Abstract
One promise of commodity investments is that they offer a long run hedge against inflation. But do they? The authors undertake a comprehensive investigation of commodities’ inflation-hedging ability across 50 commodities for 80 countries and seven centuries of data. They confirm that commodities have offered protection against inflation throughout history, especially over long, multiyear periods. Nonetheless, hedging capacity has varied remarkably—both over time and across geographical regions. Following many centuries of agricultural commodity primacy, energy commodities have taken the lead only recently. They recommend that investors should continue to include commodities in their portfolios to protect against inflation. However, not all commodity types offer the same protection level, which differs over time and across countries and geographies.
TOPICS: Commodities, global markets, performance measurement, financial crises and financial market history
Key Findings
▪ The authors examine the inflation-hedging ability of commodities using data from seven centuries.
▪ Commodities offer protection against inflation, although hedging capacity varies over time and between countries.
▪ Following many centuries of the primacy of agricultural commodities, energy commodities have taken the lead recently.
A central and time-old problem in finance is the erosion of the value of money with the passage of time. Related to this issue, and within the context of portfolio management, is the question of which asset classes can effectively protect investors against inflation. Commodities are one such asset class, offering a rate of return that is related to the inflation rate (Greer 2000). Commodities are positively correlated with inflation and therefore offset the erosion of value by increasing in value in times of heightened inflation (Conover et al. 2010; Arnold and Auer 2015; Levine et al. 2018). Another important characteristic is that commodities have been available and readily accessible to investors throughout history, unlike modern assets such as stocks, bonds, or futures.
The inflation-hedging capacity of commodities has been widely studied. Numerous studies document the inflation-hedging properties of both individual commodities, such as gold, silver, energy, or timber (Fulli-Lemaire 2012; Bampinas and Panagiotidis 2015; Salisu, Ndako, and Oloko 2019; Zhang et al. 2011) and aggregate commodity baskets (Crawford, Liew, and Marks 2013; Fulli-Lemaire 2012; Zaremba, Umar, and Mikutowski 2019). Such studies frequently rely on data going back just a few decades—although some have used data going back to the 19th century (Bampinas and Panagiotidis 2015). Mahlstedt and Zagst (2016) demonstrate that inflation-hedging properties largely depend on long-run changes in the economy’s state.
What emerges from the literature is that commodities, to varying degrees, offer protection against inflation and that their inflation-hedging capacity varies over time. Nonetheless, existing studies rely on limited study periods and seldom go beyond individual countries or commodity groups. Meanwhile, neither commodity behavior nor the character of national economies is static. Multidecade commodity cycles and structural changes in economies challenge the long-run stability of the commodity-inflation relationship. Taking energy commodities as an example, it is true that these have been shown to serve as a solid inflation hedge (see, for instance, Fulli-Lemaire 2012). However, the role of oil in a modern service-based economy may be completely different in the forthcoming decades compared to its role in the 20th century. Furthermore, other energy sources may potentially replace oil’s dominant position, just as oil and gas displaced coal.
These long-run changes require a truly broad look at the inflation-hedging properties of commodities. Consequently, we undertake a comprehensive investigation of commodities’ hedging capacity, which is unprecedented in the published literature. We use a unique dataset that spans 750 years and consider the inflation-hedging capacity of commodities as a general class and as energy, agricultural, and industrial commodity aggregates. We also consider individual commodities. Notably, we evaluate a vast number of observations for individual commodities spanning periods from 54 years (for coal gas) to 755 years (for wheat, barley, gold, and silver). Using commodity aggregates, we then consider how inflation-hedging capacity has evolved over the last seven centuries. Finally, we investigate the effectiveness of commodity aggregates as a hedge against inflation across countries, using an extensive sample comprising 82 countries classified geographically. Therefore, we present the most comprehensive overview of commodities’ hedging capabilities, providing insights across time, classes, and geographies and at the individual commodity level.
To keep our analysis clear and simple, we rely on the simple Pearson’s correlation coefficient, which indicates the level of co-movement between inflation and commodities. We opt for correlation analysis, as it is not only intuitive and easy to understand, but also indicative of both the direction and magnitude of hedging capacity (see Spierdijk and Umar 2014).
We find that over our entire sample period comprising seven centuries of annual data, commodities as a class offer protection against inflation. The effect is particularly strong for long investment horizons spanning several decades. For most of our sample period, agricultural commodities are the most effective inflation hedge. Following the Industrial Revolution at the beginning of the 19th century, industrial and energy commodities became increasingly important. This is especially true for the second half of the 20th century, during which energy commodities took the lead and exhibited the greatest inflation-hedging capacity. We also find that commodities offer effective protection against inflation across countries. Our general recommendation is that investors should not shy away from including commodities in their portfolios to protect against inflation. Although the inflation-hedging capacity of certain types of commodities has changed, commodities continue to offer protection against inflation.
The remainder of this article is organized as follows. The next section presents the data and methodology, and the third section discusses the results of our analysis. The fourth section concludes the study.
DATA AND METHODOLOGY
Our study uses long-run annual commodity data sourced from the Global Financial Data (GFD) database. Our aggregate measure is the GFD Commodity Composite Index, which aggregates spot prices for approximately 50 commodities on an annual basis starting in 1265 and ending in 2018. This index is then split into three subindices, which we also consider, covering agricultural, industrial, and energy commodities. Where available, indices are based on US prices and English data. The commodity data are compiled from different sources, including stock exchanges and history books, to form a continuous time series (Cole 1938; Clark 2004; Zaremba, Umar, and Mikutowski 2019). Our final set of indices is at the individual commodity level, obtained from the GFD, and falls under the three subindex classifications (see Exhibit 1). Sample lengths for individual commodity time series range from a total of 755 years for some agricultural commodities and precious metals (e.g., barley, wheat, gold) to 54 years for coal and gas.
Inflation-Hedging Capacity of Commodities
NOTES: This exhibit reports correlation coefficients between inflation and a general commodity index, three indices representative of energy, agricultural, and industrial commodities, and finally, individual commodities for which data are available. The Corr. column reports estimated Pearson’s correlation coefficients for a given period. N represents the number of observations in years. The full sample comprises 755 years. Statistical significance at the 1%, 5%, and 10% levels is denoted by asterisks ***, **, and *, respectively.
The reliance on commodity spot prices is an obvious limitation of our study. The commodity premium is usually harvested with commodity futures, which are much more liquid and convenient to trade, as they do not incur storage and transportation costs. Nevertheless, the history of modern futures markets is too short to allow us to perform a comprehensive analysis spanning centuries. Given the close correlation between spot and future returns, in the long run, we expect that the overall conclusions regarding the inflation-hedging capacity of spot prices will hold for investments in commodity futures as well. Consistent with this, Ankrim and Hensel (1993) and Levine et al. (2018) demonstrate that changes in spot prices are the primary driver of the inflation-hedging ability of commodities. We also note the work of Froot, Kim, and Rogoff (1995), who show that that there are short-term deviations from the law of one price in commodities. While these deviations do not persist over the long term, they can nevertheless be over a century long (e.g., English to Dutch barley prices). This implies that although commodities overall may act as a hedge against inflation, as suggested by the main results, this may not always be the case in individual countries because of differing commodity prices and price volatilities. This should be borne in mind when considering results relating to commodities’ inflation-hedging capacity in specific geographic regions and individual countries.
For our general commodity index and subindices, we use commodity prices expressed in British pounds and the United Kingdom’s inflation rate. For analyses of individual countries, we use local inflation rates and commodity prices in local currencies. As with commodity prices, inflation rates are an amalgamation of data from different sources. For example, UK consumer price changes are mostly obtained from Brown and Hopkins (1956, 1957, 1959) and O’Donoghue, Goulding, and Allen (2004) and reflect the consumption basket for British consumers over the centuries. Information detailing the construction of all inflation series is available upon request from the authors.
Notably, a limitation of this approach is that early consumption baskets comprise relatively few products. For example, 13th- to 15th-century sets contain only 11 consumables, encompassing farinaceous products (e.g., rye, barley, peas), meat and fish (e.g., sheep, herrings), drinks (malt), and textiles (canvas).
Descriptive statistics for inflation and commodity returns are reported in Appendix A and Appendix B, respectively. One remarkable observation from our preliminary data analysis, presented in Appendix B, is that the average long-run inflation-adjusted commodity return is negative, amounting to approximately −0.14% per year. In other words, in real terms, commodity spot prices decline rather than increase over time. Although this finding is initially surprising and counterintuitive, it is consistent with the so-called Prebish–Singer hypothesis (Prebisch 1950; Singer 1950), which suggests that commodity prices display a negative secular trend (see Harvey et al. 2010 and Carpantier 2019 for further evidence and discussion). In other words, macroeconomic forces and technological development drive down spot prices in the long run. Cotton is a good example: Once a luxurious commodity in European courts, following the Industrial Revolution, it became a common material used in the manufacture of t-shirts and trousers (Beckert 2015; Berg 2009).
However, these characteristics of commodity spot prices do not negate the overall benefits of commodity investments, especially when exposure is gained through commodity futures. Levine et al. (2018), who study commodity futures prices in the 20th century, acknowledged that commodity return premiums are associated with other return components, such as carry, rather than spot returns. In other words, our observations provide additional support for the widely held view that the commodity premia may be more efficiently and conveniently harvested with commodity futures rather than with physical commodities.
Following Spierdijk and Umar (2014), we rely on Pearson’s correlation coefficient to establish commodities’ inflation-hedging capacity. As our data are of an annual frequency, we rely on yearly price changes in the baseline approach. However, we repeat the estimations for extended measurement periods ranging between 5 and 50 years for robustness. Correlation reflects the strength of a linear relationship between two variables. The greater the correlation between returns on a commodity (or commodity index) and the inflation rate, the greater the specific commodity’s or commodity type’s inflation-hedging capacity. It intuitively follows that if inflation is positively correlated with returns on commodities, then a general increase in price levels is offset by an increase in commodity prices. By holding commodities, investors are protected against the erosion of value.
We begin our analysis by providing an overview of correlations between commodity indices and inflation. Specifically, we consider a composite commodity index, three subindices—namely energy, agricultural, and industrial commodities—and individual commodity indices over the entire sample period. For the aggregate index and three subindices, we use the full data sample spanning seven centuries. Therefore, reported correlation coefficients are estimated using annual inflation and annual commodity price data from 1264 to 2018, comprising 755 observations. For individual commodities, we use the full available series. Usually, these series are of shorter and variable length.
Although an analysis of the full study period provides us with some preliminary insights into the inflation-hedging capacity of commodities in general, it suffers from a limitation. It ignores the potentially changing relationship between inflation and commodities over time. Therefore, in the second step, we calculate rolling correlation coefficients for inflation, the GFD Commodity Composite Index, and the three subindices. We use a historical window of 100 years to calculate rolling correlation coefficients. By estimating rolling correlations, we can analyze how commodities’ inflation-hedging capacity changes over time (Spierdijk and Umar 2014). In the final part of the analysis, we seek to establish whether commodities offer protection against inflation across 84 countries. We classify countries in our sample according to geography: Asia, Europe, North America, Africa, Oceania, and South America. We then examine correlations for our aggregate commodity prices and energy, agricultural, and industrial commodities. In our analysis, we rely on the statistical significance of correlation coefficients to establish whether commodities in general, as a class or on an individual basis, offer protection against inflation.
RESULTS
We begin our analysis of commodities’ inflation-hedging capacity with an overview of general commodity indices and individual commodities (Exhibit 1). Correlation between our aggregate measure, the (GFD) Composite Commodity Index, and inflation is positive and statistically significant (0.52) over the entire period of seven centuries. Except for industrial commodities, the correlation between inflation and the commodity indices is positive and amounts to 0.13 and 0.57 for the energy and agricultural indices, respectively. This leads us to conclude that these classes of commodities offer protection—to a varying extent—against inflation. However, the inflation-hedging capacity of energy commodities is weaker than that of agricultural commodities. The inflation-hedging capacity of industrial commodities as a class is nonexistent, as indicated by an insignificant correlation coefficient of 0.02. This latter finding, of weak hedging capacity for industrial and energy commodities, can be expected given that we consider a sample that spans seven centuries. During this period, economies transitioned from being agricultural-based to industrial-based and then, finally, to service-based. The relatively recent emergence and the rising importance of industrial commodities after the Industrial Revolution demonstrates this. As we show later, industrial and energy commodities as a class show a higher inflation-hedging capacity toward the end of our sample.
Although the correlation coefficient is very simple and intuitively understandable, it does not instantaneously reveal the observed relationship’s economic importance. The correlation between the aggregate commodity index and inflation is 0.52; however, changes in inflation rates explain only about 27% of the variation in commodity returns. This implies that even a well-crafted strategy does not mean that the commodity movements perfectly match inflation changes. Given the volatility of commodity markets, 73% of unexplained variation will result in an “inflation tracking error” of more than 8% per year.
Thus far, we have focused on inflation coefficients estimated using annual commodity price changes and inflation rates. However, when investors seek to hedge their investments against inflation, their horizon is much longer, potentially stretching into decades or even an entire lifespan. Analogously, many institutional investors, such as pension funds or endowments, use horizons exceeding one year. To account for this, we now extend our calculations to longer return intervals, specifically spanning 5 to 50 years. The results of this analysis are reported in Exhibit 2.
Inflation Hedging over Extended Periods
NOTES: This exhibit reports correlation coefficients between inflation and major commodity indices representing the aggregate commodity market, as well as energy, agricultural, and industrial commodities (GFD Indices Commodity Composite Index, GFD Indices Energy Commodity Index, GFD Indices Agricultural Commodity Index, and GFD Indices Industrial Commodity Index). The Pearson product-moment correlation coefficients are calculated for price changes measured over extended periods, ranging between 5 and 50 years. The full sample comprises 755 years of data. Statistical significance at the 1%, 5%, and 10% levels is denoted by asterisks ***, **, and *, respectively.
Many idiosyncratic shocks create short-term noise in commodity returns, but this cancels out in the long term, shedding additional light on the underlying relationship between commodities and inflation. In consequence, the long-run inflation-hedging abilities of commodities are visibly better. Overall, inflation-hedging capacity increases with the investment horizon. For the aggregate commodity index, the correlation coefficients vary from 0.59 for the 5-year horizon to as much as 0.84 for the 50-year horizon. Indeed, the long-run returns and inflation rates uncover very powerful inflation-hedging properties of commodity investments. A strong correlation indicates that commodity exposure can decrease inflation risk substantially. Also, it implies a much lower tracking error for an inflation-hedging strategy, indicating that changes in consumer prices account for approximately 72% of commodity return volatility.
Having considered composite indices, we now concentrate on the individual commodities in Exhibit 1. Given that our sample period spans seven centuries, we have data for an extensive number of individual agricultural commodities, which reflect their economic importance. Grain commodities—namely, barley (correlation of 0.54), oats (0.38), and wheat (0.50)—show a high inflation-hedging capacity. Other agricultural commodities that can also be considered as a somewhat less effective hedge against inflation, but a hedge nevertheless, are potatoes and palm oil (both 0.24), coffee (0.13), and hay and milk (both 0.11). Some animal-related commodities—namely, beef, lamb, and hogs—show a weak or nonexistent inflation-hedging capacity. Moreover, other commodities, such as eggs, butter, and cheese, offer a limited amount of protection.
Although data for individual industrial and energy commodities are limited, natural gas (correlation of 0.24) in the energy commodity class and aluminum (0.27), palladium (0.21), lead and zinc (both 0.17), and steel (0.14) in the industrial class offer some protection against inflation. Our conclusion from this analysis is that early investors would have been able to derive protection from investing in agricultural commodities, specifically, grain-type commodities, over the last seven centuries, and to a lesser extent, from holding some types of metals. Interestingly, precious metals in the form of silver and gold offer limited protection against inflation.
Exhibit 3 reports the results of our rolling correlation analysis. We first focus on our base measure, the aggregate commodity index. The correlation between inflation and general commodity returns is especially high for the first 500 years of the sample. Commodities as a class show a high inflation-hedging capacity, with correlation remaining between 0.6 and 0.8 for most of this period. However, from the beginning of the 19th century, correlation decreases, ranging between 0.2 and 0.4. Commodities continue to offer protection against inflation, but they are no longer as effective.
Rolling Correlations for Different Classes of Commodities
NOTES: This exhibit reports rolling correlations for the base measure of commodity prices, the GFD Commodity Composite Index, and the three subindices representing agricultural, energy, and industrial commodity prices. We use 100 observations to estimate rolling correlation coefficients, starting in 1265.
Before the beginning of the 19th century, the correlation between inflation and agricultural commodities closely follows that between inflation and the composite commodity index. This is likely attributable to the important role of agriculturals, which represent the bulk of commodities available at this point in time. Consistent with this, as mentioned earlier, the consumption basket for 13th- or 14th-century workers contained mostly very basic articles, such as food, drinks, and textiles.
The beginning of the 19th century coincides with the Industrial Revolution, which as Hartwell (2017) argues, saw an increase in the demand for new commodities. Associated technological development brought broader diversification in the consumption basket worldwide, lessening its dependence on food and clothes. It also coincides with a shift away from agricultural to industrial production. Consequently, the inflation-hedging capacity of industrial and energy commodities increases from the beginning of the 19th century. In prior centuries, these commodity classes’ inflation-hedging ability appears to be erratic, with correlation being sometimes positive, sometimes negative. Nevertheless, agricultural commodities show a higher inflation-hedging capacity than other commodity classes up to the second half of the 20th century. Also, until this time, the level of correlation between agricultural commodities and inflation ranges between 0.6 and 0.8, closely coinciding with the correlation between inflation and commodities as a class. This suggests that the inflation-hedging capacity of commodities as a class is attributable to agricultural commodities’ hedging capacity.
It is only during the second half of the 20th century that energy commodities show the highest level of inflation-hedging capacity—higher than that of agricultural and industrial commodities. Furthermore, the inflation-hedging capacity of energy commodities is comparable to that of commodities as a whole during this period, with correlations of around 0.4. This attests to the importance of this commodity class in more recent decades. In contrast, agricultural commodities’ inflation-hedging capacity continues to decline, with correlations of around 0.2 observed in the second half of the 20th century. Energy commodities displace agricultural commodities as the commodity class with the greatest inflation-hedging potential. To sum up, although agricultural commodities show the highest inflation-hedging capacity until the middle of the 20th century, energy commodities offer greater protection from the middle of the 20th century onward. This contrasts with the full-sample correlation analysis presented in Exhibit 1, which does not consider the changing inflation-hedging capacity of the three commodity classes.
We now turn to a geographical analysis of the inflation-hedging capacity of commodities. In Exhibit 4, we report correlations between commodity prices and inflation for the period between 1900 and 2018, subject to data availability. No differing patterns emerge across groupings. Instead, the main similarity is that the relationship between inflation and commodity prices is widespread within each geographical group. For example, commodities as a class show an inflation-hedging capacity for 15 of the 29 Asian countries. For Europe, this stands at 26 of 31 countries. A similar observation of widespread inflation-hedging ability can be made for North America, Africa, Oceania, and South America. Commodities offer protection against inflation in all Oceanian and South American countries in the sample and 8 of the 10 African countries. It appears that commodities protect against inflation in most countries. What differs is the inflation-hedging capacity itself offered by commodities across countries. For example, the correlation between commodity prices and inflation is not significant for several countries. In Asia, examples are Azerbaijan, Bahrain, Bangladesh, and Kazakhstan, among others. However, for many countries, the correlation is significant, ranging between 0.20 for Iran and 0.92 for Israel. The same can be said about Europe. Commodities are not a hedge against inflation in Cyprus, Estonia, Latvia, Lithuania, and the Slovak Republic. However, commodities appear to be a very effective hedge against inflation in Romania (0.79), Poland (0.47), and Slovenia (0.46), amongst others. An analogous observation extends to the other geographic regions. This analysis concludes that commodities, in general, hedge against inflation across geographies, although their hedging capacity differs in different places. Overall, investors stand to benefit from holding commodities, although the protection against inflation offered by doing so varies across markets.
Inflation-Hedging Capacity of Commodities across Countries
NOTES: This exhibit reports correlations between inflation and commodities as a class and energy (Energy), agricultural (Agri.), and industrial (Indust.) commodities in the respective countries. N refers to the number of observations for each country. The maximum number of observations covers the period from 1900 to 2018, totaling 119 observations. Asterisks ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.
It appears that for countries where inflation is correlated with commodities in general, energy, agricultural, and industrial commodities are also a hedge against inflation. This is expected as these classes of commodities compose the aggregate composite commodity index. For example, inflation in Hong Kong is correlated with general commodity prices (0.27) but also with energy (0.22), agricultural (0.34), and industrial (0.27) commodities. In a limited number of instances, only a single commodity class offers protection against inflation. For example, for Iran, agricultural commodities (correlation of 0.26) provide protection against inflation. For Cyprus, energy commodities (0.24) are a hedge against inflation. For Malaysia, only industrial commodities (0.21) have an inflation-hedging capacity. The conclusion is that for certain countries, a specific commodity class protects against inflation. To protect themselves from inflation, investors should invest in commodities related to the commodity class that offers protection against inflation or the most protection in a specific market. Another pertinent question relates to the commodity class that shows the greatest inflation-hedging capacity for each geographic region. To gain insight into this, we average the correlation coefficients for the composite commodity index and the three groups of commodities. We summarize the results in Exhibit 5.
Inflation-Hedging Capacity across Regions
NOTE: This exhibit reports average correlation coefficients between inflation and commodities as a class and energy (Energy), agricultural (Agri.), and industrial (Indust.) commodities across geographic regions.
Inflation-hedging capacity differs across geographic regions. Commodities as a class are most effective in South America (0.67), followed by North America (0.43). They are least effective in Oceania (0.25) and Asia (0.28). Hedging capacity also differs according to type. For example, in Oceania, energy commodities (0.26) offer the greatest protection against inflation, whereas agricultural commodities (0.17) offer the lowest. In contrast, in North America, agricultural commodities (0.45) offer the greatest protection level, whereas industrial commodities offer the lowest (0.38). In South America, all commodity classes provide comparable levels of protection.
Differences in the inflation-hedging capacity of the different commodity types can be potentially attributed to deviations from the law of one price. Such deviations mean that commodity prices behave differently across different regions and countries, whether over the short term or an extended period. Consequently, the inflation-hedging capacity of commodities will differ across regions and countries to varying extents. Reasons for deviations relate to any event or persistent state that may disrupt integration, resulting in goods markets remaining segmented (Froot, Kim, and Rogoff 1995). The overall observation is that commodities protect against inflation, regardless of the geographic region. However, the level of protection provided differs. The same holds for commodity classes. All commodity types—be they energy, agriculture, and/or industrial related—provide protection against inflation. However, carefully selecting a specific commodity type will maximize the amount of protection offered.
CONCLUSIONS
We provide further evidence in support of the inflation-hedging capacity of commodities. Our findings generally confirm the results of prior studies. Investors can protect themselves against inflation by holding commodities as an asset class. This holds for most countries. Our results differ because we take a step back in time—seven centuries, to be exact—and show that commodities have offered protection against inflation throughout history. The effect is particularly strong for extended investment horizons—spanning several years or even decades—thus benefiting long-run investors.
Notably, investors throughout our study period would have benefited by investing in agricultural commodities and, specifically, in grain-related commodities. Nevertheless, the inflation-hedging capacity of commodities has changed over time. Agricultural commodities offered high levels of protection against inflation right up to the beginning of the 19th century. After that, coinciding with the start of the Industrial Revolution, energy and industrial commodities offered a greater protection level. We attribute this to the rising demand for and the rising importance of these commodities and the broader diversity of goods in the consumption baskets used to determine inflation.
Finally, energy commodities offered the greatest level of protection during the second half of the 20th century. We also show that the inflation-hedging capacity of commodities differs across geographic regions. For example, investors in South American commodities will receive a higher level of protection against inflation than those in Asia. Hedging capacity also differs across commodity classes. In Oceania, for example, investors receive greater protection by investing in energy commodities rather than agricultural commodities.
We recommend that investors should continue looking toward commodities to protect themselves against inflation. Not all commodity classes offer the same protection level, however, and the level of protection offered changes over time. Investors should be aware of which commodity class offers the greatest level of protection in their region and should tailor their portfolio accordingly. Our analysis provides information that makes this possible.
ACKNOWLEDGMENTS
Adam Zaremba and Mateusz Mikutowski acknowledge the support of the National Science Center of Poland (projects no. 2018/31/N/HS4/01753 and 2019/33/B/HS4/01021).
APPENDIX A
DESCRIPTIVE STATISTICS FOR INFLATION ACROSS COUNTRIES
For each listed country, the descriptive statistics are presented as follows: Mean is the mean inflation observed for N, which is the country’s number of observations. Std. dev. is the standard deviation of inflation; Min is the lowest level of inflation observed for the country in question over the sample period, whereas Max is the highest level of inflation observed. Skew is the skewness coefficient, and Kurt is the level of kurtosis.
APPENDIX B
DESCRIPTIVE STATISTICS FOR COMMODITY RETURNS
For each listed commodity, the descriptive statistics are presented as follows: Mean is the mean return on a given commodity, commodity subindex, or individual commodity observed for N, the number of observations for that commodity in the sample. Std. dev. is the standard deviation of returns; Min is the lowest return observed for the commodity in question, whereas Max is the highest return observed. Skew is the skewness coefficient, and Kurt is the level of kurtosis.
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