A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks

Marcelo de Oliveira Passos; Mathias Schneid Tessmann; Jean Rodrigues Venecian; Alex Cerqueira Pinto

doi:doi:10.11648/j.acm.20251406.12

Research Article |

| Peer-Reviewed

A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks

Marcelo de Oliveira Passos

, Mathias Schneid Tessmann^*

, Jean Rodrigues Venecian

, Alex Cerqueira Pinto

Published in Applied and Computational Mathematics (Volume 14, Issue 6)

Received: 29 September 2025 Accepted: 18 October 2025 Published: 12 November 2025

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Abstract

This paper presents a multi agent computational framework that deploys heterogeneous agents to investigate how shifts in short term interest rates and in the expected path of rates shape the intrinsic value of a broad stock market index. The model elucidates the transmission channels through which monetary policy propagates to market fundamentals, operationalized via the index’s theoretical replicating portfolio. By distinguishing valuation changes rooted in fundamentals from those driven by sentiment or feedback dynamics, the framework enables the systematic identification and quantification of speculative expansions (bull markets) and contractions (bear markets), thereby advancing a more disciplined understanding of market cycles. A central innovation is an investment oriented metric that produces a weekly time series of the Value Gap (VG), defined as the deviation between the model implied intrinsic value and the observed index level. This measure supports continuous monitoring of mispricing, facilitates comparative analysis across monetary policy regimes, and offers practical signals for risk management and asset allocation. Empirical evaluation yields two principal findings. First, the adverse effect of tighter monetary policy on VG materializes only when the index constituents exhibit a negative aggregate net cash flow, indicating that balance sheet conditions condition the pass through from policy rates to valuation gaps. Second, symmetric adjustments in the policy rate—upward or downward—tend to induce correspondingly directional movements in the index’s fundamental value (VB), highlighting a robust mapping from policy stance to market-implied fundamentals. Overall, the study contributes to the literature on monetary transmission and asset pricing by clarifying the interaction between policy rates, corporate cash flow profiles, and valuation dispersion. It also delivers a transparent and implementable analytical tool for detecting market imbalances, guiding tactical positioning, and informing strategic investment decisions under evolving policy environments.

Published in	Applied and Computational Mathematics (Volume 14, Issue 6)
DOI	10.11648/j.acm.20251406.12
Page(s)	309-322
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Agent-based Computational Economics, Gap Value Index, Stock Markets, Monetary Policy Transmission

1. Introduction

This paper presents a computer-based multi-agent financial model that uses stock valuation and computer simulation techniques to estimate two time series: one for the intrinsic value of a theoretical stock index portfolio, and another for a proposed value investing index, termed the 'Gap Value' (GV). This GV metric is designed to detect and quantify market imbalances—such as speculative bubbles (bull markets) or downturns (bear markets)—by measuring the divergence between observed market prices and calculated intrinsic values.

The model addresses the central research problem concerning the mechanisms by which monetary policy adjustments are transmitted to stock market fundamentals. The primary objective is to examine how variations in short-term and expected interest rates specifically impact the intrinsic value of the stock market index. The investigation seeks to answer key research questions, including: (i) How do adjustments in the central bank’s policy rate influence the stock market’s fundamental value (VB)? and (ii) Under what specific conditions, such as the aggregate net cash flow of firms, does monetary policy adversely affect the GV?

The methodology was based on the works of Lebaron, Testfasion, and Judd, who themselves built on the seminal work of Testfasion and Judd (2006)

[19, 13, 24]

. In addition to these texts, this paper also draws on insights from simulation and specificity techniques, as described in Law and Kelton, Werker and Brenner, Shannon, Menner, and Miranda

[18, 26, 21, 20, 16]

. Additionally, works are considered as Damodaran, Abrams and Stewart III

[10, 1, 22]

, Damodaran, McKinsey & Co., and Stickney, Weil & Schipper

[10, 15, 23]

, Damondaran

[11]

for adaptations and development of the model, and examples of Mathematica usage, such as Shingareva & Lizárraga-Celaya and Blachman

[27, 6]

, Stinespring and Varian

[17, 25]

, Kendrick, Mercado & Amman for examples applied to Economics and Finance

[14]

. Thus, it seeks to advance the understanding of the scientific literature on the influences of monetary policy on the intrinsic value of stocks.

Section 2 outlines the methodology, which is centered on a computer-based model and its five constituent modules. This section also introduces the 'Gap Value' (GV) concept, a metric proposed for detecting and measuring financial market bubbles. The GV quantifies the discrepancy that arises when the market value of stocks exceeds their intrinsic value (indicative of a bull market) or, conversely, falls below it (indicative of a bear market). Section 3 presents the model's corollaries.

Section 4 presents the results of the model's application and validation tests, including a Figureical analysis of the intrinsic value elasticity and the GV specification of the stock series compared to the benchmark and expected interest rates, based on a theoretical portfolio of the Ibovespa index. Special attention is paid to the events that significantly influenced the behavior of these series. Section 5 presents the concluding remarks.

2. Model Development

2.1. Module 1 – Stocks Companies’ Cash Flow

The first step of the methodology model builds on the discounted cash flow technique (DCF). According to Damodaran, leveraged companies are best assessed based on their free cash flow to the firm (FCFF)

[10]

. FCFF is derived from EBIT (earnings before interest and taxes). Leveraged companies are those companies that use debt to finance their operations. They are not necessarily very debt-laden companies, but companies with any given burden of debt

[10, 11, 5]

Table 1 shows how this process occurs, including their meaning and data source. The cash flows for the two subsequent years were estimated using the least squares method.

Table 1. Accounts used for cash flow calculation.

Symbol	FCFF item	Meaning	Data source in period t and previous periods
(=)	NS_t	Net Sales Revenue in period t	Income Statement for period t
(-)	SC_t	Sales costs in t	Income Statement for period
(-)	OE_t	Operating Expenses in t	Income Statement for period
(=)	EBIT_t	Earning before income and taxes in period t
(+)	Depreciation/Amortization	Depreciation/Amortization in t	Cash Flow Statement for period t
(-)	Income tax (IT) + social charges	Income Tax (IT) + Social Charges in t	Income Statement for period t
(=)	Operational cash generation	Operational Cash Generation in t
(-)	Permanent current investiments (Working Capital)	Permanent Current Investments (Working Capital) in t	Income Statement and Balance Sheet for period t
=	FCFF	Free cash flow to the firm for period t

Source: Adapted from Damodaran, Abrams and Stewart III

[10, 1, 22]

. The methodology was adapted according to current accounting standards in Brazil.

2.2. Module 2 – Inter-temporal Discounting Model

This model includes the time horizon of the cash flow projections to be discounted. Before projecting a company’s cash flow, it is important to decide how many periods or stages will be included for cash flow in perpetuity. In accordance with Cuberthson & Nitzsche and Stewart III, a number of stages can be identified in a business growth to maturity, depending on the characteristics of each company

[8, 22]

. As one of the goals of the model is to build a series of weekly intrinsic values for the companies making up the stock index, they will be assumed to have two stages for the sake of simplicity. In this assumption, the first stage corresponds to the short term, while the second stage refers to an infinite time horizon (i.e., in perpetuity).

According to Bodie, Kane & Marcus and Damodaran, two-stage valuation models adopt the simplifying hypothesis that the companies will not experience any extraordinary changes in the upcoming years, yet they will experience some changes to their capital structure, growth, and productivity patterns

[7, 10]

. Therefore, the ideal is to project an adjustment period (the first stage). The dividend policy will not be definitive before the second stage, which includes the perpetuity. The first stage is expected to have a distinct level of growth with higher levels of net investments, both in tangible assets and working capital. The formula for the first stage is:

(1)

Where: IV_Astands for the intrinsic value in the first stage, FCFF₁ is the cash flow in the present period, and it refers to the benchmark/base interest rate as determined by the monetary authority. All these variables are calculated on a weekly basis. The intrinsic value in stage 1 is equal to the sum of results of a simple discount formula in a given period, where the basic interest rate i substitutes every company’s weighted average cost of capital (WACC), a variable commonly adopted in finance and valuation techniques.

The underlying hypothesis is that the companies making up t the stock theoretical portfolio have the Interest rate as a proxy of capital cost. This is a useful simplifying hypothesis, as it allows for aggregating all stock index companies without performing individual accounting calculations, which would be laborious and make the model unfeasible.

The second stage assumes that the net cash flow result is in perpetuity. The inter-temporal discounting formula in the second stage is as follows:

(2)

Where: IV_Bstands for the intrinsic value in the second stage, FCFF₃ refers to the free cash flow to the firm in the third period (t+2), i_e is the expected basic interest rate, g₂ corresponds to the growth rate in the second stage. All these variables are calculated on a weekly basis.

As shown, discount formula (2) includes an expected growth rate (g₂) and an expected interest rate (i_e). Rate g₂ is a geometric mean including the per share profit variation in period 2001-2010 plus an investors’ confidence component (). An animal spirit variable () stands for the stockholders' willingness to invest. According to Economatica data, this variable corresponds to an adjusted average rate of return on equity in the 1996-2010 period and a rate of variation obtained from the exam of the technical analysis trend graphics

[4]

. Each variable has a weighting of 0.5. It was also used to calibrate the model for the weekly changes in the investors' confidence about the company's stocks. The animal spirit () is incorporated into the g₂ calculation.

By including inter-temporal discount rates (i_band i_e), the model integrates the financial data provided by the cash flows, a variable of monetary policy, and the decision rules guiding the behavior of a representative agent. Indeed, this computer-based financial model is also multi-agent-based, and both inter-temporal discount rates can be understood as minimum attractive rates for the multiple agents making up in the model.

2.3. Module 3 – IV and GV in Stocks Theoretical Portfolio

This module targets the IV and GV of both companies and the Stocks theoretical portfolio. In general terms, the module is composed of the sum of intrinsic values in both stages. The weekly intrinsic value of a company is, therefore:

I V_{A} + I V_{B} = \sum_{t = 1}^{n} \frac{FCF F_{t}}{(1 + i)^{t}} + \frac{\frac{FCF F_{n + 1}}{(i_{e} - g_{n})}}{(1 + i_{e})^{2}}

(3)

Following the model methodology, n (number of stocks) intrinsic values are generated (building on the discounted cash flows). The concept of GV, as introduced in this paper, is aimed as an index that predicts financial market bubbles as well as bull market and bear market conditions. The GV is determined using a weekly time series that comprises the difference between intrinsic values (as shown in Module 2) and market values (number of shares x share price on the cash market) that make up the Stocks theoretical portfolio. Equation (4) is a matrix equation that calculates the GV:

G V_{(n \times 1)} = {[\begin{matrix} G V_{1}^{1} \\ G V_{1}^{2} \\ ⋮ \\ G V_{1}^{n} \end{matrix}]}_{(n \times 1)} = {[\begin{matrix} M V_{1}^{1} \\ M V_{1}^{2} \\ ⋮ \\ M V_{1}^{n} \end{matrix}]}_{(n \times 1)} - {[\begin{matrix} I V_{1}^{1} \\ I V_{1}^{2} \\ ⋮ \\ I V_{1}^{n} \end{matrix}]}_{(n \times 1)}

(4)

Where GV₍_n_xW) is the gap value, MV_{(n xW)} is the market value of the n shares in the Stocks theoretical portfolio, and IV_(nxW) is the intrinsic value. All these variables are calculated for 1 week, as represented in the vector columns. W is the number of weeks in the analysis.

The results are placed in a matrix, where the rows represent the weeks and the columns represent the weekly intrinsic values. Subtracting the values of every row vector gives the GV. The equation below shows the same in a more aggregate form:

G V_{(n \times W)} = {[\begin{matrix} G V_{1}^{1} & G V_{2}^{1} & \dots & G V_{W}^{1} \\ G V_{1}^{2} & G V_{2}^{2} & \dots & G V_{W}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ G V_{1}^{n} & G V_{2}^{n} & \dots & G V_{W}^{n} \end{matrix}]}_{(n \times W)} = {[\begin{matrix} M V_{1}^{1} & M V_{2}^{1} & \dots & M V_{W}^{1} \\ M V_{1}^{2} & M V_{2}^{2} & \dots & M V_{W}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ M V_{1}^{n} & M V_{2}^{n} & \dots & M V_{W}^{n} \end{matrix}]}_{(n \times W)} - {[\begin{matrix} I V_{1}^{1} & I V_{2}^{1} & \dots & I V_{W}^{1} \\ I V_{1}^{2} & I V_{2}^{2} & \dots & I V_{W}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ I V_{1}^{n} & I V_{2}^{n} & \dots & I V_{W}^{n} \end{matrix}]}_{(n \times W)}

(5)

Stressing the result of the GV matrix and using an alternative notation gives:

GV_(nxW)=MV_(nxW)–IV_(nxW)(6)

Where:

G V_{(n \times W)} = {[\begin{matrix} M V_{1}^{1} - I V_{1}^{1} & M V_{2}^{1} - I V_{2}^{1} & \dots & M V_{W}^{1} - I V_{W}^{1} \\ M V_{1}^{2} - I V_{1}^{2} & M V_{2}^{2} - I V_{2}^{2} & \dots & M V_{W}^{2} - I V_{W}^{2} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ M V_{1}^{n} - I V_{1}^{n} & M V_{2}^{n} - I V_{2}^{n} & \dots & M V_{W}^{n} - I V_{W}^{n} \end{matrix}]}_{(n \times W)}

(7)

For the sake of easy reading of the matrix above, the second column is omitted in order to obtain:

(8)

Matrix (8) can also be partitioned in the following row-vectors:

G V_{(1 \times W)}^{1} = {[\begin{matrix} M V_{1}^{1} - \sum_{t = 1}^{1} \frac{FCF F_{1}^{1}}{(1 + i_{b, 1})^{1}} + \frac{\frac{FCF F_{3}^{1}}{(i_{e, 1} - g_{e, 1, 1})}}{(1 + i_{e, 1})^{2}} & \dots & M V_{W}^{n} - \sum_{t = 1}^{1} \frac{FCF F_{1}^{1}}{(1 + i_{b, W})^{1}} + \frac{\frac{FCF F_{3}^{1}}{(i_{e, W} - g_{e, W, n})}}{(1 + i_{e, W})^{2}} \end{matrix}]}_{(1 \times W)}

G V_{(1 \times W)}^{2} = {[\begin{matrix} M V_{1}^{2} - \sum_{t = 1}^{1} \frac{FCF F_{1}^{2}}{(1 + i_{b, 1})^{1}} + \frac{\frac{FCF F_{3}^{2}}{(i_{e, 1} - g_{e, 1, 2})}}{(1 + i_{e, 1})^{2}} & \dots & M V_{W}^{n} - \sum_{t = 1}^{1} \frac{FCF F_{1}^{1}}{(1 + i_{b, W})^{1}} + \frac{\frac{FCF F_{3}^{1}}{(i_{e, W} - g_{e, W, n})}}{(1 + i_{e, W})^{2}} \end{matrix}]}_{(1 \times W)}^{2}

(9)

G V_{(1 \times W)}^{n} = {[\begin{matrix} M V_{1}^{n} - \sum_{t = 1}^{1} \frac{FCF F_{1}^{n}}{(1 + i_{b, 1})^{1}} + \frac{\frac{FCF F_{3}^{n}}{(i_{e, 1} - g_{e, 1, n})}}{(1 + i_{e, 1})^{2}} & \dots & M V_{W}^{n} - \sum_{t = 1}^{1} \frac{FCF F_{1}^{1}}{(1 + i_{b, W})^{1}} + \frac{\frac{FCF F_{3}^{1}}{(i_{e, W} - g_{e, W, n})}}{(1 + i_{e, W})^{2}} \end{matrix}]}_{(1 \times W)}

Summing up the row vectors in the matrix system (9) – which represent the n weekly time series of GVs of all stocks in the Stocks theoretical portfolio – gives the aggregate weekly time series of GVs as follows:

\sum_{t = 1}^{n} G V_{(1 \times W)} = {[\begin{matrix} G V_{1}^{1} + \dots + G V_{1}^{n} & G V_{2}^{1} + \dots + G V_{2}^{n} & \dots & G V_{W}^{1} + \dots + G V_{W}^{n} \end{matrix}]}_{(1 \times W)}

(10)

Returning to the notion of GV and considering the system of row vector in (9) gives:

\sum_{t = 1}^{n} G V_{(1 \times W)} = [\begin{matrix} (M V_{1}^{1} - I V_{1}^{1}) + \dots + (M V_{1}^{n} - I V_{1}^{n}) & \dots & (M V_{W}^{1} - I V_{W}^{1}) + \dots + (M V_{W}^{n} - I V_{W}^{n}) \end{matrix}]

(11)

2.4. Module 4 – Gap Value Elasticity in Relation to Benchmark and Expected Interest Rates

GV elasticities are deduced from equations (8) using the software package Mathematica 7 as follows. Differentiating (8) in relation to ib, which is a weekly benchmark interest rate, gives the matrix equation (12), which shows the several elasticity values of the intrinsic values of every share in the Stocks theoretical portfolio in relation to the Monetary Authority’s benchmark interest rate. Elasticity (12) herein determines the effect of, for instance, a 1-percentage-point variation on the intrinsic value of a share in the Bovespa Index.

\frac{\partial G V_{(n \times W)}}{\partial i_{b}} = {[\begin{matrix} M V_{1}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{b, 1})^{2}} & \dots & \dots & M V_{W}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{b, W})^{2}} \\ M V_{1}^{2} + \frac{FCF F_{1}^{2}}{(1 + i_{b, 1})^{2}} & \dots & \dots & M V_{W}^{2} + \frac{FCF F_{1}^{2}}{(1 + i_{b, W})^{2}} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ M V_{1}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{b, 1})^{2}} & \dots & \dots & M V_{W}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{b, W})^{2}} \end{matrix}]}_{(n \times W)}

(12)

Partitioning matrix (12) gives the row values that represent the elasticity curve of all Stocks`s stocks in relation to the several levels of interest rates determined by Monetary Authority. Summing up these row vectors gives the series of Stocks`s GV elasticity in relation to the Interest rate rate, the first objective of this paper. The vector calculations are as follows:

\frac{\partial G V_{(1 \times W)}}{\partial i_{b}} = {[\begin{matrix} (M V_{1}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{b, 1})^{2}} + . . . + M V_{1}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{b, 1})^{2}}) & \dots & (M V_{W}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{b, W})^{2}} + . . . + M V_{W}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{b, W})^{2}}) \end{matrix}]}^{}

(13)

After that, matrix (8) is differentiated in relation to the expected interest rate. The calculations, similar to those provided before, give the series of GV for every Stocks`s stock in relation to the expected interest rate, as well as the series of GV of the Stocks`s theoretical portfolio as a whole in relation to this very variable (expected interest rate). Therefore, result (14) below attains the second objective of this paper.

\frac{\partial G V_{(n \times W)}}{\partial i_{e}} = {[\begin{matrix} M V_{1}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{e, 1})^{2} \cdot (i_{e, 1} - g_{e, 1, 1})^{2}} + \frac{2 FCF F_{3}^{1}}{(1 + i_{e, 1})^{3} \cdot (i_{e, 1} - g_{e, 1, 1})} & \dots & \dots & M V_{W}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{e, W})^{2} \cdot (i_{e, W} - g_{e, W, 1})^{2}} + \frac{2 FCF F_{3}^{1}}{(1 + i_{e, W})^{3} \cdot (i_{e} - g_{e, W, 1})} \\ M V_{1}^{2} + \frac{FCF F_{1}^{2}}{(1 + i_{e, 1})^{2} \cdot (i_{e, 1} - g_{e, 1, 2})^{2}} + \frac{2 FCF F_{3}^{2}}{(1 + i_{e, 1})^{3} \cdot (i_{e, 1} - g_{e, 1, 2})} & \dots & \dots & M V_{W}^{2} + \frac{FCF F_{1}^{2}}{(1 + i_{e, W})^{2} \cdot (i_{e, W} - g_{e, W, 2})^{2}} + \frac{2 FCF F_{3}^{2}}{(1 + i_{e, W})^{3} \cdot (i_{e} - g_{e, W, 2})} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ M V_{1}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{e, 1})^{2} \cdot (i_{e, 1} - g_{e, 1, n})^{2}} + \frac{2 FCF F_{3}^{n}}{(1 + i_{e, 1})^{3} \cdot (i_{e, 1} - g_{e, 1, n})} & \dots & \dots & M V_{W}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{e, W})^{2} \cdot (i_{e, W} - g_{e, W, n})^{2}} + \frac{2 FCF F_{3}^{n}}{(1 + {i_{e}}_{e, W})^{3} \cdot (i_{e} - g_{e, W, n})} \end{matrix}]}_{(n \times W)}

(14)

Partitioning matrix (12) gives the row values that represent the elasticity curve of all Stocks stocks in relation to the several levels of interest rates determined by Monetary Authority thought W weeks. Now let each expression contained in the matrix (14) cells be

, where s stands for the number of stocks in the Stocks`s theoretical portfolio (listed in alphabetical order), and w stands for the week to which a given share’s market value and intrinsic value estimation correspond. From that follows:

\frac{\partial G V_{(1 \times W)}}{\partial i_{b, w}} = [\begin{matrix} \frac{\partial G V_{1}^{1}}{\partial i_{b, 1}} & \frac{\partial G V_{2}^{1}}{\partial i_{b, 2}} & . . . & \frac{\partial G V_{W}^{1}}{\partial i_{b, W}} \end{matrix}]

\frac{\partial G V_{(1 \times W)}}{\partial i_{b, w}} = [\begin{matrix} \frac{\partial G V_{1}^{2}}{\partial i_{b, 1}} & \frac{\partial G V_{2}^{2}}{\partial i_{b, 2}} & . . . & \frac{\partial G V_{W}^{2}}{\partial i_{b, W}} \end{matrix}]

(15)

\frac{\partial G V_{(1 \times W)}}{\partial i_{b, w}} = [\begin{matrix} \frac{\partial G V_{1}^{n}}{\partial i_{b, 1}} & \frac{\partial G V_{2}^{n}}{\partial i_{b, 2}} & . . . & \frac{\partial G V_{W}^{n}}{\partial i_{b, W}} \end{matrix}]

Summing up the row vectors of system (15) gives the series of Stocks`s gap value elasticity in relation to the expected Interest rate rate, the second objective of this paper. This gives the series as follows:

\frac{\partial G V_{(1 \times W)}}{\partial i_{b, w}} = [\begin{matrix} (\frac{\partial G V_{1}^{1}}{\partial i_{b, 1}} + \frac{\partial G V_{1}^{2}}{\partial i_{b, 1}} + . . . + \frac{\partial G V_{1}^{n}}{\partial i_{b, 1}}) & . . . & (\frac{\partial G V_{W}^{1}}{\partial i_{b, W}} + \frac{\partial G V_{W}^{2}}{\partial i_{b, W}} + . . . + \frac{\partial G V_{W}^{n}}{\partial i_{b, W}}) \end{matrix}]

(16)

Analogously, a number of vector calculations finally gives the series of Stocks`s gap value elasticity in relation to the expected interest rates throughout the W weeks included in the analysis:

\frac{\partial G V_{(1 \times W)}}{\partial i_{e, w}} = [\begin{matrix} (\frac{\partial G V_{1}^{1}}{\partial i_{e, 1}} + \frac{\partial G V_{1}^{2}}{\partial i_{e, 1}} + . . . + \frac{\partial G V_{1}^{n}}{\partial i_{e, 1}}) & . . . & (\frac{\partial G V_{W}^{1}}{\partial i_{e, W}} + \frac{\partial G V_{W}^{2}}{\partial i_{e, W}} + . . . + \frac{\partial G V_{W}^{n}}{\partial i_{e, W}}) \end{matrix}]

(17)

Where the cells correspond to:

\frac{\partial G V_{1}^{1}}{\partial i_{e, 1}} = M V_{1}^{1} + \frac{FCF F_{1}^{1}}{(1 + i_{e, 1})^{2} \cdot (i_{e, 1} - g_{e, 1, 1})^{2}} + \frac{2 FCF F_{3}^{1}}{(1 + i_{e, 1})^{3} \cdot (i_{e, 1} - g_{e, 1, 1})}

\frac{\partial G V_{1}^{1}}{\partial i_{e, 1}} = M V_{1}^{2} + \frac{FCF F_{1}^{2}}{(1 + i_{e, 1})^{2} \cdot (i_{e, 1} - g_{e, 1, 2})^{2}} + \frac{2 FCF F_{3}^{2}}{(1 + i_{e, 1})^{3} \cdot (i_{e, 1} - g_{e, 1, 2})}

(18)

and so forth until:

\frac{\partial G V_{W}^{n}}{\partial i_{e, W}} = M V_{W}^{n} + \frac{FCF F_{1}^{n}}{(1 + i_{e, W})^{2} \cdot (i_{e, W} - g_{e, W, n})^{2}} + \frac{2 FCF F_{3}^{n}}{(1 + {i_{e}}_{, W})^{3} \cdot (i_{e} - g_{e, W, n})}

(19)

Where g_e,w,s is the expected growth for week w by the company’s shareholders, i_b,w is the benchmark interest rate (Interest rate) in week w, and i_e,w is the expected interest rate for week w.

3. Corollaries of the Model

The GV results, particularly from equation (5) onwards, fall in three categories: downside, upside, and balance (IV and MV are equal). These categories are shown in Table 2. As Table 2 shows, the GV elasticity in relation to the benchmark interest rate (Interest rate defined by Monetary Authority) is negative only in B; it is positive in all other conditions.

This means that the transmission mechanism of monetary policy will affect Stocks`s GV negatively only when the companies that make up this index have, altogether, negative net cash generation. Otherwise, coeteris paribus, Monetary Authority’s decisions to increase (reduce) the benchmark interest rate will invariably result in increased (reduced) Stocks`s GV.

Table 2. Corollaries of the model.

Possible interactions between GV and share market conditions
Condition	Possible results	Conclusion
1	and	Stocks' potential of losses increases: bull market, downside, or speculative bubble condition.
2	and	Stocks’s potential of profits increases: bear market, upside, or share market downturn condition.
3	and	Condition of intrinsic value balance across the shares in the Stocks theoretical portfolio. No profit nor loss potential.
Possible conditions between Stocks`s cash flow, GV and GV elasticity in relation to the effects of changes to the benchmark interest rate –through transmission mechanism – on the stocks in the Stocks`s theoretical portfolio.
A	MV >IV (downside), and FCFF< 0 (negative cash flow)
B	MV < IV (upside), and FCFF< 0 (negative cash flow)
C	MV >IV (downside), and FCFF> 0 (positive cash flow)
D	MV < IV (upside), and FCFF< 0 (positive cash flow)

Source: Elaborated by the authors

4. Simulations

To test the agent-based computational model (ABM) while disregarding the specific drivers of recent economic events and shocks, the study utilizes data from the post-2008 financial crisis period. The dataset, applied to a theoretical stock portfolio, is derived from 816 accounting statements covering the 2008–2010 triennium (a 156-week time series). Subsequent subsections analyze the events of each year within this period, assessing their influence on the elasticity curve of the Ibovespa's IV and GV relative to changes in benchmark and expected interest rates. The simulations were conducted in Excel by calibrating the growth rate parameters (g2) as specified in equation (11).

All the following subsections provide Figure analysis for the computer-based simulations. The subsections are divided according to the year to which they refer. The weekly series correspond to the following row vectors: 1) IV – intrinsic value vector for the Ibovespa`s theoretical portfolio, which is the sum of the 52 weekly time series of the intrinsic values estimated by the computer-based model for the 68 stocks in the Ibovespa`s theoretical portfolio; (2) MV – market value vector for the Ibovespa`s theoretical portfolio; (3) Selic defined by COPOM short-term interest rate, represented as effective interest rates that were weekly compounded; and (4) Expected interest rate – containing expected values as published by the Central Bank of Brazil in the Focus Report for the respective weeks of the period under scrutiny.

4.1. Effect of the Interest Rates (Benchmark and Expected) on the Stocks' IV and GV in 2008

The increased expected inflation (referred to by the Central Bank of Brazil as a "benign scenario" deriving from an excess of aggregate demand over supply) led Copom to interrupt in April 2008 the policy of progressively mild interest rates that started in September 2005. As a result, the benchmark interest rate goal, which was 11.25% since September 2007, increased 50 basis points (bps) in April 2008, and suffered other increases upon three other monetary authority meetings. It eventually reached 13.75% p.a. in December 2008. The ex-ante real interest rate, calculated by the Central Bank of Brazil for a period of one year after surveying analysts in the private sector, increased throughout the first nine months of 2008. In October, the expectations for the benchmark interest rates had a reduction tendency, which led to a rate of 7.2% p.a. by the end of the year (0.7 percentage points higher than that registered for the same month in 2007)

[3, 4]

Monetary authority’s contractionary monetary policy measures at the beginning of 2008 continued the decisions of previous meetings in 2007, in which the committee members assessed that the international economic conjuncture and the expanding domestic economic activity required some prudential measures from the monetary policy maker. The Committee eventually decided to keep the Interest rate at 11.25% p.a., without bias, and opted to monitor the macroeconomic conjecture and thus gain time to deliberate about potential changes to the monetary policy in subsequent meetings. As the expected inflation was increasing, the Central Bank increased the Interest rate in 50 bps in two meetings. Assuming that risks of increasing prices still existed in July, the Central Bank decided to increase the Interest rate to 13% p.a., without bias

[4].

The committee still believed in a tendency of increasing prices in September (the already mentioned “benign scenario”). The committee, thus, opted for a new increase on 75 bps in the Interest rate, without bias, even in a scenario of international economic recession (see Figure 1). In October and December, the monetary authority finally noticed the effects of the economic slowdown and the increased economic uncertainty resulting from the international financial crisis that was also affecting several sectors in the Brazilian economy (especially the credit channels) as well as the consumers’ and entrepreneurs’ confidence. As for the dynamics of monetary aggregates, a reduction of 2.3% was registered for the average daily balance of narrowly defined money supply (M1). M1 velocity of money remained relatively stable, and the monetary base (as measured according to the average daily balances) increased 1.5% in the year.

The Central Bank of Brazil assumed other expansionary pressures on the monetary supply, which led to an increase of 933 million Brazilian Reais in the monetary base (using the criterion of available balance by the end of the period). The Monetary Authority, therefore, decided to implement changes to the rules of compulsory deposits, which translated into: reductions in rates, increases in the amounts deducted from callable reserves, changes in earnings on reserve requirements, together with discounts on amounts to be deposited as an incentive to negotiation of assets among medium- and small-sized financial institutions.

Figure 1 synthesizes the explanations provided so far and shows the negative effects of having increased real interest rates (benchmark and expected) on the intrinsic value of the Stocks theoretical portfolio. Obviously, the Stocks intrinsic value was also affected by other variables that are beyond the scope of the model such as: 1) the default of the three mentioned financial institutions, and worsening animal spirits among the entrepreneurs in the productive sector; 2) reduced volume of foreign investments in shares (Figure 2); 3) the devaluated real exchange rate’s effect on the companies making up the Stocks theoretical portfolio; and 4) the remarkably reduced international trade flows.

Download: Download full-size image

Figure 1. Computer-based weekly series of variation effects of expected and short-term interest rates on the intrinsic values in the Stocks theoretical portfolio in 2008.

Source: Estimates as provided by the authors' computer-based model; Security Exchange Commission’s standardized financial statements for the 68 companies making up the Stocks theoretical portfolio in fiscal year 2008; Central Bank of Brazil’s Focus Report; BMF&Bovespa; Monetary Policy Committee

[4]

As for the Stocks performance, it is worth noting the Petrobras stock split that took place in the seventh week of the year. In addition, the period from January from May witnessed a number of repeated records of increased index values, which reached 73,516 point on May 20th. From late May to the end of year, the Stocks experienced a sharp drop (of 42.1% in relation to the prevailing level by the end of 2007) and increased volatility.

Figure 2 shows that the GV is positive until the 40th week and is negatively correlated with the real interest rates (benchmark and expected), as mentioned in the previous section. From then on, the GV is negative, reflecting Lehman Brothers', Fannie Mae's, and Freddie Mac's collapse. This moment of structural collapse in the GV series evinces that the intrinsic value of the Stocks`s theoretical portfolio declined at a fast pace and started a progressive upside (tendency of profit). A characteristic phenomenon of fundamental analyses based on the notion of value investing in periods of a bear market.

Download: Download full-size image

Figure 2. Computer-based weekly series of variation effects of expected and short-term interest rates on the GV (GV = MV – IV) in the Stocks theoretical portfolio in 2008.

[4, 9]

The result described herein shows the model’s power to detect and measure speculative bubbles in the stock market, as well as to identify when they emerge and disappear (Figure 2). Results of this nature are of special interest to policymakers (especially those concerned with making and executing monetary policy), financial executives, and the representative agent of the computer-based model. They help policymakers and financial executives measure and detect speculative bubbles in the share market. They also inform the model representative agent’s decision: if the GV is declining and the agent trust in a positive future scenario for the Ibovespa tendency in the long term, s/he will opt for increasing investments in this index; if the value is increasing, however, s/he may decide to keep his/her levels of investments or sell shares if this increase magnitude is great enough to yield him/her the desired profit.

4.2. Effect of the Interest Rates (Benchmark and Expected) on the Stock's Intrinsic Value and GV in 2009

The quarterly growth rates of real GDP in 2009 reveal that only the service sector remained relatively unaffected by the financial crisis, which had its epicenter in August 2008. Industrial and agricultural GDP contracted during the first three quarters of the year, showing signs of recovery only in the final quarter. The intensification of the global crisis in late 2008 triggered a domestic recession characterized by declining credit availability, deteriorating expectations, and heightened risk aversion. In response to the rapidly shifting international environment, the Central Bank of Brazil reversed its contractionary monetary stance, halting a sequence of four rate hikes implemented between April and September 2008 and initiating a cycle of substantial interest rate reductions.

Between January and July 2009, the Monetary Policy Committee (Copom) reduced the Selic rate by a cumulative 500 basis points, bringing it to 8.75% per annum. The initial cuts of 100 and 150 basis points were based on projections that declining inflationary pressures and subdued economic activity would align the IPCA trajectory with the inflation targets set by the National Monetary Council (CMN). Subsequent reductions of 100 basis points in April and June sought to stimulate industrial production, capacity utilization, employment, and confidence among investors and consumers. In July, the rate was lowered by an additional 50 basis points, after which Copom maintained a more cautious stance, keeping the Selic unchanged through December.

The expansionary monetary policy introduced in mid-2008 led to a 5.7% increase in M1 in 2009, although its velocity remained stable. The daily average balance of the monetary base rose by 14.9%, reflecting a 14.3% increase in issued currency and a 16.8% rise in bank reserves. Broader aggregates also expanded, with M2, M3, and M4 growing by 8.6%, 15.5%, and 16.1%, respectively. In parallel, capital markets experienced a sharp contraction in late 2008, with reduced asset prices and issuance activity. However, during the second half of 2009, primary markets for equities, debentures, and promissory notes recovered, supporting improved expectations for 2010. The Ibovespa closed 2008 at 68,588 points—an 82.7% increase year-on-year—and in 2009 posted a 145.2% gain in dollar terms, driven both by stock price appreciation and the sharp depreciation of the real exchange rate.

Download: Download full-size image

Figure 3. Computer-based weekly series of variation effects of expected and short-term interest rates on the intrinsic values in the Stocks theoretical portfolio in 2009.

[4, 9]

The second quarter 2009 saw a recovery of the Brazilian balance of trade. In this period, the government also took countercyclical fiscal policy measures – i.e., reducing the tax on industrialized products (IPI) for durable consumer goods. The period also witnessed increased public expenditure and increased volume of bank credit to the private sector. Risk rating agencies Fitch Ratings and Moody's updated the country's sovereign debt rating to investment grade in the third quarter of 2009. The Brazilian economy was booming by the end of the quarter. Finally, the fourth quarter saw a remarkable increase in the Ibovespa values. Notice, however, that IV did not follow this tendency in that quarter, since the expected interest rates increased. This shows that the intrinsic value was negatively affected by the expected interest rate variations.

Figure 4 shows that these circumstances, in general, led to a MV and IV recovery. It also shows that the GV remained negative until the 40th week, i.e., it remained below the intrinsic value in the period, in an upside condition. This took place because of the financial crisis and the aforementioned events. From the 40th week on, however, expectations change in response to the economic recovery, expansionary factors as explained above, and the award of a good investment grade. The GV became thereafter positive (i.e., a downside condition).

Download: Download full-size image

Figure 4. Computer-based weekly series of variation effects of expected and short-term interest rates on the GV (GV = MV – IV) in the Stocks theoretical portfolio in 2009.

[4, 9]

4.3. Effect of the Interest Rates (Benchmark and Expected) on the Stock's Intrinsic Value and GV in 2010

In 2010, the Central Bank of Brazil maintained the Selic rate at 8.75% per annum throughout the first quarter, marking the lowest level since the series began in 1999. However, during the second and third quarters, the Monetary Policy Committee (Copom) implemented a cumulative increase of 200 basis points, bringing the rate to 10.75% per annum, where it remained for the last three meetings of the year. The annual IPCA inflation rate reached 5.91%, close to the upper bound of the 2.5%–6.5% target range established by the National Monetary Council (CMN). As a result, the effective accumulated interest rate stood at 9.7%, while the real accumulated rate deflated by the IPCA reached 3.7%

[2].

Expected real rates rose from 5.1% at the end of 2009 to 6.2% by the end of 2010, with contracts proving highly volatile in the second semester and closing the year at 12.03% per annum. In December, the CMN and the Central Bank introduced macroprudential regulatory measures aimed at strengthening financial regulation, safeguarding institutional stability within the National Financial System (SFN), and ensuring a sustainable credit expansion, while remaining aligned with monetary policy decisions.

Figure 5 illustrates a decline in the intrinsic value (IV) and market value (MV) series during the period under analysis, as well as a negative correlation between these series and both benchmark and expected interest rates. The capital market registered an exceptional event with Petrobras’ stock offering, which reached a trading volume of BRL 120.2 billion and spurred a significant expansion in the primary market for debentures, promissory notes, and shares registered with the Brazilian Securities and Exchange Commission (CVM). Overall, the volume of primary market issues increased by 341% compared to the previous year, with the correlation between IV and MV reaching 99% in 2010.

Brazilian GDP expanded by 7.5% in 2010, the highest growth rate in over two decades. Nevertheless, international conditions introduced considerable uncertainty. The deterioration of economic expectations in the United States, coupled with credit contraction in China and fiscal crises in key Eurozone economies (Portugal, Greece, Spain, Italy, and France), heightened global market instability and weakened the market value of Brazilian companies listed on the stock exchange. These developments underscored the vulnerability of Brazilian firms whose export performance remained strongly tied to demand growth in China, Europe, and the United States, with the Chinese market gaining increasing relative importance over the preceding decade.

Amid this unfavorable external environment, Brazil also faced inflationary pressures at home, prompting Copom to sustain its cycle of interest rate increases. Higher interest rates, combined with investor uncertainty, weighed negatively on the growth value (GV) of the Ibovespa’s theoretical portfolio, reflecting a more cautious market outlook.

Download: Download full-size image

Figure 5. Computer-based weekly series of variation effects of expected and short-term interest rates on the intrinsic values in the Stocks theoretical portfolio in 2010.

Source: Estimates as provided by the authors' computer-based model; Security Exchange Commission’s standardized financial statements for the 68 companies making up the Stocks theoretical portfolio in fiscal year 2007; Central Bank of Brazil’s Focus Report; BMF&Bovespa; Monetary Policy Committee

[4, 9]

Figure 6 shows the elasticity trajectory for the Stocks GV in relation to increases in the benchmark and expected interest rates. It also associates the dynamics of Stocks`s GV the major economic events of the period: the lowering of the risk ratings of Portugal's and Greece’s debts in April 27th, and the expansion of the industrial and service GDP that started some weeks before April 27th.

Download: Download full-size image

Figure 6. Computer-based weekly series of variation effects of expected and short-term interest rates on the GV (GV = MV – IV) in the Stocks theoretical portfolio in 2010.

[4, 9]

In the third quarter, more specifically in September, the Stocks reached the historical record of ca. 70,000 points. The IPCA rates were indicating that the inflationary process had been restrained, and the Focus Report pointed a growth of 7% in the Brazilian economy by the end of 2010. Consequently, Brazil saw an inconsistency between its strong economic growth and the Ibovespa growth setback (60,000 points). This inconsistency was associated with the effects of the European crisis and the Brazilian investors’ replacement of variable-income assets with fixed-income assets. Despite this adverse scenario, the GV behavior was found to be largely positive. The higher MV compared to IV pointed to a downside condition.

5. Final Remarks

The computer-based financial model described herein is a multi-agent model and incorporates techniques from finance (the share valuation model), computational economics, and monetary economics. The agents in the model are the shareholders of the companies making up the stock's theoretical portfolio. These agents’ expectations are linked to these companies’ profit rates. The expected profit rates are combined in a valuation formula, i.e., that of free cash flow to the firm, with the benchmark and expected interest rates, which serve as inter-temporal discounting rates or minimum attractive rates for negotiating the given stocks.

According to Bodie, Kane & Marcus, share valuation techniques can be top-down or bottom-up in fundamental analysis. The analyst uses the former when s/he first desires to assess the macroeconomic environment, then the sector in which the company operates, and finally the company’s accounting statements and management quality

[7]

. Inversely, it uses the second technique when s/he desires to assess: first the company's accounting statements and management quality, then its sector, and finally the macroeconomic environment of the company. The model described herein used the bottom-up approach, as multi-agent computational simulations are usually used with a view to studying complex tendencies that emerge from the micro level of the systems to their macro level.

The analysis of the model results evinces the correlation between the series of intrinsic values and market value and the correlation between the weekly series of IV and of GV with the trajectories of the benchmark and expected interest rates. In addition, the analysis also sought to show the effect of exogenous factors on the series under study. In other words, it sought to correlate the model-generated trajectories with such events as the US financial institution's default, the Petrobras` stock split, the expansionary fiscal and monetary policy adopted by the Brazilian government, the macro-prudential decisions of market regulation, and the European financial crisis.

The proposed model was tested by first estimating the cash flows of each company included in the Ibovespa theoretical portfolio over the triennium under analysis. These flows were then projected for the subsequent years 2011 and 2012, and discounted to obtain intrinsic value estimates for every stock. The individual estimates were aggregated and weighted according to each firm’s relative share in the theoretical portfolio, yielding the overall intrinsic value (IV) of the index. On this basis, the model introduced the concept of growth value (GV), defined as the difference between the market value of the index and its intrinsic value.

This procedure demonstrates how the model can reproduce the dynamics of the Ibovespa through theoretically consistent estimates, validating the central thesis proposed. Moreover, the GV series provides a practical tool for identifying and measuring speculative bubbles as well as periods of bear market conditions, thereby offering original insights into market behavior and the mechanisms underlying financial instability.

Another relevant conclusion of the model is that the transmission mechanism of monetary policy will affect Stocks`s GV negatively only when the companies that make up this index have an aggregated negative net cash generation. As a suggestion for future research, the developed model could be used to implement the elasticities between fluctuations in global interest rates and the capital structure of companies that make up financial market indices. Furthermore, they can also use the model presented for other markets and with recent data, which was not the scope of our work, so that its focus could be concentrated on modeling in light of discussions of recent economic dynamics.

Abbreviations

CMN	National Monetary Council
Copom	Comitê de Política Monetária (Monetary Policy Committee)
CVM	Comissão de Valores Mobiliários (Brazilian Stock Market Regulatory Comission)
DCF	Discounted Cash Flow
EBIT	Earnings Before Interest and Taxes
EBITt	Earning Before Income and Taxes in Period t
FCFF	Free Cash Flow to the Firm
FCFFt	Free Cash Flow to the Firm for Period t
FCFF1	Cash Flow in the Present Period
FCFF3	Free Cash Flow to the Firm in the Third Period (t+2)
GV	Gap Value
IPI	Tax on Industrialized Products
IT	Income Tax (Imposto de Renda)
IV	Intrinsic Value (Valor Intrínseco)
IVA	Intrinsic Value in the First Stage
IVB	Intrinsic Value In The Second Stage
MV	Market Value
SFN	National Financial System
VG	Value Gap
WACC	Weighted Average Cost of Capital

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	ABRAMS, J. B. Quantitative business valuation: a mathematical approach for today`s professionals. New York: McGraw-Hill, 2001.
[2]	BANCO CENTRAL. Boletim do Banco Central do Brasil – Relatório Anual. Brasília: Banco Central, 2010. Available at: http://www.bcb.gov.br/pec/boletim/banual2010/rel2010p.pdf
[3]	BANCO CENTRAL. Boletim do Banco Central do Brasil – Relatório Anual. Brasília: Banco Central, 2009. Available at: http://www.bcb.gov.br/pec/boletim/banual2009/rel2009apendp.pdf
[4]	BANCO CENTRAL. Boletim do Banco Central do Brasil – Relatório Anual. Brasília: Banco Central, 2008. Available at: http://www.bcb.gov.br/pec/boletim/banual2008/rel2008p.pdf
[5]	BISCIARI, P.; DURRÉ, A.& NYSSENS, A. Stock market valuation in the United States. Brussels: National Bank of Belgium, 2003.
[6]	BLACHMAN, N. Mathematica: a practical approach. Englewood Cliffs, New Jersey: Prentice-Hall, 1992.
[7]	BODIE, Z.; KANE, A. & MARCUS, A. J. Investments. 8^thed. New York: McGraw-Hill, 2009.
[8]	CUTHBERTSON, K.; NITZSCHE, D. Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange. 2nd ed. New York: JohnWiley& Sons, 2004. https://doi.org/10.1002/0470012297
[9]	CVM – Comissão de Valores Mobiliários (Brazilian Stock Market Regulatory Comission). Available at: http://www.cvm.gov.br/
[10]	DAMODARAN, A. Investment Valuation: tools and techniques for determining the value of any asset. New Jersey: John Wiley & Sons Ltd, 2012. https://doi.org/10.1002/9781119200171
[11]	DAMODARAN, A. The little book of valuation: how to value a company, pick a stock and profit. New Jersey: John Wiley & Sons Ltd, 2011. https://doi.org/10.1002/9781118203532
[12]	ECONOMÁTICA System for Investment Analysis. http://www.economatica.com.br/
[13]	JUDD, K. L. Computationally intensive analyses in Economics. In: TESTFATSION, L. & JUDD, K. L. Handbook of computational economics (vol. 2). Amsterdam: Elsevier, 2006. https://doi.org/10.1016/S1574-0021(05)02028-3
[14]	KENDRICK, D. A.; MERCADO, P. R. & AMMAN, H. Computational economics. Princeton University Press, 2005. https://doi.org/10.1515/9781400842822
[15]	McKINSEY& COMPANY, Inc. Valuation: measuring and managing the value of companies. New Jersey: John Wiley & Sons, 2000. https://doi.org/10.7551/mitpress/1410.001.0001
[16]	MIRANDA, M. J. Applied computational economics and finance. Massachussets: The MIT Press, 2002.
[17]	STINESPRING, J. R. Mathematica for Microeconomics: learning by example. Academic Press/Harcourt Inc.: San Diego, California, 2002. https://doi.org/10.1016/B978-0-12-672051-4.X5000-8
[18]	LAW, A. M., and KELTON, W. D. Simulation modeling and analysis. 2nd ed. Singapore: McGraw-Hill, 1991.
[19]	LEBARON, B. Agent-based computational finance. In: TESTFATSION, L. & JUDD, K. L. Handbook of computational economics (vol. 2). Amsterdam: Elsevier, 2006. https://doi.org/10.1016/S1574-0021(05)02024-6
[20]	MENNER, W. A. Introduction to modeling and simulation. Johns Hopkins, APL Technical Digest, v. 16, n. 1, p. 6-17, 1995.
[21]	SHANNON, R. E. System simulation: the art and science. Englewood Cliffs, New Jersey: Prentice-Hall, 1975.
[22]	STEWART III, G. B. The quest for value: a guide for senior managers. New York: Harpers Collins Publishers Inc, 1991.
[23]	STICKNEY, C., WEIL, R. L. & SCHIPPER, K. Financial accounting: an introduction to concepts, methods and uses. Forth Worth: The Dryden Press, 2009. https://doi.org/10.1016/S1574-0021(05)02027-1
[24]	TESTFATSION, L. Agent-based computational economics: a constructive approach to economic theory. In: TESTFATSION, L. e JUDD, K. L. Handbook of computational economics. Vol. 2. Amsterdam: Elsevier, 2006.
[25]	VARIAN, H. R. Economic and financial modelling with Mathematica. New York: Telos, 1993. https://doi.org/10.1007/978-1-4612-2775-8
[26]	WERKER, C. & BRENNER, T. Empirical calibration of simulation models. Eindhoven Institute of Technology: Netherlands, 2004. Available at: https://papers.econ.mpg.de/evo/discussionpapers/2004-10.pdf
[27]	SHINGAREVA, I & LIZÁRRAGA-CELAYA, C. Maple and mathematica: a problem solving approach for mathematics. Vienna: Springer Vienna, 2009. https://doi.org/10.1007/978-3-211-73265-4

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Passos, M. D. O., Tessmann, M. S., Venecian, J. R., Pinto, A. C. (2025). A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks. Applied and Computational Mathematics, 14(6), 309-322. https://doi.org/10.11648/j.acm.20251406.12

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Passos, M. D. O.; Tessmann, M. S.; Venecian, J. R.; Pinto, A. C. A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks. Appl. Comput. Math. 2025, 14(6), 309-322. doi: 10.11648/j.acm.20251406.12

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Passos MDO, Tessmann MS, Venecian JR, Pinto AC. A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks. Appl Comput Math. 2025;14(6):309-322. doi: 10.11648/j.acm.20251406.12

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@article{10.11648/j.acm.20251406.12,
  author = {Marcelo de Oliveira Passos and Mathias Schneid Tessmann and Jean Rodrigues Venecian and Alex Cerqueira Pinto},
  title = {A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks
},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {6},
  pages = {309-322},
  doi = {10.11648/j.acm.20251406.12},
  url = {https://doi.org/10.11648/j.acm.20251406.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251406.12},
  abstract = {This paper presents a multi agent computational framework that deploys heterogeneous agents to investigate how shifts in short term interest rates and in the expected path of rates shape the intrinsic value of a broad stock market index. The model elucidates the transmission channels through which monetary policy propagates to market fundamentals, operationalized via the index’s theoretical replicating portfolio. By distinguishing valuation changes rooted in fundamentals from those driven by sentiment or feedback dynamics, the framework enables the systematic identification and quantification of speculative expansions (bull markets) and contractions (bear markets), thereby advancing a more disciplined understanding of market cycles. A central innovation is an investment oriented metric that produces a weekly time series of the Value Gap (VG), defined as the deviation between the model implied intrinsic value and the observed index level. This measure supports continuous monitoring of mispricing, facilitates comparative analysis across monetary policy regimes, and offers practical signals for risk management and asset allocation. Empirical evaluation yields two principal findings. First, the adverse effect of tighter monetary policy on VG materializes only when the index constituents exhibit a negative aggregate net cash flow, indicating that balance sheet conditions condition the pass through from policy rates to valuation gaps. Second, symmetric adjustments in the policy rate—upward or downward—tend to induce correspondingly directional movements in the index’s fundamental value (VB), highlighting a robust mapping from policy stance to market-implied fundamentals. Overall, the study contributes to the literature on monetary transmission and asset pricing by clarifying the interaction between policy rates, corporate cash flow profiles, and valuation dispersion. It also delivers a transparent and implementable analytical tool for detecting market imbalances, guiding tactical positioning, and informing strategic investment decisions under evolving policy environments.
},
 year = {2025}
}

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TY  - JOUR
T1  - A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks

AU  - Marcelo de Oliveira Passos
AU  - Mathias Schneid Tessmann
AU  - Jean Rodrigues Venecian
AU  - Alex Cerqueira Pinto
Y1  - 2025/11/12
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251406.12
DO  - 10.11648/j.acm.20251406.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 309
EP  - 322
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251406.12
AB  - This paper presents a multi agent computational framework that deploys heterogeneous agents to investigate how shifts in short term interest rates and in the expected path of rates shape the intrinsic value of a broad stock market index. The model elucidates the transmission channels through which monetary policy propagates to market fundamentals, operationalized via the index’s theoretical replicating portfolio. By distinguishing valuation changes rooted in fundamentals from those driven by sentiment or feedback dynamics, the framework enables the systematic identification and quantification of speculative expansions (bull markets) and contractions (bear markets), thereby advancing a more disciplined understanding of market cycles. A central innovation is an investment oriented metric that produces a weekly time series of the Value Gap (VG), defined as the deviation between the model implied intrinsic value and the observed index level. This measure supports continuous monitoring of mispricing, facilitates comparative analysis across monetary policy regimes, and offers practical signals for risk management and asset allocation. Empirical evaluation yields two principal findings. First, the adverse effect of tighter monetary policy on VG materializes only when the index constituents exhibit a negative aggregate net cash flow, indicating that balance sheet conditions condition the pass through from policy rates to valuation gaps. Second, symmetric adjustments in the policy rate—upward or downward—tend to induce correspondingly directional movements in the index’s fundamental value (VB), highlighting a robust mapping from policy stance to market-implied fundamentals. Overall, the study contributes to the literature on monetary transmission and asset pricing by clarifying the interaction between policy rates, corporate cash flow profiles, and valuation dispersion. It also delivers a transparent and implementable analytical tool for detecting market imbalances, guiding tactical positioning, and informing strategic investment decisions under evolving policy environments.

VL  - 14
IS  - 6
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Author Information

Marcelo de Oliveira Passos

Organizations and Markets Graduate Program, Federal University of Pelotas (UFPel), Pelotas, Brazil

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http://orcid.org/0000-0002-9516-8855
Mathias Schneid Tessmann

Economics & Business School, Brazilian Institute of Education, Development and Research (IDP), Brasília, Brazil

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http://orcid.org/0000-0001-9320-0340
Jean Rodrigues Venecian

Organizations and Markets Graduate Program, Federal University of Pelotas (UFPel), Pelotas, Brazil

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http://orcid.org/0000-0001-9610-1815
Alex Cerqueira Pinto

Management Graduate Program (PPGA), University of Brasilia (UNB), Brasília, Brazil

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http://orcid.org/0000-0002-2315-1798

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Passos, M. D. O., Tessmann, M. S., Venecian, J. R., Pinto, A. C. (2025). A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks. Applied and Computational Mathematics, 14(6), 309-322. https://doi.org/10.11648/j.acm.20251406.12

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Passos, M. D. O.; Tessmann, M. S.; Venecian, J. R.; Pinto, A. C. A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks. Appl. Comput. Math. 2025, 14(6), 309-322. doi: 10.11648/j.acm.20251406.12

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Passos MDO, Tessmann MS, Venecian JR, Pinto AC. A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks. Appl Comput Math. 2025;14(6):309-322. doi: 10.11648/j.acm.20251406.12

Copy | Download

@article{10.11648/j.acm.20251406.12,
  author = {Marcelo de Oliveira Passos and Mathias Schneid Tessmann and Jean Rodrigues Venecian and Alex Cerqueira Pinto},
  title = {A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks
},
  journal = {Applied and Computational Mathematics},
  volume = {14},
  number = {6},
  pages = {309-322},
  doi = {10.11648/j.acm.20251406.12},
  url = {https://doi.org/10.11648/j.acm.20251406.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20251406.12},
  abstract = {This paper presents a multi agent computational framework that deploys heterogeneous agents to investigate how shifts in short term interest rates and in the expected path of rates shape the intrinsic value of a broad stock market index. The model elucidates the transmission channels through which monetary policy propagates to market fundamentals, operationalized via the index’s theoretical replicating portfolio. By distinguishing valuation changes rooted in fundamentals from those driven by sentiment or feedback dynamics, the framework enables the systematic identification and quantification of speculative expansions (bull markets) and contractions (bear markets), thereby advancing a more disciplined understanding of market cycles. A central innovation is an investment oriented metric that produces a weekly time series of the Value Gap (VG), defined as the deviation between the model implied intrinsic value and the observed index level. This measure supports continuous monitoring of mispricing, facilitates comparative analysis across monetary policy regimes, and offers practical signals for risk management and asset allocation. Empirical evaluation yields two principal findings. First, the adverse effect of tighter monetary policy on VG materializes only when the index constituents exhibit a negative aggregate net cash flow, indicating that balance sheet conditions condition the pass through from policy rates to valuation gaps. Second, symmetric adjustments in the policy rate—upward or downward—tend to induce correspondingly directional movements in the index’s fundamental value (VB), highlighting a robust mapping from policy stance to market-implied fundamentals. Overall, the study contributes to the literature on monetary transmission and asset pricing by clarifying the interaction between policy rates, corporate cash flow profiles, and valuation dispersion. It also delivers a transparent and implementable analytical tool for detecting market imbalances, guiding tactical positioning, and informing strategic investment decisions under evolving policy environments.
},
 year = {2025}
}

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TY  - JOUR
T1  - A Multi-agent Computational Model for the Transmission of Monetary Policy to the Intrinsic Value of Stocks

AU  - Marcelo de Oliveira Passos
AU  - Mathias Schneid Tessmann
AU  - Jean Rodrigues Venecian
AU  - Alex Cerqueira Pinto
Y1  - 2025/11/12
PY  - 2025
N1  - https://doi.org/10.11648/j.acm.20251406.12
DO  - 10.11648/j.acm.20251406.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 309
EP  - 322
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20251406.12
AB  - This paper presents a multi agent computational framework that deploys heterogeneous agents to investigate how shifts in short term interest rates and in the expected path of rates shape the intrinsic value of a broad stock market index. The model elucidates the transmission channels through which monetary policy propagates to market fundamentals, operationalized via the index’s theoretical replicating portfolio. By distinguishing valuation changes rooted in fundamentals from those driven by sentiment or feedback dynamics, the framework enables the systematic identification and quantification of speculative expansions (bull markets) and contractions (bear markets), thereby advancing a more disciplined understanding of market cycles. A central innovation is an investment oriented metric that produces a weekly time series of the Value Gap (VG), defined as the deviation between the model implied intrinsic value and the observed index level. This measure supports continuous monitoring of mispricing, facilitates comparative analysis across monetary policy regimes, and offers practical signals for risk management and asset allocation. Empirical evaluation yields two principal findings. First, the adverse effect of tighter monetary policy on VG materializes only when the index constituents exhibit a negative aggregate net cash flow, indicating that balance sheet conditions condition the pass through from policy rates to valuation gaps. Second, symmetric adjustments in the policy rate—upward or downward—tend to induce correspondingly directional movements in the index’s fundamental value (VB), highlighting a robust mapping from policy stance to market-implied fundamentals. Overall, the study contributes to the literature on monetary transmission and asset pricing by clarifying the interaction between policy rates, corporate cash flow profiles, and valuation dispersion. It also delivers a transparent and implementable analytical tool for detecting market imbalances, guiding tactical positioning, and informing strategic investment decisions under evolving policy environments.

VL  - 14
IS  - 6
ER  -

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