# A Two-Regime Markov-Switching GARCH Active Trading Algorithm for Coffee, Cocoa, and Sugar Futures

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## Abstract

**:**

## 1. Introduction

**Hypothesis**

**1.**

## 2. Literature Review of the Use of MS-GARCH Models

- To invest in the simulated commodity future if the investor expects to be in the low-volatility ($k=1$) regime at $t+1$ or
- To invest in the U.S. risk-free asset if the investor expects to be in the high-volatility ($k=2$) regime.

## 3. Methods and Materials

#### 3.1. The Rationale behind MS and MS-GARCH Models, the Input Data Processing Method, and the Trading Strategy Simulation’s Parameters

- (1)
- To estimate the parameter set of a MS or MS-GARCH (with Gaussian or t-student pdf).
- (2)
- To forecast the smoothed probability (${\xi}_{k=2,t+1}$) of being in the distress regime at $t+1$ with Equation (15).
- (3)
- To follow the next trading algorithm:
- If ${\xi}_{k=2,t+1}>0.5$,
- To invest in a risk-free asset (such as the three-month Treasury bill).

- Else
- To invest in the managed commodity as risky asset.

#### 3.2. Data Processing

Algorithm 1. The MS-GARCH based trading algorithm’s pseudocode. |

For date 1 to 1057:- To determine the current balance in the portfolio (cash balance + market value of holdings).
- To execute the Markov-switching model analysis in Equation (6) with either GARCH, ARCH, or constant standard deviation (either with Gaussian or t-student probability density function). This was by using the future’s return historical data from 20 September 1991 to the simulated date ($t$).
- To calculate, by using Equation (14), the forecasted smoothed probability ${\xi}_{s=2,t+1}$ related to being in a distress or bad-performing regime at $t+1$.
- If ${\xi}_{s=2,t+1}>0.5$, then:
- To invest in the risk-free asset (the theoretical U.S. Treasury bill exchange traded fund or ETF)
- Else:
- b.
- To invest in the risky asset (the commodity future contract simulated)
- 5.
- To price the value of the portfolio with a market-to-market (with closing market prices at $t$) procedure.
End |

## 4. Results and Discussion

## 5. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The historical one-month cocoa future price and the distress regime period estimated with a two-regime, Gaussian time-fixed standard deviation MS model.

**Figure 3.**The historical performance and commodity investment level in each of the six simulated portfolios in the one-month cocoa future market.

**Figure 4.**The historical performance and commodity investment level in each of the six simulated portfolios in the one-month sugar future market.

**Figure 5.**The historical performance and commodity investment level in each of the six simulated portfolios in the one-month coffee future market.

Refinitiv RIC | Security Name | Ticker Used | Exchange |
---|---|---|---|

CCc1 | ICE-US Cocoa 1-month continuation future | Cocoa | CME-NYMEX |

SBc1 | ICE-US Sugar No.11 1-month continuation future | Sugar | CME-NYMEX |

UST3MT=RR | U.S. 3-month Treasury bill | USTBILL | OTC |

**Table 2.**Recursive fit test of single- and two-regime stochastic process, with different standard deviation models and different probability density function (PDFs).

MS Model | Coffee | Cocoa | Sugar | |
---|---|---|---|---|

Single-Gaussian | −2699.3597 | −3214.9534 | −3109.5732 | |

Single-tStud | −2919.3981 | −3329.3646 | −3216.1418 | |

MS-Gaussian | −2963.2332 | −3332.1498 | −3218.7971 | |

MS-tStud | −2974.622[Best] | −3350.0588 | −3258.1922 | |

MSARCH-Gaussian | −2953.759 | −3325.6856 | −3216.1543 | |

MSARCH-tStud | −2967.7068 | −3341.8939 | −3255.5772 | |

MSGARCH-Gaussian | −2967.1237 | −3366.9723 | −3238.0013 | |

MSGARCH-tStud | −2974.2583 | −3372.5889[Best] | −3259.7268[Best] |

**Table 3.**Performance summary of the simulated portfolios with the buy-and-hold strategy in the three commodities of interest (figures in %, with the exception of the Sharpe ratio).

Portfolio | Accumulated Return | Mean Return | Return Std. Dev. | Lowest Weekly Return | Sharpe Ratio |
---|---|---|---|---|---|

Coffee | 164.7353 | 0.0922 | 4.2668 | −16.2170 | 0.0215 |

Cocoa | 594.5557 | 0.1835 | 4.301 | −23.0542 | 0.0426 |

Sugar | 365.5376 | 0.1456 | 4.5201 | −17.3969 | 0.0322 |

USTBILL | 41.457 | 0.0498 | 0.0414 | - | - |

**Table 4.**Performance summary of the simulated portfolios in the cocoa one-month futures’ market (figures in %, with the exception of the Sharpe ratio).

Portfolio | Accumulated Return | Mean Return | Return Std. Dev. | Lowest Weekly Return | Sharpe Ratio |
---|---|---|---|---|---|

Cocoa-MS-Gaussian | 431.843 | 0.1583 | 3.9399 | −14.1671 | 0.0325 |

Cocoa-MS-t Student | 512.7569 | 0.1717 | 2.4549 | −9.5813 | 0.0307 |

Cocoa-MSARCH-Gaussian | 504.4178 | 0.1704 | 4.062 | −23.0489 | 0.0377 |

Cocoa-MSARCH-t Student | 801.2475 | 0.2082 | 2.8363 | −23.0475 | 0.0386 |

Cocoa-MSGARCH-Gaussian | 594.5557 | 0.1835 | 4.301 | −23.0542 | 0.038 |

Cocoa-MSGARCH-t Student | 389.2472 | 0.1504 | 3.9084 | −23.0339 | 0.0297 |

**Table 5.**Performance summary of the simulated portfolios in the sugar one-month futures’ market (figures in %, with the exception of the Sharpe ratio).

Portfolio | Accumulated Return | Mean Return | Return Std. Dev. | Lowest Weekly Return | Sharpe Ratio |
---|---|---|---|---|---|

Sugar-MS-Gaussian | 146.2971 | 0.0854 | 2.7338 | −12.6382 | 0.014 |

Sugar-MS-tStud | 56.4792 | 0.0424 | 0.844 | −4.7119 | 0.0022 |

Sugar-MSARCH-Gaussian | 306.4918 | 0.1328 | 2.7631 | −11.4508 | 0.0288 |

Sugar-MSARCH-tStud | 27.1906 | 0.0228 | 0.9576 | −6.6802 | −0.0059 |

Sugar-MSGARCH-Gaussian | 710.7164 | 0.1982 | 4.1223 | −17.3937 | 0.0348 |

Sugar-MSGARCH-tStud | 167.8353 | 0.0933 | 2.1446 | −17.3852 | 0.0108 |

**Table 6.**Performance summary of the simulated portfolios in the coffee one-month futures’ market (figures in %, with the exception of the Sharpe ratio).

Portfolio | Accumulated Return | Mean Return | Return Std. Dev. | Lowest Weekly Return | Sharpe Ratio |
---|---|---|---|---|---|

Coffee-MS-Gaussian | 11.3484 | 0.0102 | 4.0688 | −11.8899 | −0.0062 |

Coffee-MS-tStud | 72.9009 | 0.0519 | 4.0685 | −11.8863 | −0.0003 |

Coffee-MSARCH-Gaussian | 11.6724 | 0.0105 | 4.07 | −11.8899 | −0.0062 |

Coffee-MSARCH-tStud | 4.2611 | 0.004 | 4.0444 | −11.8857 | −0.012 |

Coffee-MSGARCH-Gaussian | 90.5161 | 0.061 | 4.1543 | −11.8899 | 0.0022 |

Coffee-MSGARCH-tStud | −5.366 | −0.0052 | 3.8614 | −16.2139 | −0.0102 |

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**MDPI and ACS Style**

De la Torre-Torres, O.V.; Aguilasocho-Montoya, D.; del Río-Rama, M.d.l.C.
A Two-Regime Markov-Switching GARCH Active Trading Algorithm for Coffee, Cocoa, and Sugar Futures. *Mathematics* **2020**, *8*, 1001.
https://doi.org/10.3390/math8061001

**AMA Style**

De la Torre-Torres OV, Aguilasocho-Montoya D, del Río-Rama MdlC.
A Two-Regime Markov-Switching GARCH Active Trading Algorithm for Coffee, Cocoa, and Sugar Futures. *Mathematics*. 2020; 8(6):1001.
https://doi.org/10.3390/math8061001

**Chicago/Turabian Style**

De la Torre-Torres, Oscar V., Dora Aguilasocho-Montoya, and María de la Cruz del Río-Rama.
2020. "A Two-Regime Markov-Switching GARCH Active Trading Algorithm for Coffee, Cocoa, and Sugar Futures" *Mathematics* 8, no. 6: 1001.
https://doi.org/10.3390/math8061001