Practical problems with the data analysis

During the course of the research several practical problems arose, particularly in applying Prospect Theory. The problems will be fully discussed in this Section 5.4:

5.5.1 Prospect Theory

This research mainly concentrated on the original Prospect Theory developed by Kahneman and Tversky (1979), and not the subsequent Cumulative Prospect Theory developed later (Kahneman and Tversky 1992). While the concept of Cumulative Prospect theory was utilised insofar that there are distinct probability weighting functions depending on whether the outcome is positive or negative, cumulative probabilities were not derived due to paucity data. There were insufficient data points to arrive at meaningful results. This is unlikely to have had any significant impact on the results or conclusions, which are in any event very broad and intended to be indicative.

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Kahneman and Tversky used uniform bets to develop their theories, that is to say that each cohort of respondents was given the same set of questions using the same monetary values.

In this research the size of company varies. It was thus necessary to scale the monetary values in an attempt to arrive at consistent comparable responses across all 3 companies.

The numbers used in the Risk Aversion Questionnaire were chosen to reflect high value, medium value and low value projects relative to the size of each company. Fortunately in the case of QD and BINS the size of companies was similar. However in the case of VGOLD, a Gold Mining Company, the company was around 8 times larger. Conveniently, their revenue is dollar based and the Rand/Dollar exchange rate was 8 to one. Thus the questions were presented to the VGOLD Board in Dollar terms. This meant that a single set of numerical questionnaires could be applied to all three companies.

5.5.3 Negative probabilities and profit margin

When asked to attach a cash value to a set of prospects, often the respondent would provide an answer which gave rise to a negative probability. For example in the first question A of the Risk Bias Questionnaire respondents were asked to attach a value to a project with payoffs of 10m and 3m with probabilities of 20% and 80% respectively. The minimum payoff in this example is 3m, and maximum payoff is 10m. The statistical expected value is 4.4m. Some respondents gave answers well below 3m. The theoretical probability which provides a payoff of any result below 3m is negative, which is clearly undefined. In these cases the minimum value which did not give rise to a negative probability was chosen. Part of the reason for this choice by respondents was due to the “risk” profit margin built into the respondents’ answers. The subjective inconsistency built into such profit margins by respondents within and across companies is a flaw in the Kahneman and Tversky (1979, 1992) methodology as applied to this research.

5.5.4 Mean vs. median

Kahneman and Tversky (1992) used the median results from the responses derived from their student populations. In this study the median was also used. A test was done to check that there was no significant difference in results from using the mean. It must however be pointed out that the mean of a set of results from a Board may be more subject to bias than a set of median results from a group of students whose decisions are completely

independent. In a Board some members are likely to be far more influential than others, and

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the CEO may have the casting vote. The degree of bias may change with different project types or issues where the knowledge or conviction of Board members vary. This bias is also highly likely to vary across Boards. Thus neither the median nor the arithmetic mean may reflect the decision making outcome of the group.

5.5.5 Mixed prospects

For mixed prospects, that is where the questions in the Risk Bias Questionnaire have a positive and a negative payoff, a decision needs to be taken as to whether the prospect is indeed positive or negative. In this study it was assumed that the sign of the expected value of the prospect determined whether it was positive or negative.

5.6 Summary

In this Chapter 5 the results of the Risk Readiness, Risk Aversion and Risk Bias Questionnaires were presented. The results can be summarised as follows:

 The 3 companies exhibited varying degrees of Risk Readiness, with BINS being most Risk Ready, and QD being least Risk Ready.

 Companies exhibited varying degrees of Risk Aversion facing gains with all 3 companies varying between neutrality and slight risk aversion. Facing losses, the results were more clear cut, with BINS and QD being risk neutral, and QD exhibiting risk tolerant tendencies.

 The Risk Bias Questionnaire showed that for all 3 companies there was a linear relationship between gains and perceived value suggesting that Boards did not face diminishing sensitivity in the face of losses and gains to the extent predicted by Prospect Theory (Kahneman and Tversky, 1992).

 There did not appear to be evidence of loss aversion, whereby Boards would value gains and losses differently.

This concludes the summary of the results of the Risk Readiness, Risk Aversion and Risk Bias Questionnaires. In Chapter 6 below the results of the RepGrid analysis will be discussed. Chapter 7 deals with further theory development. In Chapter 8 the main results will be summarised.

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Main Findings and the Repertory Grid Analysis