# How Long Does It Last to Systematically Make Bad Decisions? An Agent-Based Application for Dividend Policy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{t}) are made considering exclusively expected levels for indicators, for example comparing the expected internal rate of return of the proposed investment project (E

_{t}(IRR

_{t}

_{+1})) with the expected required rate of return (E

_{t}(k

_{D}

_{,t+1})).

## 2. Theoretical Background

## 3. The Model

#### 3.1. The Problem

_{t}) are right for the period [−t, 0]:

_{t}> 0. If NE

_{t}≤ 0, we cannot discuss about a dividend policy.

_{t}

_{−1}(IRR

_{t}) and on their expectation regarding the evolution of the market—E

_{t}

_{−1}(kM

_{t}) (this is the market return for projects with a similar risk2):

_{1}(IRR

_{2}) ≥ E

_{1}(kM

_{2}), then: DIV

_{1}= 0

_{1}(IRR

_{2}) < E

_{1}(kM

_{2}), then: DIV

_{1}= NE

_{1}

_{t}) are right for the period [−t, 0]. They are determining a stock of wealth for shareholders, which can induce in shareholders a status of safety and also a state of trust for the manager’s performance. A company’s return is, to a large extent, the effect of some decisions made in the past. As an effect, investors can judge one manager’s performance (the return in one year, source for dividend payments) even if this is the effect of the choices made in the past. Moreover, even the results of some projects are not desirable from a financial viewpoint, in real life their effects are combined with the other projects’ effects, finally, the shareholders having access only to some synthetic indicators at the company’s level (like cash flows, net earnings or return on equity). The initial stock of wealth allows the management to make some wrong decisions because their impact is not fatal for the company.

#### 3.2. Shareholders’ Typology and Behavior

_{t}

^{i}is the percent in total shares (which correspond to the voting power), with x

_{t}

^{A}+ x

_{t}

^{B}+ x

_{t}

^{C}+ x

_{t}

^{D}= 1. Each of classes of shareholders (agents) is characterized by some features, described below.

**Class A**represents the decider (the power). In our study, they are the group of shareholders that make systematically bad decisions, until the power is switched. Agents from this class are overconfident in their decisions (De Bondt and Thaler 1995; Hirshleifer 2001), even if they are wrong. Due to the outputs produced, the behavior of this class of shareholders can be suspected by agency problems, even if they are not real. Additionally, it seems reasonable to anticipate that Class A will suggest that the other shareholders should support their decisions, probably insisting on arguments like trust the expertise of the management which is acting in the benefits of the other shareholders.

**Class B**represents the opposition, respectively, the group of shareholders that understand that the decisions of the Class A are bad, but are not in power. Their rationality is useless for convincing agents from Class A, and even Class B can be associated with keywords like financial rationality, abilities, or literacy6.

**Class C**includes the shareholders that can change their decision. They can learn from past errors (for them, evolution is the keyword). Initially, x

_{t}

^{C}= 0. Firstly, they support the power (they are in Class D), but they change their vote.

**Class D**is a residual in this model: x

_{t}

^{D}= 1 − x

^{A}− x

^{B}− x

_{t}

^{C}. Initially, we assume that they support the power, but they can migrate to Class C.

^{A}and x

^{B}are fixed (constant in time), with x

^{A}∈ (0, 0.5) and x

^{B}∈ (0, 0.5), and x

^{C}and x

^{D}are variable. Initially, x

_{0}

^{C}= 0.

^{B}+ x

_{t}

^{C}> 50%). As in Dragotă (2016), the switch in power in AGM is determined exclusively by the changes in the voting preferences of Class C. Shareholders from Class C analyze the quality of decisions based on the results recorded by the company. As such, they do not evaluate the quality of the decision regarding the dividend payments made at the present moment (t) (see Section 3.1), but the quality of the decisions made in the past moments, as a proxy for the quality of the present decision (see also Table 2). The decision’s quality is quantified comparing the recorded performance with the required one. We considered that the performance is proxied by the realized return of equity (ROE

_{t}). Similarly, the required level of performance is quantified through a required rate of return (ROE

_{t}

^{*}). The evolution of ROE is described in Section 3.3. In Section 3.4 we discuss how they estimate their required rate of return.

_{t}has an acceptable level (is higher or, at least, equal to the required rate of return, ROE

_{t}

^{*}), deciding if they support the power; and (b) if they support the power, they vote for the recommended dividend policy. Additionally, the AGM is the moment when the agents from Class C can change their voting preference: (i) if ROE

_{t}≥ ROE

_{t}

^{*}, they are satisfied and keep their voting preference (they will continue to support the power); (ii) if ROE

_{t}< ROE

_{t}

^{*}, they change their voting preferences, voting against the power. As a result, shareholders from Class A are imposing their viewpoint until: x

_{t}

^{B}+ x

_{t}

^{C}> 0.5.

_{t}

^{C}is determined based on the rule defined in Dragotă (2016):

_{t}

^{C}= x

_{t−1}

^{C}+ α

_{t}·M

_{t}·x

_{t−1}

^{D}

_{t}

^{C}) increase from financial exercise to financial exercise if they are unsatisfied by the level of the rate of return; however, they can change their opinion if the results are satisfying them, becoming more trustful in management’s decision.

_{t}

^{C}should be at least equal cu 0: x

_{t}

^{C}≥ 0.

_{t}is a random variable uniformly distributed on [0,1], which can be interpreted as a magnitude of the interest to change the power (as in Dragotă 2016). If M

_{t}= 0, this can be interpreted as a total indifference to the level of return, but also as a conservative attitude (a high level for conservatism, see Hirshleifer 2001). If M

_{t}= 1, the entire population of agents from class D will change their voting preference, joining the class C of agents, immediately after the level of realized return is below the required rate of return. M

_{t}is dependent of different factors that can have an impact on wealth and for this reason is not constant in time7.

_{t}

^{C}can be written as:

_{t}

^{C}= x

_{t−1}

^{C}+ α

_{t}·M

_{t}(1 − x

^{A}− x

^{B}− x

_{t−1}

^{C}) = x

_{t−1}

^{C}(1 − α

_{t}·M

_{t}) + (1 − x

^{A}− x

^{B})α

_{t}·M

_{t}

#### 3.3. Evolution of Return on Equity

_{0}can be considered as a benchmark. It is determined by the ratio between net earnings recorded in the year 0 (NE

_{0}) and the level of equity in the previous year:

_{0}. The level of total assets at the moment 0, TA

_{0}is considered as an initial stock of shareholders’ wealth and is another input in the model.

_{0}is only a punctual benchmark. Some aleatory factors can influence even this normal ROE. Even if the company maintains constant its level of assets, most probably ROE

_{1}will be different than ROE

_{0}. Even if it is considered that no bad decisions are made, it can be assumed that ROE

_{t}is a random variable. Each year, NE

_{t}is determined by the ROE

_{t}(the return at which the capital is invested) and the stock of capital in the previous year, by the accounting identity:

_{t}) can be determined as a function by the level of the total assets in the previous year (TA

_{t}

_{−1}), net earnings (NE

_{t}) and dividend payments (DIV

_{t}):

_{t}has t components: (1) a component resulted as the return of equity at which initial stock of assets is invested; (2) the result of the investments made in the first financial exercise (t = 1); and (3) the result of the investments made in the second financial exercise (t = 2), …, (t) the result of the investments made in the last financial exercise (t = t − 1). The components (2), (3), … (t) are a function of the internal rates of returns (IRR) corresponding to the invested capital in each financial exercise.

_{t−1}(IRR

_{t}), with the expectations regarding the capital market return, E

_{t}

_{−1}(kM

_{t}).

_{t}≠ E

_{t}

_{−1}(IRR

_{t}). IRR

_{t}= E

_{t}

_{−1}(IRR

_{t}) only in the case of a perfect forecast. Since management is making a bad decision, IRR

_{t}can be considered as a random variable, normally distributed, with a mean $\left[{E}_{t-1}\left(IR{R}_{t}\right)\xb7\left(1-bd\right)\right]$ and a finite standard deviation9

^{,}10.

_{t}

_{−1}(IRR

_{t}) is the expectation made by the Class A agents, and it is not optimal (it can be assumed by Class B shareholders make a better prediction).

#### 3.4. Required Rates of Return

_{t}

_{−1}(kM

_{t}) and ROE

_{t}

^{*}.

_{t}

_{−1}(kM

_{t}) and decides to pay dividends only if E

_{t}

_{−1}(kM

_{t}) > E

_{t}

_{−1}(IRR

_{t}).

_{t}

^{*}), investors can consider different benchmarks (for a survey, see Dragotă et al. 2013). However, basically, all of these benchmarks can be reduced to two fundamental approaches. On the one hand, they expect a rate of return, related to the characteristic of the project (for instance, in CAPM they require a rate of return higher than risk-free rate and they claim also a risk premium—otherwise they will reject the project) (Ross et al. 2010). On the other hand, investors analyze the alternatives available on the capital market (if they do not invest in the proposed project, what alternatives are available?).

_{t}).

_{t}

^{*}) = 0). If shareholders decide to maintain the management in function only if the company records a level of ROE higher than ROE

_{t}

^{*}, we can state τ = 1 (they are totally intolerant in the case of a lack of performance). This coefficient can be related to some socio-cultural factors (e.g., Schwartz 2006).

#### 3.5. Model Inputs

_{0}).

_{t}

_{−1}(kM

_{t}) to be normally distributed16, with a mean of 2.5 and a standard deviation of 2.5. Of course, the program allows for considering a larger range.

#### 3.6. Implementation in NetLogo

## 4. Numerical Results: Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. The NetLogo Code

## References

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1 | De facto, a dividend is defined as apart from net income, and the dividend payout decision is conditioned by the available cash flows, and not by net earnings. If one company records net earnings, but do not record a higher (or equal) amount of cash flows, as long as both dividends and financing investment projects require cash payments, the dividend policy is only a matter of (theoretical) accounting (Dragotă et al. 2019). In this study, we will consider a simplified case, respectively, profit ≡ cash flow. Signaling theories on dividends (e.g., Bhattacharya 1979; Kalay 1980) state that companies that pay dividends signal that they have sufficient cash for paying them, while non-payers can be suspected as not having it. |

2 | It can be noted that this rate of return is not a realized one. Investors expect to record this promised rate of return, so an adequate notation is still E _{t−1}(kM_{t}). |

3 | Taxation can have an impact on dividend payments (see, among others, Dragotă et al. 2009). Walter (1956) analyzes the impact of taxation, too. |

4 | The model can be easily generalized for the case of multiple classes of shares, with different voting power, according to the company’s statute (see, for instance, (Nenova 2003), for the case of dual classes of shares). |

5 | A similar result occurs if the new shareholders (the buyers) replicate the behavior of the former shareholders (the sellers). |

6 | As observation, when the impact of factors like financial literacy or education is discussed, it has to be interpreted cautiously. For instance, Mare et al. (2019) found that insurance literacy has an impact on financial decisions, but education (in general) does not. |

7 | Individuals prefer in many situations the status quo (the “anchoring” effect) (Samuelson and Zeckhauser 1988). As an effect, in this paper, we considered that Class C agents do no change their voting preference instantly. In a different context, Harari (2015, pp. 264–67) provides historical evidence regarding this “anchoring” effect and explains it by a necessity of human beings to make sense of their decisions. If they should accept the fact that their past decision was wrong, they should accept that their past “sacrifices” were unuseful. |

8 | This statement is formalized in the corporate finance literature through classical selection criteria, like the net present value (NPV) > 0 and IRR > the required rate of return (Ross et al. 2010; Dragotă et al. 2013). |

9 | Theoretically, the realized IRR can take values in the (−∞, ∞) interval. |

10 | Some readers can have objections to this manner of formulation, considering that the expected rate of return is a function of the realized rate of return, and not vice versa. In our simple formulation, if we consider E _{t−1}(IRR_{t}) as function of IRR_{t}, IRR_{t} should be generated randomly. |

11 | Similar to the formulation of IRRt, if we consider E _{t−1}(kM_{t}) as function of kM_{t}, kM_{t} should be generated randomly. |

12 | Shareholders’ wealth at moment t (W _{t}) is structured in two components: the initial capital invested in company and the capitalized dividends. |

13 | In the entire paper we consider the real rates of returns, even it is not specified expressly. In a more general context, we can assume that it is not important if we prefer real or nominal rates of returns as long as all the comparisons and considerations regarding these rates are consider the coherence between rates (e.g., compare real rates of returns with real rates of return, and nominal rates of returns with nominal rates of returns). |

14 | Most of the papers in finance stipulate that this required rate of return is related to the assumed risk. |

15 | This variable can be also connected to the aversion to loss (Shefrin and Statman 1985; Odean 1998). |

16 | We have considered a normal distribution, and not a fat-tail one (e.g., McGroarty et al. 2019) for this variable due to the NetLogo limitations. |

17 | According to Wikipedia (https://en.wikipedia.org/wiki/List_of_oldest_companies, accessed on 23 July 2019), the oldest company still in function is Nishiyama Onsen Keiunkan (founded in 705 AD, so with an age less than 1400 years). Of course, such a long period of existence can be explained by making good decisions. From this perspective, it is implausible that, for a company to function for so many years, making systematically bad decisions, large levels of DSMBD can be interpreted as a failure before the change of the decider. |

**Figure 2.**Two forecasts for future level of cash flows–for each class of agents—A (with green) and B (with blue). The two classes estimate the level of indicator (the estimated cash flow) through its probability distribution. The forecast made by one class of agents (B—in the left, with blue) is better than the second one (A—in the right, with green). In (

**a**), if the realized cash flow is N (from normal, very plausible for the first class of agents’ forecast), it can be interpreted by the second class of agents as an unfavorable scenario of evolution (but still plausible, according to their forecast). A realized cash flow equal to O (from optimistic) should confirm the good forecast made by class A (even it is only a relatively unusual good performance based on the forecast made by class B). (

**b**) depicts an even greater dissonance between the two forecasts. In this case, if the realized cash flow is N, class A can realize that the forecast was indeed wrong, but, also, they can consider that an extreme event occurred.

**Figure 5.**Average DSMBD versus the tolerance for manager’s performance, when bd = 0.1 and S1 is considered.

**Figure 7.**Average DSMBD versus the impact of making bad decisions, when τ = 0.5 and S1 is considered.

**Figure 8.**Average DSMBD versus the tolerance for manager’s performance, when bd = 0.1 and S2 is considered.

**Figure 9.**Average DSMBD versus the impact of making bad decisions, when τ = 0.5 and S2 is considered.

Indicator | Notation | Relation or Definition | Observations |
---|---|---|---|

Annual general meeting of shareholders | AGM_{t} | ||

Average ROE calculated for the past five years | APROE_{t} | $APRO{E}_{t}=\frac{1}{5}{\displaystyle {\displaystyle \sum}_{t=t-5}^{t-1}}RO{E}_{t}$ | Used in ROE* estimations |

Cash flow | CF | Difference between cash in-flows and cash out-flows. | |

Coefficient of impact of bad decisions | bd | It can take values between 0 (this means the forecast is optimal) and 1 (this means that the forecast is totally inadequate). | |

Coefficient of intolerance for the manager’s performance | τ | τ ∈ [0, 1]. If this tolerance is maximal, τ = 0. Input in the model. | |

Cost of investment | I_{0} | ||

Decision made by the management | DEC_{t} | ||

Discount rate | k | The shareholders’ required rate of return. | |

Dividend payout ratio | DPR_{t} | $DP{R}_{t}=\frac{DI{V}_{t}}{N{E}_{t}}$ | |

Dividends paid to shareholders | DIV_{t} | ||

Duration of systematically making bad decisions | DSMBD | Output of the model. | |

Internal rate of return for the investment projects | IRR_{t} | It is the discount rate (k) (solution of the equation) for NPV = 0 (k = IRR). | |

Magnitude of interest to change the power | M | M ∈ [0, 1]. Input in the model. | |

Net earnings | NE_{t} | ||

Net present value | NPV | $NPV=-{I}_{0}+{\displaystyle {\displaystyle \sum}_{t=1}^{n}}\frac{C{F}_{t}}{{\left(1+k\right)}^{t}}+\frac{R{V}_{n}}{{\left(1+k\right)}^{n}}$ | |

Percentage of shareholders per Class of shareholders | x^{i}_{t} | In this paper, we consider n = 4 classes of shareholders (i = A, B, C, D), defined in Section 3.2. ${{\displaystyle \sum}}_{i=1}^{n}{x}_{t}^{i}=1$. | |

Residual value | RV | The cash flow resulted at the end-life of the investment project | |

Realized capital market return | kM_{t} | Random variable, normal distributed, with a mean $\left[{E}_{t-1}\left(k{M}_{t}\right)\right]$ and a finite standard deviation | |

Realized internal rate of return | IRR_{t} | Random variable, normal distributed, with a mean $\left[{E}_{t-1}\left(IR{R}_{t}\right)\xb7\left(1-bd\right)\right]$ and a finite standard deviation | |

Realized rate of return on assets | ROA_{t} | In this paper, ROA = ROE | |

Realized rate of return on equity | ROE_{t} | $RO{E}_{t}=\frac{N{E}_{t}}{T{A}_{t-1}}$ | In this paper, ROA = ROE |

Required rate of return on equity | ROE*_{t} | $RO{E}_{t}^{\ast}=\tau \xb7max\left(APRO{E}_{t};{E}_{t-1}\left(IR{R}_{t}\right);k{M}_{t}\right)$ | |

Total assets | TA_{t} | In this paper, TA = TE. Input in the model. | |

Total equity | TE_{t} | In this paper, TA = TE. Input in the model. | |

Shareholders’ wealth | W_{m} |

Financial Exercise (Year) | Phase | Content |
---|---|---|

0 | ||

1 | 1.1 | The company records output results: ROE_{1} and NE_{1}. |

1.2 | If NE_{1} ≤ 0, DIV_{1} = 0.Otherwise, the management (the controlling shareholder) anticipates E _{t−1}(IRR_{t}), respectively E_{1}(IRR_{2}) | |

1.3 | AGM: The management (the controlling shareholder) proposes a dividend policy: If E _{1}(IRR_{2}) ≥ E_{1}(kM_{2}), then: DIV_{1} = 0If E _{1}(IRR_{2}) < E_{1}(kM_{2}), then: DIV_{1} = NE_{1} | |

1.4–1.5 | AGM: shareholders analyze the performance of the company at the present moment, as a proxy for the quality of the management’s decisions. We consider that, at this moment, the power remains in function. | |

2 | 2.1 | The company records output results: ROE_{2} and NE_{2}. |

2.2 | If NE_{2} ≤ 0, DIV_{2} = 0.Otherwise, the management (the controlling shareholder) anticipates E _{t−1}(IRR_{t}), respectively E_{2}(IRR_{3}) | |

2.3 | AGM: The management (the controlling shareholder) proposes a dividend policy: If E _{2}(IRR_{3}) ≥ E_{2}(kM_{3}), then: DIV_{2} = 0If E _{2}(IRR_{3}) < E_{2}(kM_{3}), then: DIV_{2} = NE_{2} | |

2.4 | AGM: shareholders analyze the performance of the company at the present moment, as a proxy for the quality of the management’s decisions: $if\{\begin{array}{c}RO{E}_{2}\ge RO{E}_{2}^{\ast},\mathrm{then}:{x}_{2}^{C}\le {x}_{1}^{C}\\ RO{E}_{2}RO{E}_{2}^{\ast},\mathrm{then}:{x}_{2}^{C}\ge {x}_{1}^{C}\end{array}$ Notes: $RO{E}_{t}^{\ast}=\left(1-\mathsf{\tau}\right)\xb7\mathrm{max}\left(RO{E}_{0};{E}_{t-1}\left(IR{R}_{t}\right);k{M}_{t}\right)$ x _{t}^{C} = x_{t−1}^{C} + α_{t} ·M_{t} (1 − x^{A} − x^{B} − x_{t−1}^{C}) = x_{t−1}^{C} (1 − α_{t} ·M_{t}) + (1 − x^{A} − x^{B})α_{t} ·M_{t} | |

2.5 | AGM: vote: x _{2}^{B} + x_{2}^{C} ≤ 0.5, the management remains in powerIf x _{2}^{B} + x_{2}^{C} > 0.5, then the power is switched (the end of the discussion) | |

3 | 3.1 | The company records output results: ROE_{3} and NE_{3}. |

3.2 | If NE_{3} ≤ 0, DIV_{3} = 0.Otherwise, the management (the controlling shareholder) anticipates E _{t−1}(IRR_{t}), respectively, E_{3}(IRR_{4}) | |

… | … | |

t | t.1 | The company records output results: ROE_{t} and NE_{t}. |

t.2 | If NE_{t} ≤ 0, DIV_{t} = 0.Otherwise, the management (the controlling shareholder) anticipates E _{t−1}(IRR_{t}), respectively, E_{t}(IRR_{t+1}) | |

t.3 | AGM: The management (the controlling shareholder) proposes a dividend policy: If E _{t}(IRR_{t+1}) ≥ E_{t}(kM_{t+1}), then: DIV_{t} = 0If E _{t}(IRR_{t+1}) < E_{t}(kM_{t+1}), then: DIV_{t} = NE_{t} | |

t.4 | AGM: shareholders analyze the performance of the company at the present moment, as a proxy for the quality of the management’s decisions: $if\{\begin{array}{c}RO{E}_{t}\ge RO{E}_{t}^{\ast},\mathrm{then}:{x}_{t}^{C}\le {x}_{t-1}^{C}\\ RO{E}_{t}RO{E}_{t}^{\ast},\mathrm{then}:{x}_{t}^{C}\ge {x}_{t-1}^{C}\end{array}$ Notes: $RO{E}_{t}^{\ast}=\left(1-\mathsf{\tau}\right)\xb7\mathrm{max}\left(RO{E}_{0};{E}_{t-1}\left(IR{R}_{t}\right);k{M}_{t}\right)$ x _{t}^{C} = x_{t−1}^{C} + α_{t} · M_{t} (1 − x^{A} − x^{B} − x_{t–1}^{C}) = x_{t−1}^{C} (1 − α_{t} · M_{t}) + (1 − x^{A} − x^{B})α_{t} · M_{t} | |

t.5 | AGM: vote: x _{t}^{B} + x_{t}^{C} ≤ 0.5, the management remains in powerIf x _{t}^{B} + x_{t}^{C} > 0.5, then the power is switched (the end of the discussion; DSMBD is determined) | |

… | … | … |

… | … | … |

Financial Exercise (Year) | Total Assets at the Beginning of the Period | Net Earnings | Return of Equity |
---|---|---|---|

0 | TA_{−1} | NE_{0} | ROE_{0} |

1 | TA_{0} | $N{E}_{1}=RO{E}_{1}\xb7T{A}_{0}=N{E}_{0}\xb7RO{E}_{0}\xb7\left(1+{\epsilon}_{ROE}\right)$ | $RO{E}_{1}=RO{E}_{0}\left(1+{\epsilon}_{ROE}\right)$ |

2 | $T{A}_{1}=T{A}_{0}+N{E}_{1}-DI{V}_{1}$ | $N{E}_{2}=N{E}_{0}\left(1+{\epsilon}_{ROE}\right)+\left(N{E}_{1}-DI{V}_{1}\right)\left[{E}_{1}\left(IR{R}_{2}\right)\left(1-bd\right)\right]\left(1+{\epsilon}_{IRR2}\right)$ | $RO{E}_{2}=\frac{N{E}_{2}}{T{A}_{1}}$ |

3 | $T{A}_{2}=T{A}_{1}+N{E}_{2}-DI{V}_{2}$ | $\begin{array}{ll}N{E}_{3}=& N{E}_{0}\left(1+{\epsilon}_{ROE}\right)+\left(N{E}_{1}-DI{V}_{1}\right)\left[{E}_{1}\left(IR{R}_{2}\right)\left(1-bd\right)\right]\left(1+{\epsilon}_{IRR2}\right)\\ & \hspace{1em}\hspace{1em}\hspace{1em}+\left(N{E}_{2}-DI{V}_{2}\right)\left[{E}_{2}\left(IR{R}_{3}\right)\left(1-bd\right)\right]\left(1+{\epsilon}_{IRR3}\right)\end{array}$ | … |

… | … | … | … |

n − 1 | $T{A}_{n-2}=T{A}_{n-3}+N{E}_{\mathrm{n}-2}-DI{V}_{n-2}$ | … | … |

n | $T{A}_{n-1}=T{A}_{\mathrm{n}-2}+N{E}_{n-1}-DI{V}_{n-1}$ | $N{E}_{n}=N{E}_{0}\left(1+{\epsilon}_{ROE}\right)+{\displaystyle {\displaystyle \sum}_{t=1}^{n-1}}\left(N{E}_{t}-DI{V}_{t}\right)\left[{E}_{t}\left(IR{R}_{t+1}\right)\left(1-bd\right)\right]\left(1+{\epsilon}_{IRR,t+1}\right)$ | $RO{E}_{n}=\frac{N{E}_{n}}{T{A}_{n-1}}$ |

Financial Exercise | TA_{t} | NE_{t} | ROE_{t} | E_{t–1}(IRR_{t}) | E_{t–1}(kM_{t}) | DIV_{t} | x^{A}_{t} | x^{B}_{t} | x^{C}_{t} | x^{D}_{t} | APROE_{t} | IRR_{t} | kM_{t} | bd | 1 − τ | ROE_{t}* | Mt |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

(m.u.) | (m.u.) | (%) | (%) | (%) | (m.u.) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | (%) | ||

0 | 1000 | 25.00 | 2.50 | 25.00 | 1.00 | 1.00 | 0.00 | 98.00 | 2.50 | ||||||||

1 | 1000 | 38.50 | 3.85 | 2.64 | 2.90 | 38.50 | 1.00 | 1.00 | 0.00 | 98.00 | 2.77 | ||||||

2 | 1000 | 56.00 | 5.60 | 9.32 | 0.65 | 0.00 | 1.00 | 1.00 | 0.00 | 98.00 | 3.17 | 2.38 | 2.90 | 10.00 | 90.00 | 2.86 | 20.00 |

3 | 1056 | −13.90 | −1.32 | 4.48 | 3.14 | 0.00 | 1.00 | 1.00 | 19.60 | 78.40 | 1.82 | 8.39 | 0.65 | 10.00 | 90.00 | 7.55 | 20.00 |

… | … | … | … | … | … | … | … | … | … | … | … | … | … | … | … | … | … |

Input | Notation | Level | Numerical Simulation | Distribution of the Variable | Remarks |
---|---|---|---|---|---|

Initial stock of total assets (equal to total equity) (initial wealth in our program) | TA_{0} | Fixed | 1000 | Constant | This level is configurable in slider “Initial-Total-Assets”. |

Initial return on equity | ROE_{0} | Fixed | 2.5% | Constant | In the case of APROE calculations for the first periods (before the period of bad decisions), we have assumed also that ROE was equal to this level. |

Expected market return | E_{t–1}(kM_{t}) | Random | Range between 0% and 5% | Normally distributed, with a mean of 2.5 and a standard deviation of 2.5. | At the beginning of each iteration, its value is changing. |

Expected internal rate of return for the new projects | ${E}_{t-1}\left(IR{R}_{t}\right)$, ∀ t | Random | Range between 0% and 5% | Normally distributed with a mean of 2.5 and a standard deviation of 0.8 | eIRR in NetLogo |

The impact of making bad decision | bd | Fixed | 0.1 | Constant | It can take values between 0 (this means the forecast is optimal) and 1 (this means that the forecast is totally inadequate). It can be set from the interface and ranges between 0%–100%. |

The tolerance for the manager’s performance | τ | Fixed | 50% (but it can be set from the interface and ranges between 0%–100%) | Constant | It can be considered also as a resilience for changing the power. |

The magnitude of interest to change the power | M | Random | 0.2 | Random (multi-values, each agent has its own value of this variable) | Range between 0% and 100% |

S1 | S1-1 | S1-2 | S1-3 | S1-4 | S1-5 | S1-6 | S1-7 | |
---|---|---|---|---|---|---|---|---|

Parameters | The tolerance for the manager’s performance (τ) | 0 | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | 1 |

The impact of making bad decision (bd) | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | |

Average DSMBD (ticks) | 12.29 | 12.54 | 14.73 | 19.17 | 24.28 | 31.43 | 43.52 | |

DSMBD interval (min, max) | [10, 14] | [10, 16] | [11, 23] | [12, 27] | [15, 38] | [16, 39] | [24, 54] |

S1 | S1-8 | S1-9 | S1-10 | S1-11 | S1-12 | S1-13 | |
---|---|---|---|---|---|---|---|

Parameters | The tolerance for the manager’s performance (τ) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

The impact of making bad decision (bd) | 0 | 0.3 | 0.5 | 0.7 | 0.9 | 1 | |

Average DSMBD (ticks) | 20.26 | 19.05 | 17.73 | 16.92 | 16.31 | 16.04 | |

DSMBD interval (min, max) | [14, 27] | [12, 27] | [12, 26] | [12, 25] | [12, 24] | [12, 20] |

S2 | S2-1 | S2-2 | S2-3 | S2-4 | S2-5 | S2-6 | S2-7 | |
---|---|---|---|---|---|---|---|---|

Parameters | The tolerance for the manager’s performance (τ) | 0 | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | 1 |

The impact of making bad decision (bd) | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | |

Average DSMBD (ticks) | 12.72 | 17.92 | 24.97 | 59.14 | 260.57 | 1203.71 | 4555.86 | |

DSMBD interval (min, max) | [10, 15] | [10, 43] | [11, 85] | [12, 166] | [49, 741] | [263, 2252] | [933, 12489] |

S2 | S2-8 | S2-9 | S2-10 | S2-11 | S2-12 | S2-13 | |
---|---|---|---|---|---|---|---|

Parameters | The tolerance for the manager’s performance (τ) | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

The impact of making bad decision (bd) | 0 | 0.3 | 0.5 | 0.7 | 0.9 | 1 | |

Average DSMBD (ticks) | 65.62 | 54.23 | 50.71 | 50.32 | 49.18 | 48.13 | |

DSMBD interval (min, max) | [20, 171] | [12, 164] | [12, 144] | [12, 141] | [12, 138] | [12, 116] |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dragotă, V.; Delcea, C. How Long Does It Last to Systematically Make Bad Decisions? An Agent-Based Application for Dividend Policy. *J. Risk Financial Manag.* **2019**, *12*, 167.
https://doi.org/10.3390/jrfm12040167

**AMA Style**

Dragotă V, Delcea C. How Long Does It Last to Systematically Make Bad Decisions? An Agent-Based Application for Dividend Policy. *Journal of Risk and Financial Management*. 2019; 12(4):167.
https://doi.org/10.3390/jrfm12040167

**Chicago/Turabian Style**

Dragotă, Victor, and Camelia Delcea. 2019. "How Long Does It Last to Systematically Make Bad Decisions? An Agent-Based Application for Dividend Policy" *Journal of Risk and Financial Management* 12, no. 4: 167.
https://doi.org/10.3390/jrfm12040167