The Cost of Carry Model

Author: Xin Jing

Date: 2021/11/16

This is a replication of a thesis. The title of the thesis is Does knowledge of the cost of a carry model improve commodity futures price for forecasting ability?

The thesis is a case study on the importance of the cost of carry model as well as the future prices in forecasting cash prices. The case study in the thesis uses the London Metal Exchange Lead Contract, while I use Shanghai Futures Exchange copper contract in my research following the pipeline.

Project Introduction

Table of Contents

• 1. Data
  • 1.1 Descriptive statistics
  • 1.2 Graphs
  • 1.3 Auto-Correlation coefficients
• 2. Statistical Tests
  • 2.1 Ordinary Least Square Regression
    • Augmented Dickey-Fuller unit root tests
    • Results for OLS
  • 2.2 Error Correction Models
    • Engle Granger Test and Johansen Test
    • Results for the B&K Regression Model
    • Results for the Vector Error Correction Model
      • One Cointegrating Vector
      • Three Cointegrating Vector
• 3. Comparison of model prediction

Models

Keywords

Cost of carry model; Vector error correction model; Engle-Grangle test; Johansen test

File

• carry_model_1204.html: demonstrates thr research results

DataSet

• CU.xlsx: contains the data of SHFE copper
  • in four levels: cash price, future price, inventory, interest rate of government bonds.
  • in the historical period of 2009/12/31 - 2020/07/03

Project Research

Project Introduction

Table of Contents

• 1. Data
  • 1.1 Descriptive statistics
  • 1.2 Graphs
  • 1.3 Auto-Correlation coefficients
• 2. Statistical Tests
  • 2.1 Ordinary Least Square Regression
    • Augmented Dickey-Fuller unit root tests
    • Results for OLS
  • 2.2 Error Correction Models
    • Engle Granger Test and Johansen Test
    • Results for the B&K Regression Model
    • Results for the Vector Error Correction Model
      • One Cointegrating Vector
      • Three Cointegrating Vector
• 3. Comparison of model prediction

Keywords

Cost of carry model; Brenner and Kroner Model; Error correction model; Engle-Grangle test; Johansen test

File

• carry_model_1204.html: demonstrates thr research results

DataSet

• CU.xlsx: contains the data of SHFE copper
  • in four levels: cash price, future price, inventory, interest rate of government bonds.
  • in the historical period of 2009/12/31 - 2020/07/03 \newpage

Models

The thesis introduces five models to predict cash price. Two simple models involve only the lagged futures price, as shown in equations $(1)-(2)$. Brenner and Kroner suggested a more complexed model in 1995, as shown in equation $(3)$. Single equation models impose substantial restrictions on the data and so to assess the accuracy of these restrictions a vector error correction model is proposed, see equation $(4)$

• OLS:
  $$ DP_t = a_0 + a_1 DF_{t|t-1} + e_t \tag{1} $$ $$ DP_t = b_0 + b_1 (F_{t|t-1} - P_{t-1}) + e_t \tag{2} $$
• Brenner and Kroner Model(1995):
  $$ \begin{equation} DP_t = g_0 + g_1 DF_{t|t-1} + g_2 Dr_{t|t-1} + g_3 DI_{t-1} + g_4 D\sigma_{t-1} + g_5 D\rho(1){t-1} + g_6ECT{t-2} + e_t \tag{3} \end{equation} $$

The error correction term, $ECT_{t-2}$ is the residual, $e_{t-1}$ from the regression: $$ P_{t-1} = h_0 + h_1 F_{t-1|t-2} + h_2 r_{t-1|t-2} + h_3I_{t-2} + h_4 \sigma_{t-2} + h_5\rho(1){t-2} + e{t-1} $$

• Vector Error Correction Model: $$ DX_t = M_1 DX_{t-1} + S^{'}ECT_{t-2}^{} + L + E_t\tag{4} $$ $DX_t$ is the change in vector $X$, $M_1$ is the matrix of parameters, $S$ is the vector of speed of adjustment parameters, $L$ is a vector of constant terms and $E_t$ is the vector of residuals. $ECT^{t-2}$ are the residuals, $e_t$ from the following regression. $$ P{t-2} = j_0 + j_1 F_{t-1|t-2} + j_2 r_{t-1|t-2} + j_3I_{t-2} + j_4 \sigma_{t-2} + j_5\rho(1){t-2} + e{t-1}$$ with $i_i$ and $j_i$ as estimated parameters.