MULTI-AGENT BASED MODELING APPLIED TO PORTFOLIO SELECTION IN THE DOOM-LOOP OF SOVEREIGN DEBT CONTEXT

Rosa, Paulo Sérgio; Gartner, Ivan Ricardo; Ralha, Célia Ghedini

doi:10.1590/0101-7438.2019.039.01.0057

Paulo Sérgio Rosa ^****Corresponding author.

Programa de Pós-Graduação em Administração / FACE, Universidade de Brasília (UnB), Campus Darcy Ribeiro, 70910-900 Brasília, DF, Brazil. E-mails: psrosabsb@gmail.com; irgartner@unb.br

http://orcid.org/0000-0003-4481-1916

Ivan Ricardo Gartner

Programa de Pós-Graduação em Administração / FACE, Universidade de Brasília (UnB), Campus Darcy Ribeiro, 70910-900 Brasília, DF, Brazil. E-mails: psrosabsb@gmail.com; irgartner@unb.br

Célia Ghedini Ralha

Departamento de Ciência da Computação, Universidade de Brasília (UnB), Campus Darcy Ribeiro, 70910-900 Brasília, DF, Brazil. E-mail: ghedini@unb.br

^**Corresponding author.

Parameter	Setup Process	Option Values	Cumulative Density Function
Number of assets of the market portfolio	Fixed	6	-
Investment strategy	Random draw $\in ℝ ~ U (0,1)$	Random assets	0.25
		Weighted by IBOVESPA participation	0.50
		Segment	0.75
		Technical analysis	1.00
Portfolio rebalance period (months)	Random draw $\in ℝ ~ U (0,1)$	Monthly	0.16
		Bimestrial	0.33
		Quarterly	0.50
		Every 4 months	0.66
		Every 5 months	0.83
		Semi-annual	1.00
Stop gain/loss limit	Random draw	Active	0.50
	$\in ℝ ~ U (0,1)$	Not Active	1.00
	Random draw $\in ℝ ~ N (15 %,2 %)$	Limit in percentage if stop is active	-

Agent Type	Portfolio Performance		Median	Max.	Mean percentile	Mean percentile	Performance Above Inflation (cases)
Agent Type	μ	σ	Median	Max.	Mean percentile	Mean percentile	Performance Above Inflation (cases)
AgT - Risk-Averse	267.89	87.43	256.20	830.26	623.66	101.00	84%
AgT - Risk-Neutral	187.12	130.89	156.13	1,265.71	869.39	21.39	38%
AgT - Risk-Seeking	110.11	131.52	71.69	1,510.70	939.78	1.59	15%

Periods	$μ_{A g T = 1}$	$σ_{A g T = 1}$				Results
	$μ_{A g T = 2}$	$σ_{A g T = 2}$	${\hat{S h}}_{1,2}$	Z_{1, 2}	p-value_{1, 2}
	$μ_{A g T = 3}$	$σ_{A g T = 3}$	${\hat{S h}}_{1,3}$	Z_{1, 3}	p-value_{1, 3}
01/2006-06/2008	60%	16%
	87%	33%	0.06	2.15	0.032^**	Rejects H ₀
	116%	52%	0.12	2.95	0.003^***	Rejects H ₀
07/2008-12/2010	26%	22%
	18%	45%	0.08	2.75	0.006^***	Rejects H ₀
	2%	72%	0.18	3.89	0.000^***	Rejects H ₀
01/2011-06/2013	4%	25%
	-16%	51%	0.06	1.73	0.084^*	Do Not Rejects H ₀
	-33%	82%	0.11	2.07	0.038^**	Rejects H ₀
07/2013-01/2017	40%	28%
	24%	56%	0.156	3.88	0.000^***	Rejects H ₀
	3%	89%	0.347	5.23	0.000^***	Rejects H ₀
2006-2017 (full period)	168%	32%
	87%	65%	0.81	12.50	0.000^***	Rejects H ₀
	10%	106%	1.74	15.12	0.000^***	Rejects H ₀

1. for each agent agI _n do
2. α_{t, n, k} ← weight preference for risky assets
3. $R f_{t}_{, n, k} \leftarrow (1 - α_{k})$
4. calculate the new weight vector ω_{(t, n, k)} , using the assets $s t k_{i} \in m a r k e t p o r t f o l i o_{t}$
5. calculate the new value to invest (or to borrow) in the risk-free asset
6. calculate the new value to invest in each asset stk _i , according to ω_{t, n, k}

1. for each asset $s t k_{i} \in {market portfolio}_{t}$
2. asset return $μ_{i, t} \leftarrow \frac{P r i c e_{i, t}}{P r i c e_{i, t - 1}} - 1$
3. risk-free asset return $μ_{R f} \leftarrow {Riskfree yield}_{t}$
4. for each agent agI _n do
5. calculate the return of the portfolio_{t, n, k}
6. calculate the new value of the portfolio_{t, n, k}

Investors	ρ_ij
AgT₁, AgT₂	0.60
AgT₁, AgT₃	-0.17
AgT₂, AgT₃	0.68

Brasil

Brasil

MULTI-AGENT BASED MODELING APPLIED TO PORTFOLIO SELECTION IN THE DOOM-LOOP OF SOVEREIGN DEBT CONTEXT* * A preliminary version of this study was published in the book “Multi-Agent Based Simulation XVIII”, by Springer (2018). *

ABSTRACT

MULTI-AGENT BASED MODELING APPLIED TO PORTFOLIO SELECTION IN THE DOOM-LOOP OF SOVEREIGN DEBT CONTEXT^* * A preliminary version of this study was published in the book “Multi-Agent Based Simulation XVIII”, by Springer (2018). *