Commodities as an Asset Class in Portfolio Management

Table of Contents

List of Abbreviations

List of Formulas

List of Figures

List of Tables

List of Symbols

1 Introduction
1.1 Problem Definition and Ambition
1.2 Research Methodology

2 Portfolio Management
2.1 Basics of Portfolio Management
2.1.1 Risk
2.1.2 Return
2.2 Modern Portfolio Theory
2.2.1 Idea and Assumptions of Markowitz’s Portfolio Selection Model
2.2.2 Statistical Basics
2.2.3 Efficient Frontier
2.3 Capital Market Theory
2.3.1 Capital Asset Pricing Model
2.3.1 Capital Market Line and Market Portfolio
2.3.2 Security Market Line
2.4 Criticism

3 Commodities
3.1 Commodities Definition
3.1.1 Commodity Classes
3.1.1.1 Energy
3.1.1.2 Precious Metals
3.1.1.3 Industrial Metals
3.1.1.4 Agriculture
3.1.2 Economics of Commodity Markets
3.1.2.1 Commodity Futures Exchanges
3.1.2.2 Driving Forces behind the Current Commodity Bull Market
3.1.2.3 Market Participants
3.1.3 Exposure to Commodities
3.1.3.1 Futures
3.1.3.2 Index Investments
3.1.3.3 Stocks
3.1.3.4 Funds
3.1.3.5 Physical Commodities
3.2 Criticism

4 Investing in Commodity Futures Indices
4.1 Mechanics of an Investment in Commodity Futures
4.1.1 Relationship between Futures Prices and Spot Prices
4.1.2 Backwardation and Contango
4.2 Sources of Index Return
4.2.1 Spot Return
4.2.2 Roll Yield
4.2.3 Collateral Yield
4.2.4 Diversification and Rebalancing Return
4.3 Commodity Futures Excess Returns
4.3.1 Insurance Perspective in the Theory of Normal Backwardation
4.3.2 Hedging Pressure Hypothesis
4.3.3 Theory of Storage and Convenience Yield
4.3.4 Weather Fear Premium
4.4 Comparison of Commodity Indices
4.4.1 Commodity Index Components
4.4.1.1 Reuters/Jefferies CRB Index
4.4.1.2 S&P GSCITM
4.4.1.3 Dow Jones-AIG Commodity Index
4.4.1.4 Deutsche Bank Liquid Commodity Index
4.4.1.5 Rogers International Commodities Index
4.4.2 Risk and Return Comparison
4.5 Criticism

5 Commodity Futures and Traditional Asset Classes in a Portfolio Context
5.1 Commodity Futures vs. Traditional Asset Classes
5.1.1 Evidence Supporting Commodity Futures as an Asset Class
5.1.2 Traditional Assets: Equity and Bonds
5.1 Comparison of Commodity Futures and Traditional Assets
5.1.1 Risk and Return Comparison
5.1.2 Asset Classes and the Business Cycle
5.1.3 Correlation Between and Amongst Different Asset Classes
5.2 Portfolio-Optimization with Commodity Futures
5.2.1 Commodity Futures as an Inflation Hedge
5.2.2 Commodity Futures and the Efficient Frontier
5.3 Criticism

6 Conclusion
6.1 Résumé and Target Achievement
6.2 Perspectives

Appendix

Bibliography

List of Abbreviations

illustration not visible in this excerpt

List of Formulas

Formula 1: Expected Return of a Single Investment

Formula 2: Variance of a Single Investment

Formula 3: Standard Deviation of a Single Investment

Formula 4: Annualization of Returns

Formula 5: Annualization of Standard Deviation

Formula 6: Lower Partial Moments

Formula 7: Skewness

Formula 8: Kurtosis

Formula 9: Arithmetic Return

Formula 10: Geometric Return

Formula 11: Discrete Return

Formula 12: Arithmetic Mean

Formula 13: Continuous Return

Formula 14: Expected Return of a Portfolio

Formula 15: Covariance of a two-asset Portfolio

Formula 16: Correlation Coefficient

Formula 17: Variance of a Portfolio

Formula 18: Calculation of a two-asset Minimum-Variance-Portfolio

Formula 19: Capital Market Line

Formula 20: Beta

Formula 21: Security Market Line

Formula 22: Future Value of Financial Assets

Formula 23: Future Value of Commodity Futures

Formula 24: Total Return for Commodity Futures

Formula 25: Commodity Futures Price in the Theory of Storage

Formula 26: Convenience Yield

Formula 27: Roll Return

List of Figures

Figure 1: Categorization of Risk and Risk Measures

Figure 2: Efficient Frontier for a two-asset-Portfolio

Figure 3: Efficient Frontier, Indifference Curve and Optimal Portfolio

Figure 4: Capital Market Line

Figure 5: Security Market Line

Figure 6: Reuters/Jefferies-CRB Index Performance

Figure 7: Term Structure of Commodity Prices

Figure 8: Commodity Indices: Basis for Returns

Figure 9: Roll Yield

Figure 10: Annualized Return vs. Time in Backwardation

Figure 11: Risk Premium

Figure 12: Expectational Variance

Figure 13: Commodity Convenience Yields vs. the Percentage Usage of Stocks/day

Figure 14: Commodity Curves & Convenience Yields

Figure 15: Commodity Volatility & Convenience Yields

Figure 16: Commodity Weights of the DBLCI

Figure 17: Inflation Adjusted Asset Class Performance

Figure 18: Risks and Returns of Different Asset Classes

Figure 19: Growth of a $1 Investment in Commodities

Figure 20: Distributions of Stocks and Commodity Futures

Figure 21: The Business Cycle and the Performance of different Asset Classes

Figure 22: Average Returns over the Business Cycle

Figure 23: Average Returns over the Business Cycle Stages

Figure 24: Average Performance of different Asset Classes over the Business Cycle

Figure 25: Correlation between different Asset Classes

Figure 26: Correlation of different Asset Classes with Inflation

Figure 27: Correlation between Stocks, Bonds and Inflation over different horizons

Figure 28: Comparison of the Risks in different Portfolios with a given Return

Figure 29: Efficient Frontier for Stocks and Bonds, 1993-2006

Figure 30: Efficient Frontier for Stocks, Bonds and Commodities, 1993-2006

Figure 31: Efficient Frontier for Stocks and Bonds, 1993-1999

Figure 32: Efficient Frontier for Stocks, Bonds and Commodities, 1993-1999

Figure 33: Efficient Frontier for Stocks and Bonds, 2000-2006

Figure 34: Efficient Frontier for Stocks, Bonds and Commodities, 2000-2006

Figure 35: Efficient Frontier for Commodities and Bonds, 2000-2006

Figure 36: Efficient Frontier for Stocks and Bonds, 1993-2006

List of Tables

Table 1: Financial Asset Arbitrage when Abbildung in dieser Leseprobe nicht enthalten

Table 2: Financial Asset Arbitrage when Abbildung in dieser Leseprobe nicht enthalten

Table 3: Commodity Futures Arbitrage when Abbildung in dieser Leseprobe nicht enthalten

Table 4: GSCI Term Structure, July 1992-May 2004

Table 5: Return Sources of the GSCI and DJ-AIG

Table 6: GSCI Spot Returns, Collateral Yield and Roll Yield

Table 7: Monthly Index Return Correlation, January 1991 – December 2004

Table 8: Index Risk and Return Characteristics, January 1991 – December 2004

Table 9: Index Risk and Return Characteristics, August 2001 – December 2004

Table 10: Alternative Commodity Index Performance 2004-2005

Table 11: Monthly Index Returns, October and November 2004

Table 12: Skewness and Kurtosis of Selected Commodity Indices, 1995-2005

Table 13: Average Returns, July 1959-March 2004

Table 14: Annualized Commodity Index Returns vs. Other Asset Classes

Table 15: Commodity Returns During Worst Equity Periods

Table 16: Correlation Coefficients of Annual Total Returns, 1970-2004

Table 17: Inflation Risk Profile of different Asset Classes

Table 18: Performance of different Commodity Sectors with Inflation

Table 19: Oil Demand and Supply XIII

Table 20: Commodity Exchanges XIV

Table 21: Diversification Return XV

Table 22: RJ/CRB Commodity Index Weights XVI

Table 23: DJ-AIG Target Weights XVII

Table 24: Comparative Matrix of Index Constituent Markets XVIII

Table 25: Comparative Matrix of Index Construction and Methodology XIX

Table 26: Excess Return Correlations, December 1982-May 2004 XX

Table 27: Correlation of Selected Equity Indices, July1995-December 2004 XXI

Table 28: Correlation of Selected Commodity Sub-Indices XXI

Table 29: Efficient Frontiers: Risk and Return Parameters XXII

Table 30: Efficient Frontiers: Correlations XXIII

List of Symbols

illustration not visible in this excerpt

1 Introduction

1.1 Problem Definition and Ambition

Historically, commodity investments were eschewed by many investors due to their unique properties and their reputation for high volatility and riskiness^[1]. The weak performance of most commodities since the beginning of the 1980s and in contrast, the positive stock market performance are additional reasons for investors’ lacking interest.^[2]

In the past few years, however, an increasing amount of attention has been devoted to commodities as traded assets. For instance, the estimated amount of long-term investor capital tied to the Standard & Poor’s Goldman Sachs Commodity Index (S&P GSCI™) and similar instruments exceeded $130 billion in 2007, up from about $2 billion in 1996.^[3] More specifically, as of September 2004, the Goldman Sachs Commodity Index (GSCI)^[4] increased its investments from $8 billion in 2000 to more than $25 billion. The number of global institutions with exposures to the GSCI consequently increased from 50 in 2000 to an estimated 150 institutions. Another $8 to $10 billion in assets was tied to the Dow Jones-AIG Commodity Index (DJ-AIG), up from just $200 million a few years ago.^[5] Moreover, December 2004 estimates suggest that pension and mutual funds increased their investments in commodity indices from about $15 billion in the middle of 2003 to $40 billion at the end of 2004. Additionally, the Harvard University Endowment which is by many regarded as an indicator of progressive thinking in institutional portfolio management, had in 2004 already bound 13% of its funds in the commodity sector which corresponds to just under $3 billion of its 2004 $22.6 billion endowment.^[6]

In several recent academic papers commodities have been analyzed thoroughly and thus, the advantages of commodities as an asset class have become empirically evident^[7]. Various authors found that commodities demonstrated a low and even negative correlation with the returns of stocks and bonds over time and are, as historical analysis supports, a hedge against inflation^[8]. Due to these characteristics commodities are considered to provide diversification benefits across market environments by reducing the volatility and by earning superior returns when they are needed most.^[9] Further, advocates of commodities as an asset class claim that a diversified commodities portfolio has generated equity-like average excess returns and has achieved the same risk premium as the S&P 500^[10]. These unique properties of commodities combined with the bullish outlook for this asset class over the next decade with commodity prices setting new highs and in contrast, investors’ disappointment of the stock market performance after the “Dot-com Bubble” have created increasing interest of investors in commodities.^[11]

The key objective of this study is to investigate how commodities as an asset class influence the risk-return-ratio of a traditional portfolio in a passive investment strategy over various periods of time.

Hence, the diversification benefits commodities may provide when added to a traditional portfolio of e.g. stocks and bonds will be analyzed over different stages of the business cycle.

Consequently, this affords the examination and explanation of the:

- Basic concepts of portfolio management and commodities
- Different investment exposures to commodities
- Return decomposition of commodity futures
- Evidence that commodities constitute an asset class
- Comparison of the different asset classes regarding risk, return and correlation as well as the performance analysis of the single asset classes with regard to the business cycle and inflation
- Efficient frontiers of portfolios with and without commodities over different periods of time

In order to address to commodities as a whole, rather than to individual commodity futures, the work focuses on commodity indices.^[12]

1.2 Research Methodology

This work is organized into four main sections. The study opens with an explanation of the fundamentals of portfolio management, Modern Portfolio Theory (MPT) as well as Capital Market Theory (CPT) which are all necessary for the computation of the risk and return measures of the different asset classes as well as for the construction of an efficient frontier (Chapter 2).

In Section 3, the basics of commodities and the commodity markets will be explained, encompassing everything from the different commodity classes, the reasons for the current bull market, the commodity market participants and the different types of commodity exposures.

In the next chapter the theoretical basis for commodity futures investment is reviewed. The relationship between future and spot prices, the different forward curves (backwardation and contango) as well as the return sources of commodity indices will be examined. Further, the structures of various futures-based investable total return commodity indices as well as their risk-return performances are analyzed and compared.

In Section 5, it is first demonstrated that commodities constitute an asset class in their own right before the relative performance of commodity indices with traditional asset classes (stocks and bonds) is compared. In addition, the behaviour of the different asset classes over the business cycle and with regard to inflation as well as the correlation between and amongst the classes are analyzed. The section ends with the construction and comparison of efficient frontiers for portfolios with and without commodities over different time horizons based on historical inputs.

Conclusions and suggestions are discussed in the final section.

2 Portfolio Management

2.1 Basics of Portfolio Management

2.1.1 Risk

The word “risk” is usually used to describe a situation of insecurity.^[13] Insecurity or risk in the broad sense indicates that there is a possibility that the actual outcome may deviate from the expected outcome.^[14] The magnitude of the possible difference reflects the magnitude of risk.^[15] Risk is broadly interpreted as negative deviation from the expected value.^[16] However, risk may be positive or negative since the outcome can deviate both positively and negatively from the expected outcome.^[17] The term “insecurity” can be divided into “uncertainty” and “risk in the narrow sense”.^[18] Uncertainty is interpreted as the chance occurrence of an outcome where the probability distribution is not known or, in other words, that at least some aspects of a decision are beyond the control of the investor. Hence, estimation has to be made since measurement is impossible^[19]. In contrast, if it is possible to term the objective or at least the subjective probability of the outcome on a statistical basis, one speaks of risk in the narrow sense.^[20] Another definition approach is to define risk as quantifiable insecurity by combining expected values and probabilities.^[21]

In the further course of this work, the term “risk” is used to describe risk in the narrow sense.

An overview of the different types and categories of risk as well as the corresponding risk measures which are necessary for this work can be obtained from Figure 1.

[...]

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^[1] A limited number of investment vehicles, the short histories of the major commodity indices may be other reasons, amongst others, for the exclusion of commodities in a portfolio. Cf. Idzorek (2006), p. 5; Akey (2005), p. 39; Gorton (2004), p. 2.

^[2] As for example the price per ounce declined from $800 in early 1980 to under $300 in the second half of the 1990s, the Dow Jones index has risen from 800 to over 11,000 points at the same period of time. Cf. n.a. (2006a), p. 12.

^[3] Cf. Greely, Currie, Nathan (2007a), p. 3.

^[4] In February 2007, Standard & Poor’s acquired the GSCI and renamed the index to S&P GSCI. Cf. Guarino (2007), p. 1.

^[5] Cf. Sesit (2004), p. 1-3.

^[6] Cf. http://www.businessweek.com/magazine/content/04_43/b3905149_mz035.htm , as of 12.03.2008; Akey (2005), p. 4.

^[7] Cf. a.o. Erb, Harvey (2006b); Gorton, Rouwenhorst (2004); Anson (1999), Jensen, Johnson, Mercer (2000); Lummer, Siegel (1993); Kaplan, Lummer (1997).

^[8] Cf. Idzorek (2006), p. 5.

^[9] Cf. Brown (2006), p. 44; Greely, Currie, Nathan (2007a), p. 1.

^[10] Cf. Akey (2005), p. 11.

^[11] Cf. Akey (2005), p. 6.

^[12] The same is valid for stocks and bonds.

^[13] Cf. Spremann (2006), p. 91; Garz, Günther, Moriabadi (2000), p. 23; Coleman (2006), p. 25.

^[14] Cf. Frenkel, Hommel, Rudolf (2000), p. 264 ff.; Bodie, Cane, Marcus (2002), p. 155.

^[15] Cf. Correia, Flynn, Uliana, Wormald (2007), p. 3-2.

^[16] Cf. Steiner, Bruns (2002), p. 56; Götte (2005), p. 27.

^[17] Cf. Steiner, Bruns (2002), p. 55; Perridon, Steiner (2007), p. 94; Smith (1999), p. 5.

^[18] Cf. Garz, Günther, Moriabadi (2000), p. 23; Correia, Flynn, Uliana, Wormald (2007), p. 3-2.

^[19] Cf. Coleman (2006), p. 25.

^[20] Cf. Smith, Merna, Jobling (2006), p. 3-4.

^[21] Cf. Saxinger (2002), p. 738.