# Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations

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## Abstract

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## 1. Introduction

## 2. Related Works

## 3. Model

- Stylized trading agents
- Non-regulated portfolio trading agents
- Regulated portfolio trading agents

#### 3.1. Markets

#### 3.2. Agents

#### 3.3. Agents: Stylized Trading Agents

- F: Fundamentalist component (Estimation based on the fundamental prices)
- C: Chartist component (Trends)
- N: Noise

- Fundamental factor:$${F}_{t}^{i,s}=\frac{1}{{\tau}_{r}^{i}}ln\left(\frac{{p}_{t}^{s}}{{p}_{t}^{*s}}\right),$$
- Chartist factor:$${C}_{t}^{i,s}=\frac{1}{{\tau}^{i}}\sum _{j=1}^{{\tau}^{i}}ln\left(\frac{{p}_{t-j}^{s}}{{p}_{t-j-1}^{s}}\right),$$
- Noise factor:$${N}_{t}^{i,s}\sim N(0,{\sigma}_{N}^{i}),$$

#### 3.4. Agents: Non-Regulated Portfolio Trading Agents

- Cancel orders which have not been contracted yet.
- Calculate reasonable values of every asset in the same way as stylized trading agents.
- Revise the portfolio with the portfolio optimization algorithm described below.
- On the basis of the revised portfolio, make orders for the difference with those of the current portfolio.

#### 3.5. Agents: Regulated Portfolio Trading Agents

- Calculate CAR based on the current position $\mathbb{x}$ (referred to as $\mathrm{CAR}\left(\mathbb{x}\right)$).
- Calculate R.$$\begin{array}{c}\hfill R=\frac{0.08}{\mathrm{CAR}\left(\mathbb{x}\right)}\end{array}$$
- Calculate the current total share price $\mathrm{Val}\left(\mathbb{x}\right)$ using $\mathbb{x}$ and a reasonable value calculated in the same way as stylized trading agents.
- Calculate the new budget limit B.$$\begin{array}{c}\hfill B=\frac{1}{\frac{R-1}{2}+1}\mathrm{Val}\left(\mathbb{x}\right)\end{array}$$
- Under the budget limit B, re-optimize the portfolio and update $\mathbb{x}$ by Markowitz’s mean-variance approach presented in Section 3.4.
- Check the equation:$$\begin{array}{c}\hfill \mathrm{CAR}\left(\mathbb{x}\right)\ge 0.08.\end{array}$$
- If the portfolio still violates Equation (12), go to step 1 again. If not, $\mathbb{x}$ is the final position, which does not violate the CAR regulation.

#### 3.6. Parameters

- Amount of cash per market that each agent holds
- ${w}_{F}^{i}$: Weight for fundamentalist
- ${w}_{C}^{i}$: Weight for chartist
- ${w}_{N}^{i}$: Weight for noise

- Amount of cash per market that each agent holds $\to 6000$
- ${w}_{F}^{i}$: Weight for fundamentalist → exponential distribution with mean 10.0
- ${w}_{C}^{i}$: Weight for chartist → exponential distribution with mean 1.0
- ${w}_{N}^{i}$: Weight for noise → exponential distribution with mean 10.0

## 4. Experiments

- Pre-running length: 30,000 steps
- Simulation length: 60,000 steps
- Number of trials: 100 times per parameter set

#### 4.1. Experiments for Assessing Effects of Portfolio Trading Agents

- Stylized trading agents: 1000 agents (fixed)
- Non-regulated portfolio trading agents: $0,10,20,\cdots ,100$ agents
- Number of markets (number of assets): $1,2,\cdots ,10$ markets (assets)

#### 4.2. Experiments for Assessing Effects of the CAR Regulation

- Stylized trading agents: 1000 agents (fixed)
- Non-regulated portfolio trading agents: $0,10,20,\cdots ,100$ agents
- Regulated portfolio trading agents: $100,90,80,\cdots ,0$ agents
- Number of markets (number of assets): $1,2,\cdots ,10$ markets (assets)

## 5. Results & Discussion

#### 5.1. Stylized Fact Checks

#### 5.2. Effects of Portfolio Trading Agents

#### 5.3. Effects of CAR Regulation

#### 5.4. Summary of Results and its Discussion

- shocks occur more often.
- big price rises occur less frequently.
- push down market prices in total.
- markets fluctuate more.

#### 5.5. Future Work

## 6. Conclusions

- Adopting portfolio optimization as each agent’s strategy stabilizes markets.
- The existence of a CAR regulation destabilizes markets.
- CAR regulation can cause significant price shocks.
- CAR regulation may suppress price increases.
- CAR regulation pushes down market prices.
- CAR regulation fluctuates market price.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Model outline. The model consists of a number of markets in which three types of agent trade assets.

**Figure 2.**Continuous double auction mechanism for setting the market price. (

**a**) Before inputting a new order. (

**b**) Inputting 80 buy orders at 400.53 (highlighted in yellow). (

**c**) Contracting 50 orders at 400.5 and 30 orders at 400.528 (highlighted in yellow). (

**d**) After contracting.

**Figure 3.**Autocorrelation function (ACF) for logarithm returns. Error bars mean standard deviation for each lag among 500 markets in 100 simulations. The green area shows the 95% confident interval corresponding to each lag.

**Figure 4.**Autocorrelation function (ACF) for 50-step standard deviations of logarithm returns. Error bars mean standard deviation for each lag among 500 markets in 100 simulations. The green area shows the 95% confident interval corresponding to each lag.

**Figure 5.**Frequency distribution of normalized log returns. The blue plot shows the results from simulations. Error bars mean standard deviation for each lag among 500 markets in 100 simulations. The orange plot shows the Gaussian (Normal) distribution.

**Figure 6.**${N}_{DV}$ of experiments assessing the effect of portfolio trading agents. The horizontal axis is the number of non-regulated portfolio trading agents, and the vertical axis in the number of steps in which the market price is below $exp(-0.1)$ times the fundamental price. (Details are explained with Equation (14)). Each series of plots shows results for the corresponding number of markets in the simulation. Error bars show standard deviations.

**Figure 7.**${N}_{DV}$ graph assessing the effect of capital adequacy ratio (CAR) regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the number of steps in which the market price is below $exp(-0.1)$ times the fundamental price. (Details are explained with Equation (14)). Each series of plots shows a simulation series for a certain number of markets. Error bars show standard deviations.

**Figure 8.**${N}_{DV}$ graph assessing the effect of CAR regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the number of steps in which the market price is below $exp(-\mathbf{0}.\mathbf{5})$ times the fundamental price. (Details are explained with Equation (15)). Each series of plots shows a simulation series for a certain number of markets. Error bars show standard deviations. Please note that the vertical axis is logarithmic.

**Figure 9.**Kurtosis of price changes in the experiments for assessing the effect of CAR regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is kurtosis. Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Figure 10.**Mean $DV$ in experiments for assessing the effect of CAR regulation. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the mean of $D{V}_{t}$, which is defined in Equation (14). Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Figure 11.**Steps in which the market prices went up. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the mean number of Steps in which the market prices went up. Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Figure 12.**Steps in which the market prices went down. The horizontal axis is the percentage of regulated portfolio trading agents among all non-regulated and regulated portfolio trading agents. The vertical axis is the mean number of Steps in which the market prices went down. Each series of plots shows results for a certain number of markets in the simulation. Error bars show standard deviations.

**Table 1.**Kurtosis of 5 min interval (Cont 2001).

Data | Kurtosis |
---|---|

S&P 500 | 15.95 |

Dollar/DM | 74 |

Dollar/Swiss | 60 |

Data | Kurtosis |
---|---|

Nikkei 225 | $5.18$ |

TOPIX | $5.65$ |

Compositions in Nikkei225 | $5.84\pm 3.16$ |

Compositions in TOPIX | $9.09\pm 9.84$ |

Less Regulated | More Regulated | |
---|---|---|

Price shocks | Less | More |

Fat tail of lower side (A) | Low | High |

Kurtosis | High | Low |

Fat tail (B) | High | Low |

A+B => Fat tail of upper side | High | Low |

Mean of price | High | Low |

Price up/down | Less frequent | More frequent |

Level of fluctuation | Low | High |

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## Share and Cite

**MDPI and ACS Style**

Hirano, M.; Izumi, K.; Shimada, T.; Matsushima, H.; Sakaji, H.
Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations. *J. Risk Financial Manag.* **2020**, *13*, 75.
https://doi.org/10.3390/jrfm13040075

**AMA Style**

Hirano M, Izumi K, Shimada T, Matsushima H, Sakaji H.
Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations. *Journal of Risk and Financial Management*. 2020; 13(4):75.
https://doi.org/10.3390/jrfm13040075

**Chicago/Turabian Style**

Hirano, Masanori, Kiyoshi Izumi, Takashi Shimada, Hiroyasu Matsushima, and Hiroki Sakaji.
2020. "Impact Analysis of Financial Regulation on Multi-Asset Markets Using Artificial Market Simulations" *Journal of Risk and Financial Management* 13, no. 4: 75.
https://doi.org/10.3390/jrfm13040075