Experimental Investigation of Human Decision Processes in Portfolio Decision Analysis

Table of Contents

Abstract

Table of Contents

List of Figures

List of Tables

List of Abbreviations

List of Symbols

1 Introduction

2 Literature Review
2.1 Financial Portfolio Optimization
2.2 Resource Allocation
2.3 Decision Analysis

3 Theory of the Experimental Framework
3.1 Knapsack Optimization Problem
3.2 Laboratory Experiment
3.3 Verbal Protocol Analysis

4 Methodology
4.1 Experimental Design
4.1.1 Task
4.1.2 Participants
4.1.3 Experimental Procedure
4.2 Encoding Process
4.3 Analyzing Process

5 Results
5.1 Optimality and Iteration
5.1.1 Optimality α within heuristic groups
5.1.2 Optimality α regarding type of calculation
5.1.3 Optimality α regarding verbalizing effects
5.1.4 Optimality α with or without overview
5.1.5 Iterating steps
5.2 Heuristics and Metrics
5.2.1 Heuristics
5.2.2 RRS2 and DRP
5.2.2.1 Rank-Range-Part (RRS2) and Data-Range-Part (DRP2) with Updating
5.2.2.2 Outcome
5.2.3 ARS
5.2.4 Behavioural Aspects

6 Conclusion

Reference List

Appendices

Ehrenwörtliche Erklärung

Abstract

Till now operations management mainly dealt with finding appropriate models to facilitate decision making processes, but these theoretical concepts did not always help to deal with actual processes in practice. Thus the understanding of human behaviour becomes more and more important. Furthermore the behavioural aspect of the decision making process plays a big role, as everyone of us would face resource allocation situations or portfolio decisions and people always do not make optimal decisions as mathematical models would do, but rather a completely another way often based on heuristics. Therefore it is interesting to investigate how people tackle such decision making situations intuitively and which cognitive strategies they follow thereby.

This work aims to give a detailed overview about the relating literatures at first. Then decision making processes in portfolio decision situations are experimentally investigated regarding to behavioural aspects, in this case concerning knapsack problems, with the application of the methodology verbal protocol analysis. Concrete heuristics which subjects were following during the decision process could be identified and classified under the terms of certain criterions for further analysis. Hereby verbal protocol analysis helped to collect good and applicable data for determining specific behaviour of people in portfolio decision processes.

List of Figures

Figure 1: The intuitive and reasoning system (Kahneman, 2003)

Figure 2: Experiment visualization made with z-Tree

Figure 3: Model of the human cognitive system (Ericsson and Simon, 1980; Jaspers et al., 2004)

Figure 4: Schematic overview of the verbal protocol analysis method (Jaspers et al., 2004)

Figure 5: Logic task as example for the verbalization process

Figure 6: 1. Original text in German. 2. Translated in English. 3. Extract from a subject´s verbal protocol. Transcripts encoded using the vocabulary provided above. It is clear that this subject follows the heuristic RBC and also calculated the ratios mentally. In the end the subject tried to improve the result by searching for exchange options which would increase benefit.

Figure 7: Best participants in Experiment 1and 2 using RBC

Figure 8: Performance of the DBC Group in Experiment 1

Figure 9: Performance of the No Overview Group in all Experiments

List of Tables

Table 1: Treated literatures in overview

Table 2: Optimality α within heuristic methods

Table 3: Optimality α within calculation types

Table 4: Optimality α regarding verbalizing influence

Table 5: Optimality α with or without an overview

Table 6: Average iterating steps

Table 7: RRS2 and DRP2 in general and for heuristic groups

Table 8: RRS2 and DRP2 for 2 phases

Table 9: RRS2 and DRP2 data of subject 7

Table 10: ARS2 data and its relation to first selections

Table 11: Optimality α regarding first selections

List of Abbreviations

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1 Introduction

Kester et al. (2009) emphasized the importance of operations management and its challenges for companies. They claimed that operations management has severe consequences for a firm´s long-term competition position and as a relevant subfield the portfolio management is not seen as a singular process but as a span of interrelated decision-making processes that aim to refine and implement the firm´s strategic goals by effectively allocating the available resources (Kester et al., 2009). As operations management mainly dealt with finding appropriate models to facilitate decision making processes, for instance portfolio choice and resource allocation problems, and these theoretical concepts did not always help to deal with actual processes in practice, the understanding of human behaviour becomes more and more important. Thus researchers began to focus on people issues, as it is significant for the success of the application of operations management tools and techniques. Furthermore the behavioural aspect of the decision making process plays a big role, as everyone of us would face resource allocation situations and people always do not make optimal decisions as mathematical models would do, but rather a completely another way often based on heuristics. Therefore it is interesting to investigate how people tackle such resource allocation problems intuitively and which cognitive strategies they follow thereby. Thus the purpose of this work is to investigate such behavioural aspects in decision processes experimentally and how well people perform with their selected heuristics.

Bendoly et al. (2006) gave a detailed review about the investigated topics dealing with experimental and behavioural research. The few existing studies in this field are e.g. the newsvendor problem analyzed in the paper of Gavirneni and Isen (2010) or the meal allocation problem investigated by Ball et al. (1998). These are both popular areas in the operations management research. To get a more detailed overview on the literature dealing with portfolio decision analysis and resource allocation problems, an extensive literature review is done in this work, forming the first major part.

Another main part of this thesis is the experimental investigation of a resource allocation problem or rather a portfolio decision problem, the so-called knapsack problem. Since there is rarely literature about knapsack optimization problems, the chair Operations & Supply Chain Management of TU Munich started research on this topic in the last years, so that the present work could continue the studies already done by Masia (2012), Tisch (2013) as well as Li and Richter (2013). Tisch (2013) has developed knapsack problem instances, each with 10 items, and conducted the experiments with the tool z-Tree, where the participants could make their decisions with this computer software independently and anonymously. Li and Richter (2013) continued his work and added the verbal protocol analysis method to the experiment setting for better following the decision and thinking processes. A further step is made here, i.e. the experiment setting of Li and Richter (2013) is modified a little bit. The knapsack instances have 15 items and are highly correlated this time. Many of the metrics applied by Tisch (2013) are adopted or refined to adapt them to the used methodology in this study. In individual sessions or interviews the subjects have to make portfolio decision regarding knapsack problems, while they are required to verbalize their thoughts during the decision-making process. The results of Tisch (2013) as well as Li and Richter (2013) can be confirmed for some part and their findings are discussed and extended. The methodology enables to analyse the portfolio planning behaviour of the subjects, as the line of reasoning for their decision-making can be always reconstructed with it. Additionally clear trails of the decision processes regarding to the giving knapsack problems are revealed and consistent results for the analysis could be obtained. The strengths and weaknesses of the methodology are also identified, as verbal protocol analysis is a relatively new method for operations management.

2 Literature Review

Operations management includes a wide range of research fields such as product development, process design and improvement, inventory management, portfolio decision analysis and supply chain management. There is always a gap between the concepts of operations management and the actual processes in practice, as the theories often ignore important characteristics of real systems and therefore are perceived to be difficult to apply in practice (Bendoly et al., 2006). Since the 1950s researchers began to focus on people issues, because the understanding of human behaviour is significant for the success of the application of operations management tools and techniques, so that more and more studies were published on the topic behavioural operations management. Thus this work investigates the decision behaviour within knapsack optimization as a special portfolio selection and resource-allocation problem which was always defined as choosing between options that differ in costs and payoffs in the literature.

Fasolo et al. (2011) wrote a report about behavioural operations management issues especially regarding portfolio and resource allocation decisions and they pointed out the relevance of these issues to the portfolio decision analysis in their review. A formal framework for portfolio decision analysis was built to help interpreting resource allocation and portfolio decisions. The authors mainly focused on intuitive heuristics and biases which are closely connected with such decision processes. They claimed cognitive or motivational failure and justifiability being the reasons for the violation of normative models that explain resource allocation situations (Fasolo et al., 2011). The study is important to understand how people naturally and intuitively concern the every-day-situation of allocating resources. This is a crucial aspect as the human decision behaviour studied in this work is also of intuitive nature. There are two different types of biases which result from the institutional, legal or political environment: individual biases (cognitive and motivational factors) and organizational biases, as the first ones were outlined from laboratory work and the organizational ones from real experiences of the authors (Fasolo et al., 2011). Suboptimisation, partition dependence, various forms of status quo bias and scope insensitivity belonged to the individual biases and justifiability (5 arguments: equalisation, anchoring, minimum requirement, demonstrable benefits and appeal to champions) formed part of the organizational biases (Fasolo et al., 2011).

Loch and Wu (2007) intensely investigated issues of behavioural operations management in their book and reviewed many relevant literatures regarding to this. They outlined important aspects of behavioural operations management and tried to define this concept including all of these aspects which looked as follows (Loch and Wu, 2007, p. 15):

OM is concerned with the study of the design and management of transformation processes in manufacturing and service organizations, building mathematical theory of the phenomena of interest and testing the theory with field data (derived from surveys, databases, experiments, comparative case studies, ethnographic observations, etc.). Behavioural Operations Management is a multi-disciplinary branch of OM that explicitly considers the effects of human behaviour in process performance, influenced by cognitive biases, social preferences, and cultural norms.

The authors then focused on individual decision making heuristics and its biases, as this part of behavioural operations management helped to understand employee performance during operational processes. As Kahneman (2003) set intuitive judgments between automatic perceptions and deliberate reasoning and categorized intuition and reasoning as two thinking systems (Figure 1), these judgments of decision makers were related to diverse heuristics which could sometimes result in systematic biases (Loch and Wu, 2007). The importance of such heuristics is why they are a focal point in this work.

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Figure 1: The intuitive and reasoning system (Kahneman, 2003)

Bendoly et al. (2006) described the importance and benefits of experimental investigations in the context of behavioural operations management and reviewed diverse literature from 6 different journals between 1985 and 2005 to develop a framework for identifying the types of behavioural assumptions made in analytical operation management models. The investigated issues could be assigned to the areas inventory management, production management, product development, quality management, procurement and strategic sourcing, and supply chain management. The assumptions were grouped into “intentions”, “actions” and “reactions”, whereas most literature belonged to the “actions” assumption (Bendoly et al., 2006). The authors also mentioned a possible categorization of the behavioural research literature following the types of experiments: industrial, laboratory and situational experiments and in conclusion they identified future research opportunities (Bendoly et al., 2006).

Hämäläinen et al. (2013) also highlighted the importance of behavioural operational research and investigated particularly behavioural aspects related to the use of operational research methods in modeling, problem solving and decision supporting, as the insights could improve the problem solving process and help to make better decisions. They conducted four experiments with 11 different questionnaires about a department store task at the university to find out how people understand and make decisions regarding dynamic systems. The results showed that the communication phase of operational research processes was highly sensitive to various behavioural effects such as priming and framing effects (Hämäläinen et al., 2013). The findings were important to improve operational research practices.

Resource allocation is a much discussed topic that has been analyzed from many different perspectives. Operations management researchers represent one of these perspectives and in the last years more and more of them developed concrete theories as well as linear and nonlinear techniques to handle resource allocation problems especially within portfolio selection decisions. Thus behavioural issues in portfolio choice and resource allocation problems are tightly affiliated with each other and the investigation of them is relevant for the final portfolio decision analysis (Fasolo et al., 2011). A proper understanding of human behaviour and biases regarding to this would help to improve the portfolio selection process and thereby maximize the outcome. The present thesis intends to make an extensive literature review by roughly grouping relating works into general resource allocation problems of real objects and abstract financial portfolio selection cases. There is a general characterization about decision analysis subsequently. This would build a useful theoretical framework for the experimental investigation of human decision processes in portfolio decision analysis in this work.

2.1 Financial Portfolio Optimization

As portfolio management played an important role for yielding profits as well as for a firm´s long-term competition position on the markets, portfolio decisions should be made carefully and placed in the context of the whole portfolio and the achievement of strategic goals of the management. Strategic alignment, value maximization and balance are the three wide-ranging goals found by Cooper et al. (2001).

To assess probabilities and to predict values which always occurred in asset management people always made intuitive decisions based on different heuristics which could result in systematic biases. This phenomenon also concerned portfolio decisions and Tversky and Kahneman (1974) experimentally investigated the possible heuristics and biases in such decision-making processes within a mathematical model under uncertainty. They conducted diverse experiments with students and identified three types of heuristics: representativeness, availability and anchoring and adjustment. The representativeness heuristic was applied when decisions were based on the similarity between objects and could lead to biases such as the gambler’s fallacy, the conjunction fallacy, and misperceptions of randomness; the availability heuristic (information´s availability, retrievability and vividness) prompted people to look at the frequency or the probability of an event which would lead to overestimation of the probability of catastrophic events; the last identified heuristic anchoring and adjustment which was mainly applied in numerical predictions meant that people always tended to make decision adjustments from a relevant anchor value, so that these estimates could be easily manipulated (Tversky and Kahneman, 1974). A better understanding of these heuristics and biases would lead to better decisions under uncertainty.

Although expected utility theory was always applied to the analysis of portfolio decision making under uncertainty and risk, Kahneman and Tversky (1979) found examples of choice problems in which, as they said, preferences systematically violated the axioms of expected utility theory. These findings came from responses of students and university faculty to hypothetical choice problems, e.g. the purchase of different insurance programs. The investigation results helped the authors to develop the alternative prospect theory which set value for gains and losses instead for final assets and decision weights for every alternative choice or rather uncertain outcome (Kahneman and Tversky, 1979). They also claimed that the value function was (1) defined on deviations from the reference point; (2) generally concave for gains and commonly convex for losses; (3) steeper for losses than for gains (Kahneman and Tversky, 1979, p. 279). The new theory built a better framework for dealing with risky choice problems such as asset decisions.

Rapoport (1984) dealt with financial portfolio planning problems and used a computer-controlled, discrete-time, multistage betting game (MBG) to study how portfolio decisions are influenced by factors such as different investment conditions and the amount of available capital. The portfolio selection tasks in the experiments contained both risky and riskless alternatives or assets and the 28 subjects had to make about 400 betting and savings decisions in each case. Thereby Rapoport (1984) intended to investigate (1) the effect of changes in capital on the proportion of capital put in savings, and (2) the effect of the investment conditions (favorable vs. unfavorable) on saving behaviour. He found out that (1) the proportion of capital saved increases with the amount of capital on hand, and (2) the proportion of capital saved decreases with practice when the investment conditions are favorable and increases with practice when they are unfavorable. In the experiment the investment conditions had a significant effect on the portfolio decisions made by the subjects, just as the portfolio decisions influenced by the experiment setting investigated in this work.

In another research Kroll et al. (1988) tested the application of the specific mean-variance model for portfolio selection. They conducted experiments with 15 knowledgeable undergraduate students who should make choices in 40 computer-controlled portfolio selection problems with each including two independent risky assets and were provided with information about these assets. The independent variables manipulated in the laboratory experiments were the distributions of risky assets, the initial investment capital and the amount of practice. It came out that there were a high percentage of inefficient mean-variance portfolios which did not decrease with practice, a big amount of requests for useless information, many switches between the two risky assets and sequential dependencies (Kroll et al., 1988). Cognitive biases and intuition could be a reason. The authors suggested that a more general model would provide a more adequate account of portfolio decision behaviour than the mean-variance model, e.g. a focus on the human heuristics.

As Lipshitz and Strauss (1997) also investigated how decision maker or managers of a company dealt with uncertainty of portfolio planning problems, they analyzed 102 self-reports of naturalistic decision-making situations under uncertainty from students, with an inclusive method of classifying conceptualizations of uncertainty and coping mechanisms developed from related literature. Three types of uncertainty could be identified from the analysis results: inadequate understanding, incomplete information and undifferentiated alternatives; and five strategies of coping were applied by the subjects: reducing uncertainty, assumption-based reasoning, weighing pros and cons of competing alternatives, suppressing uncertainty and forestalling (Lipshitz and Strauss, 1997). Inadequate understanding was mainly solved by reduction, incomplete information by assumption-based reasoning and undifferentiated alternatives by weighing pros and cons. These findings finally helped the authors to develop the R.A.W.F.S. hypothesis or rather heuristic (Reduction, Assumption-based reasoning, Weighing pros and cons, Suppression, and Hedging) which described how decision makers conceptualize and cope with uncertainty in naturalistic settings and they suggested finally that decision makers coped with uncertainty adaptively, matching different types of uncertainty with different coping strategies (Lipshitz and Strauss, 1997). The findings could be well applied in asset selection problems.

When people had to make a decision where the outcomes of the choice alternatives were uncertain, they always needed to represent this uncertainty to base or rather support his/her decision. Thus Durbach and Stewart (2011) conducted an experiment with 28 postgraduate students to test the effects of uncertainty format on single- and multi-criteria choice by deciding about a set of investment alternatives (risky and riskless) such as funds and shares to maximize value, in terms of the quality of the final choice, the specific characteristics of the alternatives that are selected, and the difficulty experienced in making a decision. Thereby the unknown performance of each alternative with three attributes on each of the three objectives was presented to the decision makers using one of the six uncertainty formats: probability distributions; expected values with or without standard deviations; a set of five quantiles; a triangular approximation to the probability distribution (minimum–median–maximum); and a set of three representative ‘‘scenarios’’ (Durbach and Stewart, 2011). Their results showed that the use of probability distributions always overloaded subjects with information and lead to relatively poorer and more difficult decisions, while subjects found formats which had an immediate level of summary, easier to use and more profitable, such as expected values, three-point approximations and quantiles (Durbach and Stewart, 2011). This paper made a crucial contribution to the analysis of different display formats for uncertain information in financial investment situations, as a skilled application of these formats would have a big influence on the decision-making process.

Benartzi and Thaler (2001) investigated in their work whether the 1/n heuristic behaviour can be found in adults choosing how to invest their retirement savings and could confirm this. The 1/n strategy or the so-called diversification heuristic means someone simply divides the contributions evenly among the n options offered in his/her retirement savings plan. The authors used hypothetical questionnaires and cross-sectional data on retirement saving plans to examine how a particular set of investment options or rather funds being offered affects the asset allocation decisions of 180 university employees as participants. While they revealed difficult issues regarding the design of retirement saving plans, they also find out that the proportion invested in stocks depends strongly on the proportion of stock funds in the plan (Benartzi and Thaler, 2001).

In another work in the same year, Benartzi (2001) investigated the phenomenon that employees always invested a large portion of their discretionary funds in company stock, though this is a quite dubious strategy due to asset diversification. The author conducted questionnaires with 500 firms which could sponsor their retirement saving plans and the evidence could confirm this tendency. The results indicated that past returns on company stock had a substantial effect on subsequent investment decisions, even though employees were unable to predict the future performance of company stock (Benartzi, 2001). The allocations of employee´s discretionary funds to company stock were correlated with past returns but not with future returns, which showed that employees excessively extrapolated past performance. This was consistent with the representativeness assumption of Tversky and Kahneman (1974) as mentioned above. As a result of such optimism and overconfidence, there could be substantial costs for employees as they constructed highly concentrated portfolios (Benartzi, 2001), so that it became clear that past performance should not influence present portfolio decisions.

It was always assumed that investors should hold fully diversified portfolios regardless of their degree of risk aversion. Especially for risk-averse, utility-maximizing investors, diversification for the risk-seeking part of the portfolio is optimal as diversification reduces portfolio risk from the variance of the individual securities (Barasinska et al., 2012). After many studies confirmed that many private investors hold underdiversified portfolios consisting of only a small subset of available assets, called an incomplete portfolio, Barasinska et al. (2012) examined more closely the relationship between investor risk attitude and portfolio composition. The authors used data on the asset holdings of German households collected by the German Socio-Economic Panel (SOEP) and gathered information about risk attitudes of 2628 private persons in SOEP surveys by asking respondents how willing they are to take financial risks. The scale ranged from 0 (not willing to take any risks) to 10 (fully prepared to take risks). Six different asset classes were divided into three risk categories “low-risk,” “moderate-risk,” and “high-risk” and built a measure of diversification. The other measurement for portfolio composition was to look at the number of distinct asset types of selected portfolio. Based on these categories, the authors defined seven portfolio types and modelled the relationship between the self-declared risk aversion of private investors and their propensity to hold incomplete portfolios (Barasinska et al., 2012). They could confirm the assumption that households that were more risk averse tended to hold incomplete portfolios, consisting mainly of a few risk-free assets, and also found out that a household’s propensity to acquire additional assets was highly dependent on whether liquidity and safety needs were met (Barasinska et al., 2012). This behaviour could be retrieved in the knapsack experiments, as participants tried to maximize benefit without exceeding the budget.

Mehlawat (2013) dealt with a similar asset problem. He used behavioural construct of suitability to develop a multi-criteria decision making framework for portfolio selection. Suitability performance score and financial quality score of each asset were obtained by questionnaires based upon the investor´s ratings on the criteria. Thus investor preferences for investment alternatives were incorporated to support portfolio decisions. Together with asset quality on financial criteria also using investor-preferences instead of historical data two hybrid optimization models for managing trade-offs between financial and suitability criteria was developed. These models differed in the way the suitability goal was pursued by investors and were successfully tested on randomly selected assets to combine financial optimality and suitability by improving portfolio decisions. Different preferences reflect different decision behaviour and decision heuristics which is also applicable in our case.

As an interesting comparison Hsee and Weber (1999) dealt with cross-national differences in choice-inferred risk preferences between Americans and Chinese in their research. In the first study 209 students of both countries had to answer monetary decision problems in a questionnaire and the findings showed (a) that the Chinese were significantly more risk seeking than the Americans, yet (b) that both nationals predicted exactly the opposite - that the Americans would be more risk seeking. In the second study with 131 students from both countries the questionnaire consisted of three parts with problem scenarios in the areas investment, academic decisions and medicine. For the investment problem participants should make choice between savings or investment in stocks. It was found that Chinese were more risk seeking than Americans only in the investment domain and not in the other domains (Hsee and Weber, 1999). Thus the risk preference was one variable which had systematic cross-national variation. The authors took the cushion hypothesis as the reason for this effect, as Chinese from a collectivist society would more likely to receive financial support from family and relatives in need (Hsee and Weber, 1999). It can be derived from these findings that not only risk preference variation exists in a cross-national context, but also among every one of us, so that risk preference plays a crucial role in the resource allocation and portfolio decision processes.

2.2 Resource Allocation

Kester et al. (2009) made an extensive review on the issues project selection, termination and deletion decisions and took this information as a basis for their exploratory experiment with 19 key informants from 11 multinational firms to investigate their portfolio management decision-making genres. As a result three genres with different management practices were identified: formalist-reactive, intuitive, and integrative (Kester et al., 2009). They could be described as follows (Kester et al., 2009, p. 332):

- Formalist-reactive firms use rigid planning processes and their project selections based primarily on quantitative criteria and financial methods. Their approach toward innovation and their portfolio management practices are predominantly determined by responses to competitor actions and a focus on incremental innovation.
- Intuitive firms use incremental learning processes, emphasizing qualitative criteria and methods. They primarily rely on managerial experience in decision making. Portfolio decisions are predominantly guided by the insights of the senior managers and less by a strategic approach. Their attitude toward innovation depends on the risk profiles of the decision makers.
- Integrative firms use a combination of quantitative and qualitative criteria and multiple methods that combine rigid planning with the flexibility of learning. Their actions in portfolio decision-making are driven by a strategic vision and by a desire to obtain market leadership.

The authors claimed that integrative firms would have the best chances to be successful in the long run, as they combined their strategic goals with resource allocation processes, while still considering quantitative data.

As reasons and arguments also played an important role in the decision making, Shafir et al. (1993) took a closer look at this issue by reviewing and interpreting related decision studies and experiments manipulating the role of reasons in resource allocation settings, with most of the analyzed exploratory experiments carried out by the same authors in prior research. Because reasons had a strong link to uncertainty, conflict, context effects, and normative decision rules, decision makers in a company always relied on it to justify their resource allocation decisions to resolve possible conflicts. In their research the logic of reason-based choices were investigated and analyzed to examine the ways reasons influenced people´s decisions, so that it came out that an analysis of reasons was necessary to explain some aspects of important reflective choices. Nevertheless it could not completely replace value-based models (Shafir et al., 1993).

De Cremer and Van Dijk (2005) experimentally investigated how the role of leader affected behaviour in resource allocation situations. The first laboratory study was conducted with 81 students doing a resource sharing task in groups with different role assignment (leader and follower). Results showed that leaders took more than followers and also deviated more strongly from the equal division rule (De Cremer and Van Dijk, 2005). In the second similar study with 67 students leaders’ feelings of entitlement were manipulated, by legitimating a leader´s role or not. It could be demonstrated that legitimate leaders took more from the resource and deviated more strongly from the equal division rule than non-legitimate leaders (De Cremer and Van Dijk, 2005). Leaders tended to make higher allocations to the self due to their feelings of entitlement. These effects could be also investigated in knapsack decision problems conducted with groups.

After Langholtz et al. (1993, 1994, and 1995) had already investigated two-dimensional resource-allocation problems in their earlier papers, they focused on a three-dimensional complex but commonplace resource-allocation problem in this research, with allocations made on a discrete scale and optimal solutions determined with Integer Programming, compared to prior studies using continuous scale and Linear Programming (Langholtz et al., 1997). 24 participants should allocate 75 $ and 15 h to efficiently obtain as many meals as possible from three food sources over the course of a 7-day week (Langholtz et al., 1997). The authors found out that the added complexity did not influence the overall performance of the selection behaviour and that many findings of their previous research also applied to this complex three-dimensional problem: the subjects achieved solutions which are 85-90% of the optimal ones, they always spent early and reduced their consumptions before the week was out, and they tended to schedule equally among the food choices (Langholtz et al., 1997). The results are partly comparable with the decision strategies participants applied in knapsack experiments of this work.

Ball et al. (1998) intensely investigated the used strategies of people for solving resource-allocation problems, while they made intuitive decisions. They continued with the research of Langholtz et al. (1997) and in the similar experiments 20 participants were again required to make daily meal choices to maximize the number of meals they could obtain in a 7-day week when given a fixed amount of resources (given money and time) and unlike last experimental settings the research methodology verbal protocol analysis was applied this time to allow detailed analysis of the thought processes and used strategies involved in making decisions for this meal-scheduling task (Ball et al., 1998). The authors also extended the task to a 3D-problem to test if increased problem complexity would cause the subjects to adapt their decision strategy to cope with that. Similar findings as the ones from earlier research showed that participants preferred to use a CAC (Consume and Check) strategy that focused first on making daily meal selections with constant checking of remaining resources and an average meal allocation rate of 93,7% of the optimal amount and that the remaining subjects tried to use the SAS (Solve and Schedule) strategy to determine the maximum meals possible in a week before scheduling meals on a daily basis with calculations performed before any daily selections were made and an average meal allocation rate of 95,7% of the optimal amount (Ball et al., 1998). The SAS strategy did a better performance in the 2D case, but only a limited degree of strategy adaption could be identified from the 2D to the 3D problem, while the authors suggested that CAC strategy would be more successful in a more complex task setting (Ball et al., 1998). Altogether the results were consistent with existing findings from other resource-allocation literature of them, namely that people were very good at consuming nearly all their allocated resources.

While the last two papers dealt with resource allocation problems where the goal was to maximize payoff with limited resources, Gonzalez et al. (2002) extended previous research and built an experiment design where the goal was to achieve a fixed objective while minimizing the consumption of resources. 42 students were asked to find the optimum way to schedule flight hours for two different types of aircraft, each with differing personnel and fuel requirements under conditions of certainty, risk, and uncertainty. A computer provided the participants with the instructions for performing the resource-allocation problem, the resource requirements and costs for each aircraft, and the daily constraints. Their experiment findings showed that participants could solve such resource allocation problems surprisingly well, performing best under certainty and worst under uncertainty (Gonzalez et al., 2002).

Armstrong and Brodie (1994) focused on methods supporting portfolio selections in their study. Many managers believed portfolio planning methods such as diverse matrix methods to be an effective technique for strategic decision making in companies, so that these methods are widely applied in the recent 20 years, though it did not find any empirical evidence to support the use. Armstrong and Brodie (1994) identified this problem and wanted to investigate the effect of matrix methods on the decision making process. They conducted laboratory experiments based on one of the matrix methods, the Boston Consulting Group (BCG) matrix and found out that decision makers were misled by the use of this method when they made an investment decision (Armstrong and Brodie, 1994). The BCG matrix measures market attractiveness by market growth rate and it assesses the firm's ability to compete by its relative market share. But the authors showed that its application may lead managers to make decisions that are less irrational than those they make when using unaided judgment to maximize profit, with only 13% of the 1015 subjects who used the BCG matrix in their analysis invested in the obviously more profitable project (Armstrong and Brodie, 1994). Thus it was recommended for the future to make portfolio planning decisions without matrix methods which is also considered for the present portfolio decision task.

Many research about resource allocation compared optimal possible performance with observed performance in these decision situations. Busemeyer et al. (1986) continued the research on the investigation of learning effects with respect to such resource allocation problems, i.e. how subjects learned from outcome feedback and thus tried to improve their decision policies. In their study 64 subjects should work for a company that required three tasks and they had to maximize their salary each year based on the allocated time to each of these three tasks in 50 training trials (Busemeyer et al., 1986). Two of the eight factors (prior knowledge and local objective functions) that influenced the learning process were manipulated in the experiment and a learning principle called hill-climbing was used for interpreting the results. The authors showed in the end that the learning process was efficient when there was no local maximum (Busemeyer et al., 1986). Thus this paper delivered a clue to investigate possible learning effects in the knapsack problem setting.

Many research proposed that sunk costs played a big role for the decision whether to continue investment in an ongoing project, e.g. Garland (1990) found out that the willingness to continue with the investment had a linear relationship with the sunk costs. But sunk costs are often confounded with the degree a project is completed. Conlon and Garland (1993) intended to investigate this issue more closely and conducted two laboratory experiments with varied information about both sunk costs and project completion. Their results showed in the end that degree of project completion may dominate any sunk cost effects that are present in resource allocation decisions (Conlon and Garland, 1993).

Sawyer (1990) dealt with effects of risk and uncertainty on judgments of the function form and on allocation decisions related to the judged function forms, as other research on decision theory with binary choices suggested that these had separate and distinguishable effects on judgments and on the choices made based on those judgments. He conducted laboratory experiments where over 200 subjects should illustrate the form and variance of the cue-criterion relationship in two one-time immediate retention tasks. The tasks were manipulated with two levels of risk and two levels of ambiguity. Te results showed that the tasks were judged as more linear than the actual tasks when learned under uncertain conditions and that decisions to allocate time across the two activities were biased in the direction of the more certain associations (Sawyer, 1990).

To test whether people undertake costly actions to appropriate a potentially divisible resource, Shupp et al. (2013) conducted an experiment to compare individuals’ decisions across three resource allocation contests which are isomorphic under risk-neutrality, named the probabilistic single-prize contest, the probabilistic multiple-prize contest, and the deterministic proportional-prize contest. The lotteries ran in five experimental sessions, with a total of 104 subjects. There was evidence that subjects tended to make lower expenditures in the probabilistic single-prize contest than in the other two contests. While the aggregate results indicated similar behavior in the proportional-prize and multi-prize contests, individual level analysis showed that the behavior in the single-prize contest is more similar to the behavior in the multi-prize contest than in the proportional-prize contest. Furthermore the findings suggested that loss aversion was correlated with behavior in the single-prize and multi-prize contests where losses were likely to occur, but not in the proportional-prize contest where losses were unlikely.

2.3 Decision Analysis

For a better understanding of the general decision analysis process, several papers are reviewed in the following to illustrate important aspects which should be also considered for the portfolio decision analysis of the present study.

Samuelson and Zeckhauser (1988) investigated status quo effects in the decision-making processes. They reviewed a series of decision-making experiments designed to test these effects and found out that subjects were strongly affected by such status quo framing, as the stronger was an individual’s preference for a selected alternative, the weaker was the bias and the bias increased relatively with the number of choice alternatives (Samuelson and Zeckhauser, 1988). The authors thought that the status quo served as a psychological anchor for the subjects, i.e. the stronger the individual’s previous commitment to the status quo, the stronger the anchoring effect. They could experimentally confirm all their considerations using questionnaires with different decision questions and a given set of choice alternatives which were answered by altogether 486 students (Samuelson and Zeckhauser, 1988). The founded effects could be well applied for some economic phenomena like the difficulty of changing public policies and preferred types of marketing techniques (Samuelson and Zeckhauser, 1988). Besides the results also delivered a reason for the behaviour why most of the participants always used the same heuristic for the knapsack task as in their previous experiments.

A basic principle of rational choice claimed that an individual´s preferences towards (and decisions about) objects should only depend on the features or attributes of those objects, and not on extraneous, irrelevant factors. Delquié (1993) investigated violations of this principle, the so-called preference reversals, in particular which role the response mode played in certain types of preference reversals. He generalized the experiment design of Hershey and Schoemaker (1985) to control for framing effects and study biases on a larger scope. The results showed that biases did not disappear in the absence of framing, instead they revealed a clear and pervasive bias occurring under more controlled experimental conditions than previously known: direct trade-offs between two attributes X and Y were biased depending on whether X is traded off against Y, or Y traded off against X (Delquié, 1993). This provided strong support for scale compatibility in riskless and risky decision making.

As value trade-offs adequately express a decision maker´s values, they are essential both for good decision making processes and for insightful analyses of multiple-objective decisions. In his work Keeney (2002) assessed 12 common mistakes that individuals typically make in expressing and representing value trade-offs. This information was then applied for determining a useful set of value trade-offs. Keeney (2002) developed four steps from practical experience with applications requiring value trade-offs which should help people to identify the least desirable alternatives and avoid any logical mistakes.

Jacobi and Hobbs (2007) developed a model for estimating and correcting attribute-weighting biases in decision processes that result from the use of value trees when structuring value function weight elicitation. This model was based on the suggestion that people always employed an anchor-and-adjust heuristic. In their case study 11 managers (planners or midlevel executives) from Centerior Energy of Ohio were introduced to multicriteria decision-making methods for quantifying environmental externalities and other objectives in long-run electricity generation and conservation planning (Jacobi and Hobbs, 2007). Then they applied the knowledge in a brainstorming session and identified 15 planning alternatives wherefrom attribute weights were elicited. The data were then used to illustrate the existence and correction of the value tree-induced attribute-weighting biases with the use of their proposed model (Jacobi and Hobbs, 2007). The results confirmed the hypothesis that a bias existed that was consistent with anchor-and-adjust heuristic.

To enable a comparison between the two visualization methods heatmaps and parallel coordinates for interactive portfolio selection Kiesling et al. (2011) conducted experiments with 96 business administration students. The participants should solve a familiar portfolio selection problem, namely selecting courses for the forthcoming semester. Thereby the two visualization methods differently manipulated the information presented for the students, so that these two approaches could be compared by means of subjective measures such as user satisfaction or understanding of the problem, as well as by objective measures referring to effort, convergence, and the process structure (Kiesling et al., 2011). The results of the decision analysis showed a better objective performance of subjects who used the parallel coordinates visualization and that the choice of visualization method also had a considerable impact on the users’ subjective experiences when using a decision support system for portfolio selection (Kiesling et al., 2011). Furthermore the authors indicated that decision-making styles played an important role in users’ attitude toward the visualization method.

An overview on the literature treated in the three areas above is given in the Table 1.

Table 1: Treated literatures in overview

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3 Theory of the Experimental Framework

3.1 Knapsack Optimization Problem

As this master thesis deals with human behaviour within portfolio decision and resource allocation problems, the results are based on laboratory experiments concerning a zero-one knapsack problem. In the following a short overview is given on the basic model of knapsack problems.

The name comes from the imagination of a hitch-hiker filling up his knapsack by selecting from a set of possible objects the ones which will maximize his comfort, e.g. food, a sleeping bag etc. This situation is known as a single 0-1 Knapsack Problem (KP) which is one of the most important and most studied discrete programming problems and can be mathematically formulated as:

Abbildung in dieser Leseprobe nicht enthalten (1)

With the objects numbered from 1 to n, each having a weight Abbildung in dieser Leseprobe nicht enthalten (cost) and a value Abbildung in dieser Leseprobe nicht enthalten (benefit). The task is then to select objects Abbildung in dieser Leseprobe nicht enthaltenAbbildung in dieser Leseprobe nicht enthalten Abbildung in dieser Leseprobe nicht enthalten {Abbildung in dieser Leseprobe nicht enthalten}, in order to maximize the sum of the weights, with respect to a capacity constraint c. It is also a binary decision case with Abbildung in dieser Leseprobe nicht enthalten if Abbildung in dieser Leseprobe nicht enthalten is selected and Abbildung in dieser Leseprobe nicht enthalten if otherwise. Besides it should be arranged that an already selected object is not allowed to be selected again and that the sum of all given weights has to be greater or equal the capacity c. The amount of all selected items in a final solution is called a portfolio, thus this work investigates portfolio decision analysis. The 0-1 KP is an interesting study topic because 1) it can be viewed as the simplest Integer Linear Programming problem; 2) it appears as a subproblem in many more complex problems; 3) it may represent a great many practical situations, as Martello and Toth (1990) claimed by intensely investigating different knapsack problems in their book. But it is still difficult to solve such knapsack problems optimally due to the amount of time required for computing. Therefore researchers began to focus on heuristic solutions as approximation, so that intuitive decision behaviour also became an important aspect within portfolio management to better understand the decision making processes. The analysis method of the present work is based on such human decision heuristics which will be described in detail in the following chapters.

3.2 Laboratory Experiment

Katok (2011) introduced laboratory experiments and emphasized its importance for testing analytical models in operations management, as these bridged the gap between analytical models and real business problems. Especially the factors theoretical guidance, induced valuation and careful control of institutional structure made the application of laboratory studies rigorous. The author also claimed that there were three main purposes that laboratory experiments served (1) to test and refine existing theory (2) to characterize new phenomena leading to new theory and (3) to test new institutional designs (Katok, 2011). Subject recruitment methods and the experiment conduction method z-Tree as a useful computer interface were examined closely and a literature overview was given on the issue individual decision and strategic games. A visualization possibility of a knapsack experiment is shown in Figure 2. In the end Katok (2011) discussed several methodological topics related to good practices in designing and conducting good laboratory experiments, e.g. effective experimental design (focus and nuisance variables, treatment, full factorial design, a within-subjects design, dual trial design), the context (abstract frame), the subject pool (mostly students), setting incentives (induced value theory) - financial incentives always, and deception (indirect or direct; better without deception). Finally suggestions were made about future trends in the field laboratory experiments, considering how experimental work would look like.

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Figure 2 : Experiment visualization made with z-Tree

All of these aspects helped to build an appropriate experiment design and in this work the experiments are also conducted with the computer program z-Tree and the participants should to verbalize all of their thoughts concerning the experiment task. Thus a short introduction is given about the verbalization method in the following.

3.3 Verbal Protocol Analysis

The verbal protocol analysis is a think aloud method that requires participants to verbalize or rather talk aloud his/her thoughts while solving a problem or performing a task and also state aloud the line of reasoning they are using to go from the observations to their decision. The goal of think-aloud research is to give the researcher detailed insight into the processes of working memory, as the theory of Ericsson and Simon (1980) regarding verbal protocols was based on the distinction between working memory, in which concurrent reasoning takes place in verbal form, and long-term memory, where some of the ideas from working memory could eventually be stored, not necessarily in words. To understand how these verbal protocols could be obtained, Figure 3 shows a simple model of the human cognitive system which is responsible for the thinking processes and verbalizations:

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