Markov-Regime-Switching-Portfolio

Crypto currencies Trading Strategy based on Markov Switching GARCH

Data from https://www.cryptodatadownload.com/data/gemini/

Trade on a group of crypto currencies
Ensemble technical indicators in Random Forest to predict price movements
Portfolio Allocation based on volatility predictions

Specification for the strategy

Set trading frequency as hourly
Used all asset data for model training
Modeled each asset's risk profile separately

1. Sample Features

Use Cusum filter(Lam, K. and H. Yam (1997): “CUSUM techniques for technical trading in financial markets.” Financial Engineering and the Japanese Markets, Vol. 4, pp. 257–274) to sample the data points that observed significant price movements

Train the model with the selected samples.

2. Indicators

Select from a bunch of technical indicators that illustrate either momentum or volatility
- Average Directional Index
- Commodity Channel Index
- Moving Average Convergence/Divergence
- Price Momentum
- Relative Strength Index
- William's % R
- On Balance Volume
- Slope of Linear Regression
- Return Volatility

Use random forest as a regressor to predict the direction of movements
- Relatively high frequency, used non-linear model for more convexity

3. MSGARCH Model

The general Markov-Switching GARCH specification can be expressed as: (Ardia et al. 2017 https://doi.org/10.1016/j.ijforecast.2018.05.004.)

$$y_t|(s_t = k, F_{t-1}) \sim D(0, h_{k,t}, \delta_k)$$

where $D(0, h_{k,t})$, $\delta_k$ is a continuous distribution with a zero mean, time-varying variance $h_{k,t}$ , and additional shape parameters (e.g., asymmetry) gathered in the vector $\delta_k$. $s_t$ is the latent variables that evolves according to an unobserved first-order ergodic homogeneous Markov chain. $F_{t}$ is the filter of information we have by the time $t$.

An illustration of MSGARCH on SPY: the black line is the probability of being in the high volatility regime

Detect Volatility Regime for each instrument
Predict future volatility as the input of allocation model to replace realized volatility

4. Allocation Model

Rebalance weekly, based on forecast volatility, following minimum variance principle across assets
Use forecast instead of historical volatilities to construct covariance matrix

$$\max_{W} \sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{ij}$$

$$s.t. \sum_i w_i = 1,\quad w_i \ge 0, \quad for i = 1,2,3,...,n$$

where $\sigma_i$ are forecast volatilities, which are obtained from the MSGARCH model.

See the notebook here

Reference

[1] Lam, K. and H. Yam (1997): “CUSUM techniques for technical trading in financial markets.” Financial Engineering and the Japanese Markets, Vol. 4, pp. 257–274

[2] David Ardia, Keven Bluteau, Kris Boudt, Leopoldo Catania, "Forecasting risk with Markov-switching GARCH models:A large-scale performance study", International Journal of Forecasting, Volume 34, Issue 4

[3] APA. Lopez de Prado, M. (2018). Advances in financial machine learning, 38-40

[4] Jurczenko, Emmanuel, ed. Risk-based and factor investing. Elsevier, 2015. 10-12