Technical University Munich Commodities as an Asset Class - risklab

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Contents 4.1.1 Index Composition . . . . . . . . . . . . . . . . . . . . . . . . 74 4.1.2 Index Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.1.3 Rebalancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.1.4 Return Calculation . . . . . . . . . . . . . . . . . . . . . . . . 75 4.1.5 Leveraged versus unleveraged Returns . . . . . . . . . . . . . 75 4.2 The Major Market Indices . . . . . . . . . . . . . . . . . . . . . . . . 75 4.2.1 CRB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2.2 GSCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2.3 DJ-AIGCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.4 DBLCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.5 DBLCI-MR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.6 RICI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.7 Comparison of the Major Market Indices . . . . . . . . . . . . 81 4.3 Index Linked Products . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3.1 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3.2 Mutual Funds . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3.3 Exchange Traded Funds . . . . . . . . . . . . . . . . . . . . . 86 4.4 Decomposition of Index Returns . . . . . . . . . . . . . . . . . . . . . 88 5 Properties of Commodity Returns 94 5.1 Characteristics of Single Commodities . . . . . . . . . . . . . . . . . . 95 5.1.1 Risk and Return Profile . . . . . . . . . . . . . . . . . . . . . 96 5.1.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.1.3 Diversification . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.2 Properties of the DJ-AIGCI Return Components . . . . . . . . . . . 116 5.2.1 Key Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.2.2 Roll Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.2.3 Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.4 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.2.5 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6 Asset Allocation with Commodity Derivatives 140 6.1 Mean Variance Spanning . . . . . . . . . . . . . . . . . . . . . . . . . 140 6.2 Dependence to Stocks, Bonds and Inflation . . . . . . . . . . . . . . . 144 6.3 Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7 Conclusions 157 A Data Description 160 vi
Contents B Characteristics of Selected Commodities 164 B.1 Heating Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 B.2 Gasoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 B.3 Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 B.4 Aluminium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 B.5 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 B.6 Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 B.7 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 B.8 Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 B.9 Sugar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 B.10 Coffee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 B.11 Soybean Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 B.12 Lean Hogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 C Mathematical Preliminaries 183 C.1 Statistical Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 C.2 Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 C.3 Stochastic Differential Equations . . . . . . . . . . . . . . . . . . . . 193 C.4 Equivalent Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 C.5 Feynman-Kac Representation . . . . . . . . . . . . . . . . . . . . . . 197 D Program Codes 199 D.1 Portfolio Allocation with Commodities . . . . . . . . . . . . . . . . . 199 D.2 Hurdle Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 D.3 Help Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 References 208 vii
Page 1 and 2: Technical University Munich Departm
Page 3: Acknowledgements First and foremost
Page 9 and 10: List of Figures 2.1 Overview of the
Page 11: List of Tables 2.1 Oil Reserves and
Page 14 and 15: 1 Introduction point of view i.e. c
Page 16 and 17: 2 Overview of Commodity Markets Aft
Page 18 and 19: 2 Overview of Commodity Markets Fig
Page 20 and 21: 2 Overview of Commodity Markets tra
Page 24 and 25: 2 Overview of Commodity Markets The
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3 Pricing of Commodity Futures Futu
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3 Pricing of Commodity Futures thei
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3 Pricing of Commodity Futures Theo
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3 Pricing of Commodity Futures Figu
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3 Pricing of Commodity Futures Befo
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3 Pricing of Commodity Futures Clos
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3 Pricing of Commodity Futures pric
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3 Pricing of Commodity Futures Agai
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3 Pricing of Commodity Futures is g
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3 Pricing of Commodity Futures The
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3 Pricing of Commodity Futures Putt
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3 Pricing of Commodity Futures The
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3 Pricing of Commodity Futures Fina
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3 Pricing of Commodity Futures retu
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4 Commodity Indices 4.1 Characteris
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4 Commodity Indices generally publi
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4 Commodity Indices Figure 4.2: The
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4 Commodity Indices Figure 4.4: The
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4 Commodity Indices weights, its de
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4 Commodity Indices is the most liq
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4 Commodity Indices its investors
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4 Commodity Indices 4.4 Decompositi
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4 Commodity Indices Implicating, th
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4 Commodity Indices Copper (US doll
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5 Properties of Commodity Returns I
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5 Properties of Commodity Returns M
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5 Properties of Commodity Returns T
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5 Properties of Commodity Returns v
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5 Properties of Commodity Returns D
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5 Properties of Commodity Returns F
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5 Properties of Commodity Returns R
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5 Properties of Commodity Returns t
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5 Properties of Commodity Returns F
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5 Properties of Commodity Returns c
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5 Properties of Commodity Returns A
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5 Properties of Commodity Returns a
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5 Properties of Commodity Returns a
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6 Asset Allocation with Commodity D
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7 Conclusions The main focus of thi
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A Data Description Availability of
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A Data Description GSCI Spot Return
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B Characteristics of Selected Commo
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C Mathematical Preliminaries only s
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C Mathematical Preliminaries The ex
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C Mathematical Preliminaries Defini
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C Mathematical Preliminaries C.2 Pr
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C Mathematical Preliminaries 2. W h
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C Mathematical Preliminaries Then w
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C Mathematical Preliminaries Theore
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C Mathematical Preliminaries Defini
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D Program Codes [weights,value] = s
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D Program Codes warning off; % Refe
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D Program Codes muPFHurd=muPFHurd
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D Program Codes value = -value; fun
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References References [Aitken 1935]
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References (2000): Hedging Pressure
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References [Kaldor 1939] N. Kalsor
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References [Roche 1993] Roche, Juli
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References [Working 1948] H. Workin
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