# Global Asset Allocation Strategy Using a Hidden Markov Model

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Asset Allocation

#### 2.2. Momentum Investing

#### 2.3. Hidden Markov Model (HMM)

## 3. Model Specification

#### 3.1. Data Source

#### 3.2. Learning of Hidden Markov Model

#### 3.2.1. Markov Chain

#### 3.2.2. Hidden Markov Model

- (1)
- Estimate the probability of the observation(O) given the parameters of the hidden Markov model
- (2)
- Estimate the optimal state in that model given the observation(O)
- (3)
- Finally, only the most observation(O) problems in determining the optimal parameters of a hidden Markov model in a given state

#### 3.2.3. HMM Parameter Learning: Baum-Welch Algorithm

#### 3.3. Estimation of Asset Phases & Portfolio Composition

#### 3.4. Analyzing Effect of Asset Selection

#### 3.4.1. Information Ratio

#### 3.4.2. Jensen’s Alpha

#### 3.4.3. Fama’s Net Selectivity

#### 3.4.4. Treynor-Mazuy Measure

## 4. Empirical Analysis

#### 4.1. Global Asset Allocation Investment Universe

#### 4.2. Summary of Investment Result

#### 4.3. Validation of Selection Effect of HMM

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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State | Average Monthly Return | Average Monthly Sharpe | Regime |
---|---|---|---|

1 | −2.2572 | −0.6236 | Falling phase |

2 | 2.6337 | 0.9352 | Rising phase |

3 | 0.4293 | 0.1529 | Clearance phase |

Asset Class | Name | Following ETF/ETN Ticker |
---|---|---|

Stock | U.S Stock | SPY |

Europe Stock | IEV | |

Japan Stock | EWJ | |

Emerging Market Stock | EEM | |

Bond | Long-term U.S Treasury | TLT |

Mid-term U.S Treasury | IEF | |

Alternative investment | U.S REITs | IYR |

Global REITs | RWX | |

Gold | GLD | |

Commodity | DBC |

Asset Class | Name | Following ETF/ETN Ticker |
---|---|---|

Stock | U.S Large Cap Stock | JKD |

U.S. Small Cap Stock | IJR | |

U.S Growth Stock | IVM | |

Europe Stock | IEV | |

Japan Stock | EWJ | |

Korea Stock | EWY | |

Developed Market Stock | EFA | |

Emerging Market Stock | EEM | |

Bond | Long-term U.S Treasury | TLT |

Mid-term U.S Treasury | IEF | |

U.S TIPS | TIP | |

U.S Aggregate Bond | AGG | |

Emerging Bond | EMB | |

Global TIPS | GTIP | |

High Yield Bond | HYT | |

Alternative investment | U.S REITs | IYR |

Global REITs | RWX | |

Oil | OIL | |

Gold | GLD | |

Dollar | UUP | |

Commodity | DBC | |

Copper | CPER |

Name | Strategy | Benchmark | ||||
---|---|---|---|---|---|---|

HMM | MOM | EW | 60/40 | MV | ||

Asset 10 | Ann Ret (Arith) | 0.0887 | 0.0781 | 0.0693 | 0.0623 | 0.0744 |

Ann Ret (CAGR) | 0.0868 | 0.0756 | 0.0654 | 0.0605 | 0.0666 | |

Ann Std Dev | 0.1027 | 0.0999 | 0.1064 | 0.0828 | 0.1382 | |

Ann Sharp | 0.8449 | 0.7569 | 0.6148 | 0.7305 | 0.4822 | |

Win Ratio | 0.6169 | 0.6219 | 0.6070 | 0.6468 | 0.5871 | |

Maximum Draw Down | 0.2092 | 0.1819 | 0.3917 | 0.3138 | 0.3824 | |

Asset 22 | Ann Ret (Arith) | 0.0811 | 0.0711 | 0.0578 | 0.0623 | 0.0748 |

Ann Ret (CAGR) | 0.0799 | 0.0692 | 0.0548 | 0.0605 | 0.0709 | |

Ann Std Dev | 0.0893 | 0.0898 | 0.0930 | 0.0828 | 0.1099 | |

Ann Sharp | 0.8938 | 0.7704 | 0.5892 | 0.7305 | 0.6449 | |

Win Ratio | 0.6517 | 0.6318 | 0.6318 | 0.6468 | 0.6318 | |

Maximum Draw Down | 0.1612 | 0.1824 | 0.3488 | 0.3138 | 0.3789 |

Strategy | HMM | MOM | |||||
---|---|---|---|---|---|---|---|

Benchmark | EW | 60/40 | MV | EW | 60/40 | MV | |

Asset 10 | 1 months | 0.547 | 0.537 | 0.507 | 0.502 | 0.522 | 0.493 |

3 months | 0.508 | 0.598 | 0.528 | 0.492 | 0.523 | 0.487 | |

6 months | 0.531 | 0.602 | 0.520 | 0.515 | 0.551 | 0.526 | |

12 months | 0.611 | 0.674 | 0.600 | 0.574 | 0.579 | 0.505 | |

24 months | 0.680 | 0.629 | 0.635 | 0.573 | 0.545 | 0.573 | |

36 months | 0.729 | 0.572 | 0.711 | 0.633 | 0.446 | 0.669 | |

Asset 22 | 1 months | 0.537 | 0.537 | 0.542 | 0.512 | 0.522 | 0.512 |

3 months | 0.558 | 0.593 | 0.518 | 0.543 | 0.503 | 0.497 | |

6 months | 0.571 | 0.617 | 0.561 | 0.546 | 0.551 | 0.531 | |

12 months | 0.584 | 0.611 | 0.579 | 0.658 | 0.584 | 0.505 | |

24 months | 0.697 | 0.573 | 0.708 | 0.635 | 0.545 | 0.494 | |

36 months | 0.723 | 0.524 | 0.747 | 0.717 | 0.470 | 0.608 |

Strategy | HMM | MOM | ||||
---|---|---|---|---|---|---|

Benchmark | EW | 60/40 | MV | EW | 60/40 | MV |

Asset 10 | 0.2249 | 0.3002 | 0.3375 | 0.0867 | 0.1392 | 0.1671 |

Asset 22 | 0.2928 | 0.2720 | 0.3213 | 0.1326 | 0.0989 | 0.0270 |

Strategy | HMM | MOM | ||||
---|---|---|---|---|---|---|

Benchmark | EW | 60/40 | MV | EW | 60/40 | MV |

Asset 10 | 0.0632 | 0.0593 | 0.0489 | 0.0489 | 0.0424 | 0.0270 |

Asset 22 | 0.0565 | 0.0489 | 0.0348 | 0.0377 | 0.0301 | 0.0156 |

Strategy | HMM | MOM | ||||
---|---|---|---|---|---|---|

Benchmark | EW | 60/40 | MV | EW | 60/40 | MV |

Asset 10 | 0.0366 | 0.0247 | 0.0503 | 0.0178 | 0.0063 | 0.0312 |

Asset 22 | 0.0402 | 0.0277 | 0.0356 | 0.0197 | 0.0071 | 0.0151 |

Strategy | HMM | MOM | |||||
---|---|---|---|---|---|---|---|

Benchmark | EW | 60/40 | MV | EW | 60/40 | MV | |

Asset 10 | Alpha | 0.00697 | 0.00723 | 0.00427 | 0.00606 | 0.00682 | 0.00241 |

Beta | −0.00444 | 0.0586 | 0.538 | −0.111 | −0.072 | 0.621 | |

Gamma | 1.48 | 1.43 | 0.473 | 1.43 | 0.603 | 0.322 | |

Asset 22 | Alpha | 0.00663 | 0.00695 | 0.00240 | 0.00537 | 0.00568 | 0.00288 |

Beta | 0.0258 | 0.0776 | 0.651 | −0.034 | 0.0263 | 0.615 | |

Gamma | 1.34 | 0.651 | 1.24 | 1.35 | 0.665 | −0.484 |

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## Share and Cite

**MDPI and ACS Style**

Kim, E.-c.; Jeong, H.-w.; Lee, N.-y. Global Asset Allocation Strategy Using a Hidden Markov Model. *J. Risk Financial Manag.* **2019**, *12*, 168.
https://doi.org/10.3390/jrfm12040168

**AMA Style**

Kim E-c, Jeong H-w, Lee N-y. Global Asset Allocation Strategy Using a Hidden Markov Model. *Journal of Risk and Financial Management*. 2019; 12(4):168.
https://doi.org/10.3390/jrfm12040168

**Chicago/Turabian Style**

Kim, Eun-chong, Han-wook Jeong, and Nak-young Lee. 2019. "Global Asset Allocation Strategy Using a Hidden Markov Model" *Journal of Risk and Financial Management* 12, no. 4: 168.
https://doi.org/10.3390/jrfm12040168