Commodity index risk premium

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Abstract

Increasingly commodities have become an asset class in a process called financialization. Many institutional investors, looking for ways to expand their diversification opportunities, are holding positions in a commodity futures index and use them as a performance benchmark. Thus, institutional commodity holdings in commodities has expanded significantly.

In this paper we estimate the risk premium of a commodity index using analyst’s forecasts and futures prices of each of the commodities included in the index. We estimate futures and expected spot price curves using a no-arbitrage multifactor stochastic pricing model and a Kalman Filter. The model includes time-varying risk premia thus allowing for the exploration of macro variables that could explain their time variation for each family of commodities.

The proposed model has already shown to be effective for single commodities, such as oil and copper, but this paper extends its use to analyze indices of the four main commodity sectors: energy, industrial metals, precious metals and agriculture, as well as a global portfolio that mimics the S&P GSCI Index. This allows for a better understanding of how some macro variables affect different commodity sectors providing useful information for institutional investors of a commodity index.

Introduction

Many institutional investors, looking for ways to expand their diversification opportunities, have been increasing their positions in a commodity futures index and using it as a performance benchmark. There are estimates of more than a tenfold increase in institutional commodity holdings from 2003 to 2015 according to the Index Investment Data of the Commodity Futures Trading Commission (CFTC) (2015).

In this paper we estimate the risk premium of a commodity index using analyst’s forecasts and futures prices of each of the commodities included in the index. We analyze a commodity portfolio that mimics the GSCI-Goldman Sachs Commodity Index. We also explore the |explanatory power of market variables that may affect expected returns of portfolios that mimic the commodity index on four sectors: energy, industrial metals, precious metals and agriculture.

The relevance of commodity prices has been growing during recent years and will probably continue to do so with high demand for raw materials due in part to population growth (Lübbers and Posch, 2016). Also, the use of fossil fuels is expected to keep rising until 2040, even with the increase of renewable fuel production (EIA, 2016). As a result, commodity prices are due to continue to play a major role in the economy.

Moreover, commodities have increasingly been considered as an investment asset, a process known as financialization of the commodity markets. This has led to an increase in the number of transactions and the reduction in their heterogeneousness (Yang, 2013; Silvennoinen and Thorp, 2013; Daskalaki et al., 2013). Among the reasons that may have triggered this process are the low correlations between commodity returns and the return of stocks and bonds prior to the early 2000s (Bhardwaj et al., 2015; Brooks et al., 2013; Erb and Harvey, 2006). This low correlation to other financial assets has led investors to trade commodities to diversify their portfolios, impacting commodity prices (Tang and Xiong, 2012; Sanders and Irwin, 2017; Silvennoinen and Thorp, 2013). Notwithstanding financialization being a widely accepted phenomenon, it is not clear yet how it may have affected each commodity price or return (Hamilton and Wu, 2014).

Given the financial nature of commodity investment, studying their return behavior is gaining interest among researchers (Hong and Yogo, 2009; Shahzad et al., 2017; Chevallier; Sévi, 2013). The risk premium for a given maturity may be defined as the expected spot price over the futures contract price for that maturity (Hsieh and Kulatilaka, 1982). Thus, understanding risk premia is a way to analyze expected returns from commodity investments.

The nature of risk premia is controversial. According to Keynes (1930) and Hicks (1939) in the normal backwardation theory, risk premia arise because of an imbalance between buyers and sellers of an asset, which is counterbalanced by speculators who require a payment to take their positions. Currently, there is no consensus whether risk premia are positive or negative (Singleton, 2014; Bakshi et al., 2019; Gorton et al., 2013). Moreover, some authors have recently found evidence to support a time varying risk premium (Fama and French, 2016; Szymanowska et al., 2014; Hamilton and Wu, 2014).

Since the financial crisis in 2008, financialization of the commodity markets has produced a reduction in the heterogeneity of different commodities returns, increasing their correlation, especially for indexed commodities (Bhardwaj et al., 2015). Indexed commodities are gaining relevance, when compared to non-indexed ones, because of their higher liquidity and the existence of derivatives which are demanded by speculative investors, who trade in and out of all commodities in a given index (Tang and Xiong, 2012; Boyd et al., 2018). In this article we propose a new approach to estimate the risk premium1 of a commodity index by using filtered analyst’s forecasts and futures prices of each of the commodities included in the index.

The use of analyst’ expectations is not new in the literature. For instance, Cortazar et al. (2019b) compare the average analysts’ expectations of future spot prices to futures prices, to estimate a constant commodity risk premium term structure. Bianchi and Piana (2017) use expectations to determine risk premia of four different commodities. Orphanides and Kim (2005) use short-term interest rate expectations to estimate long-term interest rates. Altavilla et al. (2017) also uses analyst’ expectations to improve estimations of interest rate curves.

In this study we implement the multifactor stochastic pricing model used in Cortazar et al. (2019a) and in Cifuentes et al. (2020) to estimate the time-varying risk premium term structure of individual commodities.2 We extend this approach to estimate the risk premium of a commodity index by analyzing the behavior of portfolios of four different industries: energy, industrial metals, precious metals and agriculture, and of a global portfolio that includes them all. Each portfolio is composed of a set of commodities of its industry weighted using the same weights as in the Standard and Poor’s Goldman Sachs Commodity Index (S&P GSCI Index). Futures prices, are from NYMEX, LME, COMEX, ICE or CBOT, depending on the commodity. Analysts’ expectations data is obtained from Bloomberg. Data is from January 2014 to June 2018.

Once we have obtained the time varying risk premia of the different commodity portfolios, we explore the ability of a number of market variable to explain the time varying risk premia. The market variables that we examine are: S&P500 returns, VIX Index, NASDAQ Emerging Market Index (EMI) Returns, Term Premium, Default Premium and 5-Year Treasury Bill (Fama and French, 1989; Bhar and Lee, 2011; Hang and Yogo, 2012; Basu and Mifre, 2013; Bianchi and Piana, 2017; Szymanowska et al., 2014; Silvennoinen and Thorp, 2013; Daskalaki et al., 2014; among others). The joint analysis for several commodity sectors allows us to study not only which market variables are able to explain a given portfolio’s risk premia, but also the correlation among different commodity sectors.

The paper is organized as follows. Section 2 describes the construction of the portfolios that represent the different commodity sectors. Section 3 describes the data. Section 4 develops the model used to estimate the risk premia and Section 5 presents the results. Finally, Section 6 concludes.

Section snippets

Portfolio weights

In this section we define the individual commodity weights in each commodity portfolio. We define 5 portfolios as representative of indexed commodity investments: Energy, Industrial Metals, Precious Metals, Agriculture and a Global Portfolio which includes the four sectors.

To determine the commodity weights in each of the portfolios we use the S&P GSCI Index.3

Data

To estimate the risk premia of the commodity portfolios, data on futures and expected prices on each commodity are used.

Weekly futures prices, with maturities every 6 months from January 2014 to June 2018, are obtained from Bloomberg.6 With this data synthetic futures for all five portfolios, Energy, Industrial Metals, Precious Metals, Agriculture and the Global Portfolio, are computed using the methodology described in the

Model definition

As was stated earlier, we extend the use of the Cortazar et al. (2019a) and Cifuentes et al. (2020) model for individual commodities to estimate the risk premium of commodity portfolios, which is a non-stationary version of the canonical A0(N) model of Dai and Singleton (2000).

The general model has n stochastic factors with time varying risk premium and is estimated using a Kalman Filter.

Let St be the commodity spot price at time t, thenln(St)=Yt=hxtdxt=(Axt+b)dt+dwtwhere h is an nx1 vector

Model fit

As was described before, the model uses two sets of data, synthetic futures and synthetic analysts’ expected prices, computed by weighting the data from each commodity in the portfolio. Estimated parameters for each portfolio can be found in Appendix B.

Using both sets of data, the model estimates two curves, a futures and an expected price curve.

As an illustration, Fig. 3 shows the data and curves for the Energy Portfolio corresponding to June 24th of 2015. The model fits much better the

Market variable data

In order to study the determinants of commodity risk premia for each commodity portfolio we consider the market variables that have been most commonly proposed in the literature for this purpose (Basu and Mifre, 2013; Bianchi and Piana, 2017; Szymanowska et al., 2014; among others). The market variables considered are: S&P500 Returns, VIX Index, NASDAQ Emerging Market Index (EMI) Returns, Term Premium, Default Premium and 5-Year Treasury Bill. We describe each one of them in what follows.

S&P500

Conclusion

Deregulation of the commodity markets has contributed to making commodities a new investment asset class. This process is called the financialization of the commodity markets. In this context institutional investors, looking for ways to expand their diversification opportunities, hold positions in a commodity futures index and use them as a performance benchmark. Thus, it has become important to estimate the magnitude and drivers of the risk premium of different commodity portfolios. This paper

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