8/7/1987, 8/ 29/1989] 3/9/1995 [7/2/1994, 9/ 7/1995] 11/21/1987 [7/5/1987, 4/ 1/1989]

^0 b

Regime 3 R

^1 b

2

0.0023 [0.1668]

***

0.3052 [16.235]

0.0912

0.0191 [0.7862]

0.1112*** [4.5023]

0.0030

0.0039 [0.1622]

0.2292*** [7.8789]

0.0329

0.0056 [0.2838]

1.0940*** [36.346]

0.3761

End point 8/5/1993 [4/29/1993, 11/15/1993] 1/11/2007 [4/3/2005, 5/5/ 2009 ] 3/2/2000 [4/24/1999, 2/ 7/2001] 11/24/1993 [11/3/1993, 12/3/1993]

R2

End point

0.0117 [0.9834]

*

0.036317 [1.9845]

0.0017

0.0433 [0.8990]

0.0801* [1.9226]

0.0020

6/4/2001 [8/19/1998, 7/ 11/2002] 11/22/2011

0.0274 [1.4353]

0.0519*** [3.0754]

0.0022

11/22/2011

0.0303 [1.5547]

0.0421 [0.9548]

0.0006

11/22/2011

^1 b

^0 b

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. * Statistical significance at the 10% level. *** Statistical significance at the 1% level.

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

RSt  lRS ¼ l1;t ; RFt  lRF ¼



  2    RFt  lRF þ l2;t : exp q RFt1  lRF

ð12Þ ð13Þ

Here, lRS and lRF 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 b1; and (d) create an empirical distribution of t-statistics for b1. The results based on both daily and monthly data are reported in 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 that. 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 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 4 The model was estimated using GAUSS codes available from David Rapach’s website.

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

Oil

^0 b

0.274

^1 b

(1.0631) 0.2978 (1.1541) 0.0035 15.734** (0.02) 3/30/2001

R2 SupF Break date

Platinum

Silver

0.3390

0.0124

0.0014

(0.5716) 1.2789**

(1.0519) 0.0653***

(0.0910) 0.4691***

(2.1485) 0.0134 6.8823 (0.5) 9/28/1990

(5.5497) 0.0033 8.9161 (0.54) 3/09/1995

(28.8302) 0.0666 917.31*** (0.000) 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 SupF 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. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

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

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

Regime 1

Regime 2 2

R

^1 b

^0 b

End point

Gold

0.3706 [1.2014]

0.1816 [0.5707]

0.0012

Oil

0.3907 [0.3025]

3.6858*** [3.0426]

0.09618

Platinum

0.2877 [0.7119]

0.4645 [0.9618]

0.0062

Silver

2.9643 [1.3743]

0.2663 [0.1939]

0.0006

3/30/2001 [6/30/1997, 2/27/2004] 9/28/1990 [9/30/1987, 2/28/1994] 6/30/1999 [6/30/1995, 11/29/2002] 2/28/1985 [4/29/1983, 11/30/1994]

Regime 3 2

^1 b

^0 b ***

**

R

End point

^0 b

^1 b

R2

End point

1.7601 [3.8768]

0.9531 [2.2164]

0.0372

10/31/2011

–

–

–

–

0.1004 [0.1262]

1.3390 [1.6034]

0.01473

0.8191 [0.7905]

3.3316*** [3.2430]

0.11492

10/31/2011

0.7675 [1.4079]

1.6519*** [3.4566]

0.0747

1/31/2005 [8/30/2002, 8/29/2008] 10/31/2011

–

–

–

–

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. * Statistical significance at the 10% level. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

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

Panel A: Daily data

Gold Oil Platinum Silver

Panel B: Monthly data

^k b

t-Stat

p-Value

^k b

t-Stat

p-Value

0.2597*** 0.1314** 0.0536*** 0.2994***

8.1240 2.0655 2.8650 9.2579

0.0000 0.0180 0.0100 0.0000

0.0036 0.1338* 0.1562* 0.0520

0.0517 1.3724 1.5696 0.8041

0.5000 0.0900 0.0900 0.1700

This table reports results from a non-linear pre b1 dictive 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:

RSt  lRS ¼ l1;t ;    2    RFt  lRF ¼ exp q RFt1  lRF RFt  lRF þ l2;t : Here, lRS and lRF 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 b1, 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). * Statistical significance at the 10% level. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

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. 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 longterm MA. To see this relationship formally, let us: (a) define the short-term and long-term of the MA as S and L days, respectively; and (b) let Longt be an indicator of the trading position on day t.

Long t ¼ 1 if S

1

S X RSt1 s¼1

¼0

otherwise:

! 1

PL

! L X S Rtl ; l¼1

As in Ratner and Leal (1999), we use a number of specifications for S and L; in particular, we set S = 1, 2 and 5, and L = 50, 150 and 200. 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 Pt, are computed as follows:

Pt ¼ Long t ðP t =Pt1  1Þ þ ðLong t  1ÞðPt =P t1  1Þ  0:001jLong t  Long t1 j:

ð14Þ

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 (0.1%) 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 the result is with

P.K. Narayan et al. / Journal of Banking & Finance 37 (2013) 3878–3889 Table 8 MA technical trading rule profits. MA(1, 50)

MA(1, 150)

MA(5, 150)

MA(2, 200)

Average

Panel A: Without price band Oil 0.3209*** 0.1806*** (16.7034) (9.1589) Gold 0.1496*** 0.0919*** (16.9390) (10.3977) Silver 0.2574*** 0.1613*** (16.9524) (10.6180) Platinum 0.1762*** 0.1059*** (15.1354) (8.9990)

0.0527*** (2.6626) 0.0167* (1.8805) 0.1613*** (10.5660) 0.0329*** (2.7814)

0.0836*** (4.2265) 0.0406*** (4.5900) 0.0658*** (4.3034) 0.0494*** (4.1575)

0.1595*** (8.1879) 0.0747*** (8.4518) 0.1615*** (10.6099) 0.0911*** (4.2988)

Panel B: With 1% price band 0.1159*** Oil 0.1411*** (7.2662) (4.5606) Gold 0.0274*** 0.0186** (3.0688) (2.0908) 0.0566*** Silver 0.0965*** (6.2850) (3.7334) Platinum 0.0567*** 0.0167 (4.8132) (1.4090)

0.0153 (0.7395) 0.0157 (1.7690) 0.0138 (0.9085) 0.0068 (0.5685)

0.0137 (0.6675) 0.0124 (1.4237) 0.0109 (0.7226) 0.0047 (0.3947)

0.0715*** (3.3085) 0.0107 (1.2036) 0.0445*** (2.9124) 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 S and L days, respectively; and (b) let Longt be an indicator of the trading position of day t.

Long t ¼ 1 if S1

S X RSt1 s¼1

¼0

! P L1

! L X RStl ;

3885

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 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. 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.

l¼1

otherwise:

We use a number of specifications for S and L; in particular, we set S = 1, 2 and 5, and L = 50, 150 and 200. We allow transaction costs of 0.1% each time a long or short position is established, and the adjusted returns, or profits Pt, are computed as follows:

Pt ¼ Long t ðPt =Pt1  1Þ þ ðLong t  1ÞðPt =Pt1  1Þ  0:001jLong t  Long t1 j: 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. * Statistical significance at the 10% level. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

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. 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.

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, are much less so than those obtained from the oil and silver markets. 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 (CP) to the recent maximum (Pmax) and minimum price (Pmin); (b) TRBR emits a buy signal when CP > Pmax by at least a prespecified band—we consider a 1% price band; (c) TRBR emits a sell signal when CP < Pmin by at least a prespecified 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

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Table 9 Sub-sample MA trading rule. MA(1, 50)

MA(1, 150)

MA(5, 150)

MA(2, 200)

Average

Panel A: Without price band Sub-sample 1 Oil 0.2825*** (6.6924) Gold 0.1994*** (7.1243) Silver 0.3272*** (8.3483) Platinum 0.1418*** (8.2020)

0.15189*** (3.2432) 0.1141*** (4.0775) 0.2131*** (5.4525) 0.0887*** (5.1315)

0.0671 (1.4268) 0.0384 (1.3683) 0.0708* (1.8022) 0.0049 (0.2836)

0.0690 (1.4638) 0.0658*** (2.2926) 0.1017*** (2.5645) 0.0305* (1.7249)

0.1426*** (3.2066) 0.1044*** (3.7157) 0.1782*** (4.5419) 0.0666*** (3.8355)

0.3272*** (13.546) 0.1228*** (8.4035) 0.2012*** (8.1589) 0.1513*** (6.1120)

0.1857*** (7.4937) 0.07650*** (5.1945) 0.1134*** (4.3686) 0.0935*** (3.5273)

0.0367 (1.4733) 0.0083 (0.5633) 0.0142 (0.5431) 0.0105 (0.3948)

0.0813*** (3.2636) 0.0294* (1.9823) 0.0409 (1.5927) 0.0365 (1.2844)

0.1577*** (6.4442) 0.0593*** (3.0447) 0.0924*** (3.6658) 0.07295*** (2.8296)

0.3405*** (6.8446) 0.1427*** (13.508) 0.2457*** (12.664) 0.2111*** (11.120)

0.2217*** (4.2014) 0.0919*** (8.4911) 0.1577*** (8.0128) 0.1267*** (6.4737)

0.1089** (2.0550) 0.0126 (1.1572) 0.0128 (0.6455) 0.0596*** (3.0301)

0.1273** (2.3927) 0.0380*** (3.4717) 0.0620*** (3.1243) 0.0669*** (3.3983)

0.1996*** (3.8734) 0.0713*** (6.6569) 0.11955*** (6.1115) 0.1160*** (6.0056)

0.1545** (2.5837) 0.0678** (2.4156) 0.0910** (2.3344) 0.0385** (2.2161)

0.0003 (0.0048) 0.0088 (0.3136) 0.027415 (0.7047) 0.0089 (0.5130)

0.0989 (1.6516) 0.0537 (1.7974) 0.0436 (1.1158) 0.0212 (1.1932)

0.0883* (1.6439) 0.0449 (1.5662) 0.0707* (1.8018) 0.0267 (1.5230)

0.1654*** (6.7632) 0.0220 (1.4722) 0.0383 (1.5256) 0.0606*** (2.4271)

0.0966*** (3.8849) 0.0089 (0.5996) 0.0367 (1.4226) 0.0060 (0.2229)

0.0106 (0.4194) No signal

0.0208 (0.8351) 0.0111 (0.6846) 0.0004 (0.0146) 0.0306 (0.7871)

0.0734*** (2.9757) 0.0066 (0.4624) 0.0251 (0.9876) 0.0080 (0.4724)

0.06914 (1.2323) 0.0189* (1.7531) 0.1044*** (5.3241) 0.0693*** (3.6072)

0.1743*** (3.2904) 0.0083 (0.7573) 0.0541*** (2.7343) 0.0059 (0.3014)

0.0044S (0.0825) 0.0565** (2.2148) 0.0178 (0.8679) 0.0032 (0.1299)

0.1080*** (2.0446) 0.0161 (1.0496) 0.0001 (0.0069) 0.0084 (0.4230)

0.0328 (0.5989) 0.0033 (0.3363) 0.0441** (2.2299) 0.0201 (1.0504)

Sub-sample 2 Oil Gold Silver Platinum Sub-sample 3 Oil Gold Silver Platinum

Panel B: With 1% price band Sub-sample 1 Oil 0.1002** (2.3450) Gold 0.0669** (2.3655) Silver 0.1209*** (3.0523) Platinum 0.0380** (2.1698) Sub-sample 2 Oil Gold Silver Platinum Sub-sample 3 Oil Gold Silver Platinum

No signal No signal

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 L days, respectively; and (b) let Longt be an indicator of the trading position of day t. ! ! S L X X Long t ¼ 1 if S1 RSt1 P L1 RStl ; ¼ 0 otherwise s¼1

l¼1

We use a number of specifications for S and L; in particular, we set S = 1, 2 and 5, and L = 50, 150 and 200. We allow transaction costs of 0.1% each time a long or short position is established, and the adjusted returns, or profits Pt, are computed as follows:

Pt ¼ Long t ðPt =Pt1  1Þ þ ðLong t  1ÞðP t =Pt1  1Þ  0:001jLong t  Long t1 :j 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. * Statistical significance at the 10% level. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

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P.K. Narayan et al. / Journal of Banking & Finance 37 (2013) 3878–3889 Table 10 Profits from trading range break rules. 50 days

Table 11 Technical trading rule profits for commodity futures. 150 days

200 days

Panel A: Without price band Oil 0.0743*** (3.8291) Gold 0.0328*** (3.5821) Silver 0.0643*** (3.9263) Platinum 0.0612*** (5.1830)

0.0417** (2.1226) 0.0232(CP)** (2.6210) 0.0371** (2.4246) 0.0288** (2.4115)

0.0227 (1.1491) 0.0251*** (2.8353) 0.0322** (2.1331) 0.0260** (2.1783)

Panel B: With 1% price band Oil 0.0725*** (3.7033) Gold 0.0285*** (3.1032) Silver 0.0623*** (3.8056) Platinum 0.0510*** (4.2417)

0.0453** (2.2531) 0.0256*** (2.8890) 0.0379** (2.4805) 0.0309** (2.5925)

0.0209 (1.0388) 0.0235** (2.6506) 0.0296* (1.9651) 0.0316** (2.6455)

MA(1, 150)

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 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.

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 markets, as one referee of this journal suggested, there is nothing that stops us from examining the profitability of the 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 are the same as those obtained for the commodity spot markets, consistent with the descriptive statistics provided in Table 1.5 Detailed results are available from the corresponding author upon request.

MA(5, 150)

Panel A: MA rule-based profits with 1% price band Oil 0.1411⁄⁄⁄ 0.1159⁄⁄⁄ 0.0153 (7.2662) (4.5606) (0.7395) ⁄⁄⁄ ⁄⁄ Gold 0.0274 0.0186 0.0157 (3.0688) (2.0908) (1.7690) 0.0566⁄⁄⁄ 0.0138 Silver 0.0965⁄⁄⁄ (6.2850) (3.7334) (0.9085) Platinum 0.0567⁄⁄⁄ 0.0167 0.0068 (4.8132) (1.4090) (0.5685) Sub-sample 1

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 (Pmax) and minimum price (Pmin); (b) TRBR emits a buy signal when CP > Pmax by at least a pre-specified band—we consider a 1% price band; (c) TRBR emits a sell signal when CP < Pmin 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%. * Statistical significance at the 10% level. ** Statistical significance at the 5% level. *** Statistical significance at the 1% level.

5

MA(1, 50)

MA(2, 200)

Average

0.0137 (0.6675) 0.0124 (1.4237) 0.0109 (0.7226) 0.0047 (0.3947)

0.0715⁄⁄⁄ (3.3085) 0.0107 (1.2036) 0.0445⁄⁄⁄ (2.9124) 0.0178 (1.5121)

Sub-sample 2

Sub-sample 3

Panel B: Average profits across all trading rules for different regimes with 1% price band 0.0734⁄⁄⁄ 0.0328 Oil 0.0883⁄ (1.6439) (2.9757) (0.5989) Gold 0.0449 0.0066 0.0033 (1.5662) (0.4624) (0.3363) Silver 0.0707⁄ 0.0251 0.0441⁄⁄ (1.8018) (0.9876) (2.2299) Platinum 0.0267 0.0080 0.0201 (1.5230) (0.4724) (1.0504) 50 days

150 days

200 days

Panel C: Profits from range break trading rules with 1% price band Oil 0.0725⁄⁄⁄ 0.0453⁄⁄ 0.0209 (3.7033) (2.2531) (1.0388) ⁄⁄⁄ ⁄⁄⁄ Gold 0.0285 0.0256 0.0235⁄⁄ (3.1032) (2.8890) (2.6506) Silver 0.0623⁄⁄⁄ 0.0379⁄⁄ 0.0296⁄ (3.8056) (2.4805) (1.9651) Platinum 0.0510⁄⁄⁄ 0.0309⁄⁄ 0.0316⁄⁄ (4.2417) (2.5925) (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.

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:

 1 Et r Stþ1  cVar t frStþ1 g; 2

ð15Þ

such that, given a portfolio of pt+1 for the risky asset, the utility simply becomes:

 1

 rf ;tþ1 þ ptþ1 Et rStþ1  cp2tþ1 þ Vart r Stþ1 ; 2

ð16Þ

where r Stþ1 is the commodity spot return, rf,t+1 is the risk-free rate of return, Vart is the rolling variance of the risky asset, c is the risk aversion factor, and pt+1 is the investor’s portfolio weight in period t + 1, computed as follows:

ptþ1 ¼

Et fr Stþ1 g  r f ;tþ1 : cVart frStþ1 g

ð17Þ

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

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Table 12 Regime-wise dynamic trading strategies of a mean–variance investor. Oil Regime 1 Regime 2 Regime 3

Gold ***

0.011 (2.822) 0.010*** (21.897) 0.001*** (15.206)

Platinum ***

***

0.062 (11.00) 0.027*** (16.539) 0.0009*** (74.635)

0.015 (121.208) 0.09*** (32.941) 0.008*** (44.331)

Silver 0.250*** (3.629) 0.324*** (15.146) 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 Eq. (17). 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, c, 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 and 1.5. *** Statistical significance at the 1% level.

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

Oil Gold Platinum Silver

Risk aversion parameter

c=3

c=6

c = 12

0.0149*** (32.2523) 0.0087*** (34.9031) 0.0085*** (43.7461) 0.0062*** (16.6511)

0.0147*** (32.2025 0.0086*** (33.5244) 0.0083*** (40.8527) 0.0063*** (34.1055)

0.0144*** (31.9847) 0.0086*** (34.3783) 0.0081*** (2.7859) 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 Eq. (17). The forecasts are generated using a structural break predictive regression model (Eq. (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 contained 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 and 1.5. *** Statistical significance at the 1% level.

from investing in a risky asset if its variance is rising over time. The risk aversion factor, c, 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 shortselling, we allow for limited short-selling and borrowing at the risk-free rate by restricting the weight to lie between 0.5 and 1.5.6 The expected excess return is based on a predictive regression model of the form represented by Eq. (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.

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 and 1.5; and (c) we allow for no short-selling and borrowing by setting the weight to 0–1. 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.

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. 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 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 maximization-based profits, we wish to emphasize that the utilitybased 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 a 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 characterized 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 it 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 account.7 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 operating, 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. A disadvantage of our previous analysis was, we assumed, that the investor knows the break dates and, using those 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, 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 using technical trading rules tends to be very high and that the irrationality of technical trading is an important component of the total opportunity cost of using technical trading rules.

P.K. Narayan et al. / Journal of Banking & Finance 37 (2013) 3878–3889

we do the following. We estimate the in-sample predictive regression model with a structural break (Eq. (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 (i.e., 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 the 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 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 transaction costs and different risk aversion parameters. We find that investors can make statistically significant profits from all commodities. 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 lower 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 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. References Andrews, D.W.K., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 62, 1383–1414. Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78.

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