# Quantifying the Impact of Risk on Market Volatility and Price: Evidence from the Wholesale Electricity Market in Portugal

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Portuguese Electricity System

## 4. Data and Method

#### 4.1. Data

#### 4.2. Value-at-Risk Example

_{t}/p

_{t}

_{−1})

^{2}helps reveal the magnitude of the percentage change in the logarithm of prices over time. Including the initial price variable in the MSGARCH $(1,1)$ model indicates a consideration for the starting values of the time series.

#### 4.3. Autocorrelation and Partial Autocorrelation Properties

_{t}/p

_{t}

_{−1})

^{2}to measure the correlation between a time series at different lags. A slowly decreasing ACF indicates that long-term dependence on the data means that past observations substantially affect future observations. In other words, the influence of past values extends across a wide range of periods. The slow decrease in ACF suggests that trends in the time series tend to persist over time. This occurrence could be due to various factors, such as seasonality, trends, or other underlying structures in the data.

#### 4.4. Stability Check of Variables

#### 4.4.1. Unit Root Test

#### 4.4.2. ARCH-LM Test

#### 4.5. Method

#### 4.5.1. AR–ARCH Model Specification

#### 4.5.2. Generalized-ARCH Symmetric Model (GARCH)

#### 4.5.3. Asymmetric Threshold GARCH (p,q) Model

#### 4.5.4. Asymmetric Exponential GARCH (p,q) Model

#### 4.5.5. Markov-Switching GARCH (1,1)

## 5. Empirical Results

#### 5.1. Results of Symmetric GARCH Model

#### 5.2. Results of the Asymmetric GARCH Model

#### 5.3. Results of Markov-Switching Model

## 6. Discussion

## 7. Conclusions and Policy Implications

#### Policy Implications

## 8. Limitations and Future Research

#### 8.1. Study Limitations

#### 8.2. Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Non-logarithmic (not stationary). (

**b**) Logarithmic (stationary) hourly electricity prices (1 January 2016–30 December 2021).

**Figure 2.**Correlation chart for hourly electricity prices. (

**a**) Autocorrelation function (ACF); (

**b**) Partial autocorrelation function (PACF) hourly electricity prices (1 January 2016–30 December 2021).

**Figure 3.**Fluctuation in electricity price and capturing the temporal dependencies and trends in data by ARIMA model estimation.

**Figure 5.**Rapid elimination of shocks to variance ensures the stability of the process over time, by asymmetric EGARCH estimation, making it suitable for the magnitude of fluctuations for long-term forecasting and risk management purposes.

**Figure 6.**The negative impacts of risk volatility when employing GARCHM. Negative fluctuations can result from sudden decreases in business investment, global economic downturns, or market uncertainty. Such events can trigger a rapid price decline as investors respond to increased risks and uncertainties [41].

Variables | Mean | Std. Dev. | Min. | Max. | Sum of Wgt | Variance | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|---|

r = (log p_{t}/p_{t}_{−1})^{2} | 0.158 | 1.279 | −4.605 | 4.578 | 52.600 | 1.636 | −0.467 | 3.652 |

Price | 57.265 | 41.402 | 1.018 | 409 | 52.541 | 1714.126 | 3.463 | 18.391 |

Test | Dickey–Fuller GLS for log(p_{t}/p_{t}_{−1})^{2} | |||
---|---|---|---|---|

[lags] | DF-GLS | 1% Critical | 5% Critical | 10% Critical |

2 | −81.225 | −2.580 | −1.950 | −1.620 |

Min SIC = 0.0367399 at lag2 with RMSE 1.018224 |

ARCH-LM | chi^{2} | df | Prob > Chi^{2} |
---|---|---|---|

${price}_{t-2}$ | 1227.954 | 2 | 0.000 |

r = log(p_{t}/p_{t}_{−1})^{2} | Coef. | St. Err. | t-Value | p-Value | [95% Conf | Interval] | Sig |

${price}_{t-2}$ | −0.111 | 0.005 | −20.295 | 0 | −0.126 | −0.0998 | *** |

C | 0.019 | 0.003 | 5.848 | 0 | 0.013 | 0.0252 | *** |

${\alpha}_{t-2}$ | 0.219 | 0.005 | 46.956 | 0 | 0.216 | 0.228 | *** |

C | 0.665 | 0.002 | 284.647 | 0 | 0.661 | 0.673 | *** |

Mean dependent var | 0.000 | SD dependent var | 0.896 | ||||

Number of obs | 52,597 | Chi-square | 411.710 | ||||

Prob > chi^{2} | 0.000 | Akaike crit. (AIC) | 136,053.441 | ||||

r = log(p_{t}/p_{t}_{−1})^{2} | Coef. | St. Err. | t-value | p-value | [95% Conf | Interval] | Sig |

C | 0.017 | 0.004 | 4.885 | 0 | 0.016 | 0.025 | *** |

${\alpha}_{t-2}$ | 0.291 | 0.007 | 41.603 | 0 | 0.278 | 0.305 | *** |

${\gamma}_{t-2}$ | −0.093 | 0.009 | −10.576 | 0 | −0.118 | −0.075 | *** |

${\beta}_{t-2}$ | −0.037 | 0.002 | −21.834 | 0 | −0.041 | −0.034 | *** |

C | 0.692 | 0.003 | 223.437 | 0 | 0.686 | 0.698 | *** |

Mean dependent variable | 0.000 | SD dependent variable | 0.896 | ||||

Number of obs | 52,599 | Chi-square | |||||

Prob > chi^{2} | Akaike crit. (AIC) | 136,380.531 |

r = log(p_{t}/p_{t}_{−1})^{2} | Coef. | St. Err. | t-Value | p-Value | [95% Conf | Interval] | Sig |

C | 0.024 | 0.003 | 7.046 | 0 | 0.017 | 0.032 | *** |

${\alpha \gamma}_{t-2}$ | −0.026 | 0.005 | −5.519 | 0 | −0.035 | −0.017 | *** |

${\alpha \gamma}_{t-2}-A$ | 0.415 | 0.006 | 73.553 | 0 | 0.404 | 0.426 | *** |

${\beta \gamma}_{t-2}$ | −0.048 | 0.008 | −5.809 | 0 | −0.064 | −0.032 | *** |

C | −0.195 | 0.004 | −44.384 | 0 | −0.204 | −0.186 | *** |

Mean dependent variable | 0.000 | SD dependent variable | 0.896 | ||||

Number of obs. | 52,599 | ||||||

Prob > chi^{2} | 0.000 | Akaike crit. (AIC) | 135,481.006 | ||||

r = log(p_{t}/p_{t}_{−1})^{2} | Coef. | St. Err. | t-Value | p-Value | [95% Conf | Interval] | Sig |

C | 0.096 | 0.008 | 11.71 | 0 | 0.086 | 0.112 | *** |

${\sigma}^{2}$ | −0.104 | 0.015 | −10.93 | 0 | −0.123 | −0.085 | *** |

${\alpha}_{t-2}$ | 0.221 | 0.004 | 49.50 | 0 | 0.212 | 0.236 | *** |

${\beta}_{t-2}$ | −0.046 | 0.003 | −16.79 | 0 | −0.051 | −0.042 | *** |

C | 0.707 | 0.004 | 195.11 | 0 | 0.735 | 0.714 | *** |

Mean dependent variable | 0.000 | SD dependent variable | 0.896 | ||||

Number of obs. | 52,599 | Chi-square | 119.381 | ||||

Prob > chi^{2} | 0.000 | Akaike crit. (AIC) | 136,348.364 |

Sample: 1–52,614 | No. of obs = 52,614 | |||||

Number of states = 2 | AIC = 2.0668 | |||||

Unconditional probabilities: Transition | HQIC = 2.0670 | |||||

SBIC = 2.0676 | ||||||

Log likelihood = −54,364.995 | ||||||

Price 1 | Coef. | Std. Err. | z | p > z | [95% Conf. | Interval] |

State 1 | ||||||

C | 3.255 | 0.006 | 526.420 | 0.000 | 3.243 | 3.267 |

State 2 | ||||||

C | 4.232 | 0.006 | 683.300 | 0.000 | 4.220 | 4.244 |

$\sigma 1$ | 0.492 | 0.003 | 0.486 | 0.499 | ||

p11 | 0.603 | 0.007 | 0.590 | 0.616 | ||

p21 | 0.383 | 0.007 | 0.369 | 0.396 | ||

State 1 | ||||||

AR (L1) | 0.224 | 0.009 | 23.49 | 0.000 | 0.205 | 0.242 |

AR (L2) | 0.283 | 0.009 | 28.14 | 0.000 | 0.261 | 0.300 |

C | 3.236 | 0.005 | 554.69 | 0.000 | 3.224 | 3.247 |

State 2 | ||||||

AR (L1) | 0.223 | 0.009 | 23.98 | 0.000 | 0.204 | 0.241 |

AR (L2) | 0.297 | 0.009 | 29.93 | 0.000 | 0.278 | 0.317 |

C | 4.246 | 0.005 | 737.60 | 0.000 | 0.435 | 0.443 |

$\sigma 2$ | 0.439 | 0.002 | 0.435 | 0.443 | ||

p11 | 0.478 | 0.005 | 0.467 | 0.489 | ||

p21 | 0.499 | 0.005 | 0.488 | 0.510 |

Number of Obs. | 52.612 | Std. Err | [95% Conf. | Interval] |
---|---|---|---|---|

State1 | 0.917 | 0.021 | 1.878 | 1.959 |

State2 | 2.003 | 0.022 | 1.960 | 2.048 |

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## Share and Cite

**MDPI and ACS Style**

Entezari, N.; Fuinhas, J.A.
Quantifying the Impact of Risk on Market Volatility and Price: Evidence from the Wholesale Electricity Market in Portugal. *Sustainability* **2024**, *16*, 2691.
https://doi.org/10.3390/su16072691

**AMA Style**

Entezari N, Fuinhas JA.
Quantifying the Impact of Risk on Market Volatility and Price: Evidence from the Wholesale Electricity Market in Portugal. *Sustainability*. 2024; 16(7):2691.
https://doi.org/10.3390/su16072691

**Chicago/Turabian Style**

Entezari, Negin, and José Alberto Fuinhas.
2024. "Quantifying the Impact of Risk on Market Volatility and Price: Evidence from the Wholesale Electricity Market in Portugal" *Sustainability* 16, no. 7: 2691.
https://doi.org/10.3390/su16072691