Impact Assessments of the CAR Regulation
using Artificial Markets
Masanori HIRANO1 , Kiyoshi IZUMI2 , Hiroki SAKAJI2 ,Takashi SHIMADA2 , and Hiroyasu MATSUSHIMA2
1

Faculty of Engineering, The University of Tokyo, Tokyo, Japanhirano@g.ecc.u-tokyo.ac.jp
https://mhirano.jp/
2
School of Engineering, The University of Tokyo, Tokyo, Japan{izumi, sakaji, shimada, matsushima}@sys.t.u-tokyo.ac.jp

Abstract. In this study, we assessed the impact of capital adequacy
ratio (CAR) regulation like that in the Basel regulatory framework. To
asses impact such as destabilizing eﬀects (e.g., whether CAR regulation
destabilizes markets or not), we conducted simulations of an artificial
market, one of the computer simulations imitating real financial markets. And, we proposed a new model with continuous double auction
markets, stylized trading agents and two kinds of portfolio agent. The
portfolio agents had trading strategies incorporating Markowitz’s portfolio optimization. Additionally, the portfolio agents of one type were
under regulation. From the simulations, we found that: 1. adopting portfolio optimization as each agent’s strategy stabilizes markets; 2. the existence of CAR regulation destabilizes markets; 3. CAR regulation cancause significant price shocks; 4. CAR regulation also can suppress priceincreases; 5. CAR regulation pushes down market prices. From these results, we conclude that CAR regulation can have negative eﬀects on asset
markets.
Keywords: Artificial market · CAR regulation · Portfolio.

1

Introduction

In December 2017, the Basel Committee on Banking Supervision reached anagreement on a reformed international regulatory framework for banks [2]. Thisagreement set out changes to “Basel III”, one in a series of banking regulations
beginning with “Basel I” in 1988, aimed at avoiding serious financial incidents
fraught with so-called “systemic risk.”
Systemic risk is one of the most significant dangers to financial markets,
wherein small triggers cause huge financial shocks because of economic system
failures. For example, the financial crisis of 2007-2008 was triggered only by acrisis in the subprime mortgage market in United States. It aﬀected not only US
financial markets, but also financial markets around the globe, including thoseof Japan. Such systemic risks can seriously destabilize markets, and the current
Basel regulatory framework is designed with the intention of reducing them.

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M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA

Regarding the history of these frameworks, a modified Basel I was agreed
to in 1996 [3]. This regulatory framework included market operation risks forthe first time. The Capital Adequacy Ratio (CAR) regulation was establishedafter Basel II, and modifications to it have subsequently been made [1]. This
regulation aims to prevent banks from going bankrupt as a result of financial
shocks and obligates them to keep enough money on hand. It calls on banks to dorisk management when they hold risky assets such as equities, derivatives, andso on. However, when markets fluctuate remarkably, the risk of assets increases
and the risk management prevents banks from retaining such assets. Thus, banks
have to sell their assets, and markets destabilize as a result.
Although CAR regulation was introduced as a way of reducing systemicrisks, the possibility of it actually having a destabilizing eﬀect on markets was
suggested by Benink et al. [5]. According to that study, the CAR regulation of
the Basel II accord destabilizes markets when they have uncertainties.
Hermsen studied the destabilizing eﬀect by conducting simulations [9]. Although his research showed that Basel II has a destabilizing eﬀect on markets,it only tested its assertions with a single asset, which is far from the reality oflarge markets.
Another study by Yonenoh [13] tested the destabilizing eﬀect with multi-asset
simulations. However, the model used in it contained a number of unrealistic
assumptions. For example, the model’s markets did not have enough buy orsell orders. In addition, under the CAR regulation, agents could not obtain the
global optimized position, which means that under the regulation, agents got
lost in the diversity of assets, and using an unrealistic optimization algorithm,
they would buy or sell only one or two kinds of asset. Moreover, although thetrading strategy of the agents considered changes occurring over diﬀerent timespans, such as a day or month, the markets themselves or the changes in pricein his model did not reflect what occurs in real markets.
Thus, as a way of overcoming the shortcomings of the previous studies, we
decided to make a new model incorporating multi-asset markets and CAR regulation.
In the new model, we used artificial market simulations, one of the multiagent simulations. Simulations of this type are widely used (for example, see
Torii et al.’s work [11]), and they have a number of benefits. For instance, whena new regulation is about to be introduced, it can be tested in simulations todetermine if it will cause any harm to real markets. In addition, comparative
experiments can be conducted using simulations.
In particular, we chose Plham (Platform for Large-scale and High-frequency
Artificial Market) [12] for the artificial market simulations, on which we examined the destabilizing eﬀects of CAR regulation and made the new multi-asset
model. Moreover, we sought to reveal other eﬀects of CAR regulation throughthese simulations.

Impact Assessments of the CAR Regulation using Artificial Markets

2

3

Model

Here, we describe the new multi-asset model of the artificial market. The model
contains markets and agents of diﬀerent types, acting like traders in real financial
markets and using their own strategies. The types of agent are as follows.
– Stylized trading agents– Non-regulated portfolio agents– Regulated portfolio Agents
Each agent can buy or sell any asset in the markets subject to restrictions
such as cash, leverage, or CAR regulation (Fig. 1). The markets are based on
Torii et al.’s multi-asset artificial market [11]. The stylized trading agents are
based on Chiarella and Iori’s model [6].

Markets

time

Market N(Asset N market)



time

Price

Market 2(Asset 2 market)
Price

Price

Market 1(Asset 1 market)

time

OrdersSell or Buy

Stylized AgentsNon-regulated Portfolio Agents
Fundamental Price, Trend,
Noise, Cash, Risk, Return,
Leverage

Fundamental Price
Trend, Noise…

…

Regulated Portfolio Agents
Fundamental Price, Trend,
Noise, Cash, Risk, Return,
Leverage, CAR regulation…

Fig. 1: Model outline. The model consists of a number of markets in which three typesof agent trade assets.

In every step of the simulation, some agents are chosen and place their orders.
The number of those agents is the same number as the number of markets. Thus,
it is not fixed how many orders are placed or how many orders are contracted
in one step.
2.1

Markets

Every asset has a unique market with a continuous double auction mechanism
for setting the market price. Any sell or buy order can be placed and the prices

4

M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA
Sell Order Book

Buy Order Book

Sell Order Book

Buy Order Book

Price
400.5
400.528400.69401.2
401.321401.555
402.001Price
400.499400.387400.2
400.19400.0
399.9
399.857

Price
400.5
400.528400.69401.2
401.321401.555
402.001Price
400.53400.499400.387400.2
400.19400.0
399.9

Amount
50
38
20
1
2
30
4

Amount
40
28
5
20
3
10
2

(a) Before inputting a new order

Amount
50
38
20
1
2
30
4

Amount80 <- NEW
40
28
5
20
3
10

(b) Inputting 80 buy orders at 400.53

Sell Order Book

Buy Order Book

Sell Order Book

Buy Order Book

Price
400.5
400.528400.69401.2
401.321401.555
402.001Price
400.53400.499400.387400.2
400.19
400.0
399.9

Price
400.528400.69401.2
401.321401.555
402.001
402.02Price
400.499400.387400.2
400.19400.0
399.9
399.857

Amount
50
38
20
1
2
30
4

Amount80 <- NEW
40
28
5
20
3
10

(c) Contracting 50 orders at 400.5 and
30 orders at 400.528

Amount
8
20
1
2
30
4
12

Amount
40
28
5
20
3
10
2

(d) After contracting

Fig. 2: Continuous double auction mechanism for setting the market price.

of orders are the real number (not limited to integers). Examples of order books
are shown in Fig. 2. Before inputting a new order, usually, there are also otherorders on both sell and buy order books. (Fig. 2 (a)) Then, if one agent input
80 buy orders at 400.53, the orders are placed on a buy order book. (Fig. 2 (b))
In the case of the order books that appear in Fig. 2, the 80 new buy orders canbe contracted with existing sell orders, 50 sell orders at the price of 400.5 and
30 orders in 38 sell orders at the price of 400.528. (Fig. 2 (c)) After contracting,
only 8 sell orders in 38 sell orders at the price of 400.528 are still on the sell
book, and all contracted orders vanish. (Fig. 2 (d))
Market prices are decided separately for every asset in each market throughthe continuous double auction mechanism. Transaction fees are ignored.
Every asset has a fundamental price. This price is for agents to decide theirown estimated value for each asset, and it is determined in accordance withmultivariate geometric Brownian motion (known as a random walk). In the simulations, the mean of the Brownian motion was set at 400.0, and the variance
was set at 1.0 × 10−6 .
In addition, we assumed that there was no correlation between any pairs ofassets.
2.2

Agents

The three types of agent roughly imitate traders in real markets. Each one has
its own trading strategy or trading algorithm, which is explained below. Initially,
all agents have 50 assets per market.

Impact Assessments of the CAR Regulation using Artificial Markets

2.3

5

Agents: Stylized Trading AgentsThe stylized trading agents are based on those of Chiarella and Iori [6].
In every step, the stylized trading agents estimate their reasonable price foreach asset by using historical data and fundamental prices. They use three typesof index, which they calculate by themselves using their own unique parameters.
– F : Fundamentalist component (Estimation based on the fundamental prices)– C: Chartist component (Trends)– N : Noise
A stylized trading agent, agent i, decides its reasonable price for asset (market) s at time t, as follows.
iiAgent i has three unique weights; wFi ≥ 0 for F , wC
≥ 0 for C, and wN≥0i,sfor N (where wF + wC + wN > 0). The estimated geometric return rt is
rti,s =

1
i + wiwFi + wC
Ni
i
(wFi Fti,s + wC
Cti,s + wN
Nti,s ).

(1)

As described below, wF , wC , and wN were set to exponential distributions
with means of 10.0, 1.0, and 10.0. Fti,s , Cti,s , and Nti,s are defined with pst (theprice at time t), p∗st (the fundamental price at time t), τr (mean reversion time,
which indicates how long the agent assumes it takes for the price to go back to
the fundamental price), τ (the agent’s time horizon, which means how far backi
) (a norinto the past the historical data goes that the agent uses), and N (0, σN
mal (Gaussian) distribution). In the simulations, τr was a uniform distributioni[50, 150], τ was a uniform distribution [100, 200], and σN= 1.0 × 10−3 .
( s)
1
pt
Fti,s = i ln
(2)
τr
p∗s
t
(
)
τ
pst−j
1∑
i,s
ln
(3)
Ct =
τ j=1
pst−j−1i
Nti,s ∼ N (0, σN)(4)

On the basis of the equations above, the agent decides its reasonable pricepi,st+∆t at time t + ∆t:
(
)
i,s
s
pi,s
=
p
exp
r
∆t
.
t
t
t+∆t

(5)

Then, on the basis of this price, the agent decides whether to buy or sell onesunit share; if pi,st+∆t > pt , the agent buys one unit of asset s, and if not, the agent
sells one unit of asset s at time t.
Stylized trading agents are aimed at making enough orders for contracting.
This is because, if there were few orders on the markets’ order books, an agent’s
order would not be contracted when other portfolio agents make orders. Thus,

6

M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA

only stylized trading agents are allowed to “sell short”, which is to place sell orders without holding stock, and “margin trade”, which is to place orders without
holding enough money.
In addition, stylized trading agents can access and buy or sell any asset in
the markets, and they make decisions separately whether they will buy or selleach asset.
2.4

Agents: Non-Regulated Portfolio AgentsNon-regulated portfolio agents have a trading strategy based on portfolio optimization. This type of agent is based on Yonenoh’s multi-asset agents with risk
management [13].
In the same way as stylized trading agents, non-regulated portfolio agents canaccess all markets and can buy or sell any asset. However, in contrast to stylized
trading agents, non-regulated portfolio agents choose their position, how many
shares of each asset they will buy or sell, inclusively. That is, whether they will
buy or sell an asset depends on the other assets, and the decision also depends
on the results of the portfolio optimization.
Non-regulated portfolio agents optimize their position in each τpi step. τpi isthe term in which to keep the current position. This variable is given at random
to each agent, following an exponential distribution whose mean and standard
deviation are each 150. Thus, the agents take actions only in each τpi step. The
actions are as follows.
1. Cancel orders which have not been contracted yet.
2. Calculate reasonable values of every asset in the same way as stylized trading
agents.
3. Revise the portfolio with the portfolio optimization algorithm described below.
4. On the basis of the revised portfolio, make orders for the diﬀerence withthose of the current portfolio.
Markowitz’s mean-variance approach [10] is used in the optimization phase(the third phase above). The expected utility function is defined with a position
matrix x, matrix of reasonable values Prsn , and variance-covariance matrix ofevery asset for the last τ steps Ω. t A means the transposed matrix of A.
EU(x) = tPrsn x −

1t
xΩ x
2

(6)

The constraints are as follows. The agents have a budget, and they are notallowed to sell short. Thus, all components in x are nonnegative. Agents find xthat fits the constraints and maximizes EU(x).
Non-regulated portfolio agents have capital and leverage. In the simulations,the capital was 6,000 per market and the leverage limit was 10, which meansthat the budget limit is 60,000 per market. For example, if there are five markets,the budget limit is 300,000.

Impact Assessments of the CAR Regulation using Artificial Markets

2.5

7

Agents: Regulated Portfolio Agents

Regulated portfolio agents are almost the same as non-regulated portfolio agents.
However, they have additional constraints, which model the CAR regulation. The
CAR regulation is based on Basel I [3] and Basel II [1].
The CAR regulation in this model uses the Value at Risk (VaR) and regulates
agents when the value of assets held by each agent falls.
(CAR) =

(Capital)≥ 8%12.5 × (Markets Risk)(7)

This equation follows the rule modeling Basel I after introduction of market risk
regulation [3]. The equation above is also defined by it.
Markets risk is calculated as(Markets Risk) = (Current Total Share Price) × (1 − exp (VaR)).

(8)

The current total share price does not include cash, because cash is meant tobe a non-risk property. According to this equation, the more leverage agentstake on, the more risk they have to take on as well. The “(1 − exp (VaR))” part
indicates the possibility of deficits using VaR. Because VaR is calculated on alogarithmic scale, it is included as an exponent in this equation.
VaR is calculated as√√(VaR) = −1.0 × (99% One-sided Confidence Interval) × T × xΩ x. (9)This calculation involves taking the floor of the upper one-sided confidence interval and uses the root T multiply method [8]. x is the position matrix of all
assets. The holding term of an asset T is set to 10 steps, and Ω is the variancecovariance matrix of all assets for the last 250 steps, as described in Basel I
and II [4], whose CAR regulation uses historical data for 250 business days andexpects a holding term of 10 business days.
When the agents’ portfolio violates the regulation, they revise their portfolios
as follows.
1. Calculate CAR based on the current position x (referred to as CAR(x)).
2. Calculate R.
0.08
R=
(10)
CAR(x)

3. Calculate the current total share price Val(x) using x and a reasonable value
calculated in the same way as stylized trading agents.
4. Calculate the new budget limit B.
1
B = R−1
Val(x)(11)
2 +1
5. Under the budget limit B, re-optimize the portfolio and update x.
6. Check the equation:
CAR(x) ≥ 0.08.

(12)

7. If the portfolio still violates Eq. 12, go to step 1 again. If not, x is the final
position, which does not violate the CAR regulation.

8

M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA

2.6

Parameters

All agents have parameters. Some parameters were decided beforehand; others
were decided by conducting a parameter search over a number of simulations.
The agent parameters decided by parameter search are– Amount of cash per market that each agent holds– wFi : Weight for fundamentalisti– wC: Weight for chartisti– wN: Weight for noise
These parameters are decided by simulating with many parameter sets. In
this study, the candidates for the amount of cash were 4,000, 6,000, 8,000, and12,000, while the candidates for the weights were exponential distributions withmeans of 1.0, 3.0, 5.0, and 10.0. Then, the target kurtosis of the market pricechange was set to about 15 for five markets, 1,000 stylized trading agents, and
100 non-regulated portfolio agents. Kurtosis, κ, is defined with the logarithmic
return rt :κ=

(rt − rt )4(rt − rt )2

2 − 3.

(13)

Kurtosis was used in the parameter search, because a large kurtosis is a featureof “fat-tailed” distributions and it is a stylized fact characterizing real markets[7]. Here, events that occur rarely in accordance with a normal (Gaussian) distribution occur more often when they follow a fat-tailed distribution. Because
κ = 0 for the normal (Gaussian) distribution, it is a good index for indicating a
fat tail.

Table 1: Kurtosis of 5 min. interval [7]Data
KurtosisS&P 500
15.95
Dollar/ DM
74
Dollar/ Swiss
60
Table 2: Kurtosis of daily price changes in Japanese markets
Data
Kurtosis
Nikkei 225
5.18
TOPIX
5.65
Compositions in Nikkei225 5.84 ± 3.16
Compositions in TOPIX 9.09 ± 9.84

According to Tables 1 and 2, the possible kurtosis seems to be under 20.
The test with five markets, 1,000 stylized trading agents, and 100 non-regulated
portfolio agents showed price changes with comparatively higher kurtosis than

Impact Assessments of the CAR Regulation using Artificial Markets

9those of other simulations in this study. So, we assumed the target kurtosis tobe about 15.
In addition, we checked for “absence of autocorrelations” and “volatility clustering”, which are two of Cont’s stylized facts [7].
The parameter search yielded the following results.
– Amount of cash per market that each agent holds → 6, 000– wFi : Weight for fundamentalist → exponential distribution with mean 10.0i
– wC
: Weight for chartist → exponential distribution with mean 1.0i– wN: Weight for noise → exponential distribution with mean 10.0

3

Experiments

We designed two diﬀerent experiments: one for assessing the eﬀect of portfolio
agents, the other for checking the eﬀect of the CAR regulation.
Before explaining each experiment, we should explain the evaluation index.
The index evaluates in how many steps the market price drops abnormally. We
define “abnormal” as:( )pt≤ −0.05.
(14)
DVt = lnp∗t
In this equation, pt means the market price and p∗t means the fundamental price.
Moreover, NDV is defined as the number of steps in which Eq. 14 is true.
The common settings for the simulations were as follows.
– Pre-running length: 30,000 steps– Simulation length: 60,000 steps– Number of trials: 100 times per parameter set
3.1

Experiments for assessing eﬀects of portfolio agentsFirst, using only stylized trading agents and non-regulated portfolio agents, as
listed below, we experimented on the eﬀect of portfolio agents.
– Stylized trading agents: 1,000 agents (fixed)– Non-regulated portfolio agents: 0-100 agents (steps of 10 agents)– Number of markets (number of assets): 1-10 markets (assets)
3.2

Experiments for assessing eﬀects of the CAR regulation

Second, we included regulated portfolio agents. Here, the total number of nonregulated portfolio agents and regulated portfolio agents were fixed to 100 agents.
We experimented by changing the ratio of non-regulated portfolio agents andregulated portfolio agents.
– Stylized trading agents: 1,000 agents (fixed)– Non-regulated portfolio agents: 0-100 agents (varied in steps of 10 agents)– Regulated portfolio agents: 100-0 agents (varied steps of 10 agents)– Number of markets (number of assets): 1-10 markets (assets)

10

M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA

4

Results & Discussion

4.1

Eﬀects of portfolio agents

Figure 3 shows the results of the experiments assessing the eﬀect of portfolio
agents.
16000

14000

12000

NDV

10000

8000

markets = 10
9
8
7
6
5
4
3
2
1

6000

4000

2000
0

20

40
60
Number of non-regulated portfolio agents

80

100

Fig. 3: NDV of experiments assessing eﬀect of portfolio agents. The horizontal axis
is the number of non-regulated portfolio agents, and the vertical axis in thenumber of steps in which the market price is below exp (−0.05) times thefundamental price. Each series of plots shows results for the corresponding
number of markets in the simulation. Error bars show 1σ.

According to Fig. 3, the more non-regulated portfolio agents there are in themarkets, the fewer steps there are whose market price goes below exp (−0.05)
times the fundamental price. This means non-regulated portfolio agents stabilize
markets.
Ordinarily, portfolio optimization is thought to stabilize only individual trading returns. However, these results show that portfolio optimization can alsostabilize whole markets.
In our opinion, because portfolio optimization can find market equilibria
points, it can improve the eﬃciency of markets. In short, portfolio optimization
might help to find the correct value for each asset, and it has a stabilizing eﬀect
on markets.

Impact Assessments of the CAR Regulation using Artificial Markets

11

In addition, Fig. 3 shows that the more assets there are in portfolios, themore stable that markets become. Additionally, in the case of 5-10 markets, thestabilizing eﬀect saturates.
These results also suggest that the number of portfolio agents is in the appropriate range to examine these eﬀects, because the figure clearly shows changes
in NDV .
4.2

Eﬀects of CAR regulation

18000

16000

14000

NDV

12000

10000

8000
markets = 10
9
8
7
6
5
4
3
2
1

6000

4000

2000
0

20

40
60
Percentage of regulated portfolio agents

80

100

Fig. 4: NDV graph assessing eﬀect of CAR regulation. The horizontal axis is the percentage of regulated portfolio agents among all non-regulated and regulated
portfolio agents. The vertical axis is the number of steps in which the market
price is below exp (−0.05) times the fundamental price. Each series of plots
shows a simulation series for a certain number of markets. Error bars show 1σ.

The far left of Fig. 4 shows NDV in the case that the percentage of regulated
portfolio agents is 0%. The results here are under the same condition as in thecase that the number of portfolio agents is 100 in Fig. 3.
According to this graph, regulated portfolio agents make NDV larger, whichmeans CAR regulation causes more and more price shocks.
Moreover, when the percentage of portfolio agents regulated by Basel is 100%,
the diﬀerence in NDV between the instances of one market and ten markets is

12

M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA

very little. It suggested that CAR regulation can suppress the stabilizing eﬀect
of portfolio agents.
These results show that CAR regulation may destabilize markets.
Let us consider why this happens. CAR regulation would be invoked whenmarket prices fall and risks of holding assets increase; this means that agentswould have to sell their assets. In turn, the regulation would have more and more
impact on other agents. Thus, under these conditions, selling would induce moreselling and lead to significant price shocks.
Now, let us look for other eﬀects of CAR regulation by examining Figs. 5, 6,
and 7.

18

markets = 10
9
8
7
6
5
4
3
2
1

16

14

Kurtosis

12

10

8

6

4

2

0
0

20

40
60
Percentage of regulated portfolio agents

80

100

Fig. 5: Kurtosis of price changes in the experiments for assessing eﬀect of CAR regulation. The horizontal axis is the percentage of regulated portfolio agents among
all non-regulated and regulated portfolio agents. The vertical axis is kurtosis. Each series of plots shows results for a certain number of markets in thesimulation. Error bars show 1σ.

Figure 5 shows the kurtosis of price changes. The definition of kurtosis is thesame as in Eq. 13.
According to this figure, having more regulated portfolio agents decreases
kurtosis. This suggests that CAR regulation eliminates the fat-tail tendency
from markets.

Impact Assessments of the CAR Regulation using Artificial Markets

13

The results depicted in the NDV and kurtosis graphs suggest the following
hypothesis: CAR regulation causes more price shocks and eliminates the fat-tailtendency, and CAR regulation depresses prices and decreases chances of market
prices rising, because a rising market price indicates that there is more chance ofthe price decreasing. In addition, agents sell assets during sudden market pricerises, because the chance of a price shock also increases in the CAR regulatory
framework.
Thus, CAR regulation may depress whole markets.
Figure 6 shows the skewness of price changes. The skewness is defined as:γ=(rt − rt )3
3

.

(15)

(rt − rt )2 2

0.15

markets = 10
9
8
7
6
5
4
3
2
1

0.1

Skewness

0.05

0

-0.05

-0.1
0

20

40
60
Percentage of regulated portfolio agents

80

100

Fig. 6: Skewness of price changes in experiments for assessing eﬀect of CAR regulation. The horizontal axis is the percentage of regulated portfolio agents among
all non-regulated and regulated portfolio agents. The vertical axis is skewness.
Each series of plots corresponds to a certain number of markets in the simulation. Error bars show 1σ.

Figure 7 shows the changes in mean DVt . DVt is defined in Eq. 14; it is theratio of the market price to the fundamental price.
These two figures support the hypothesis that CAR regulation depresses
whole markets. In Fig. 6, the skewness of price changes decreases as the number

14

M. HIRANO, K. IZUMI, H. SAKAJI, T. SHIMADA, H.MATSUSHIMA
0.005

0

DVmean-0.005-0.01
markets = 10
9
8
7
6
5
4
3
2
1

-0.015

-0.02
0

20

40
60
Percentage of regulated portfolio agents

80

100

Fig. 7: Mean DV in experiments for assessing eﬀect of CAR regulation. The horizontal
axis is the percentage of regulated portfolio agents among all non-regulated andregulated portfolio agents. The vertical axis is mean of DVt , which is definedin Eq. 14. Each series of plots shows results for a certain number of markets inthe simulation. Error bars show 1σ.

of regulated portfolio agents increases. A decrease in skewness means the peakof the price change distribution shifts to the right (in the positive direction).
In Fig. 7, a greater number of regulated portfolio agents depresses the mean ofDVt .
In summary, we suppose that three dynamics due to CAR regulation are atplay: price shocks occur more often; prices recover in a step by step fashion; andprice rises above the fundamental price occur less frequently. That price shocks
occur more often is evident from the changes in NDV . That prices recover in a
step by step fashion can be expected from the first dynamic and that the skewnessof price changes goes down with more regulated agents. The third dynamic, thatprice rises above the fundamental price occur less frequently, follows from thatbesides the drop in skewness, kurtosis also falls as the number of regulated agentsincreases.

5

Conclusion

We examined the eﬀect of CAR regulation, as set out in the Basel regulatory
framework, in agent-based simulations. By using agents who buy or sell at rea-

Impact Assessments of the CAR Regulation using Artificial Markets

15

sonable prices, agents whose strategy is portfolio optimization, and agents whose
strategy is portfolio optimization under the regulation in artificial financial markets, we simulated two scenarios. The results lead us to the following 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.
Thus, we conclude that CAR regulation has negative eﬀects for markets
widely. Although it might be adequate to prevent systemic risks and chain
bankruptcy, CAR regulation can have negative eﬀects at least on assets markets
and if significant price shocks happen, there is a possibility that bankruptcies
are caused because of the price shocks.
Regarding future work, our finding that CAR regulation can suppress priceincreases is a new finding that should be the subject of verification. Moreover, weshould examine other ways to calculate risk, e.g., by using the expected shortfallin the latest CAR regulation, instead of the VaR used in this study.
Acknowledgement
This research was supported by KAKENHI (no. 15H02745) and MEXT via
Exploratory Challenges on Post-K computer (study on multilayered multiscale
space-time simulations for social and economic phenomena).

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