LINKING PSYCHOMETRIC RISK TOLERANCE WITH CHOICE BEHAVIOUR

1. LINKING PSYCHOMETRIC RISK TOLERANCE WITH CHOICE BEHAVIOUR Peter Brooks, Greg B. Davies and Daniel P. Egan FUR Conference – July 2008

2. Presentation Aims • To introduce the Barclays Wealth Risk Tolerance Scale • To introduce the effects of an exponential utility function on asset allocation • To describe an experiment that provides a link between risk tolerance scores and risk parameters. • Are different risk profiles characterised by different risk/utility parameters in choices?

3. Pre-experiment Analysis Overview • Examine risk and utility measures using simulated portfolios involving equities and bonds • Mix the simulated portfolios with different proportions of cash • Holding cash is assumed to be a riskless alternative • Calculate the optimal portfolio for different values of the risk parameter

4. Example Utility Measure 5 Year Bond/Equity Mixes Low values of  imply risk tolerant behaviour – Optimal portfolio is 100% equities Higher values of  imply risk averse behaviour – Optimal portfolio is now a mix of equities and bonds Expected Utility 

5. Optimal Portfolio Mixes with Cash 5 Year Investment Horizon • We have modelled a range of values of the risk parameter for 5 year returns • For low  – optimal portfolio is 100% Equities • For  between 0.08 and 0.16, the optimal portfolio is a mix of equities and bonds • For  greater than 0.17, the optimal asset allocation includes cash. Cash Asset Allocation % Bonds Equities 

6. Pre-experiment Analysis Overview 2 • The analysis suggests that the optimal portfolio is sensitive to the value of a risk parameter. • Assuming utility maximisation individual choices between portfolios make it possible to calibrate a risk parameter. • Choices constrain a risk parameter to a range of values where the portfolio would be preferred by a utility maximising individual. • Analysing a number of choices makes it possible to find a “best” value of the risk parameter for each individual.

7. Barclays Wealth Risk Tolerance Scale • 8 question psychometric questionnaire • Responses given on a 5-point Likert scale • Produces a score between 8 and 40 • Higher scores signal higher risk tolerance • Scores bucketed into 5 risk profiles from low up to high.

8. Experiment Aims • To test various risk measures and utility functions using actual choices • To estimate risk/utility parameters for individual respondents. • To provide a link between the risk tolerance scores and risk parameters. • Are different risk profiles characterised by different risk/utility parameters in choices?

9. Experimental Design • Create stylised distributions of the final values of an investment. • It is difficult to use distributions based upon real data. Increases in volatility cause the tails of the distribution to become long. • Long tailed distributions are difficult to display accurately to survey respondents. • Take log-normal distribution and set the mean and standard deviation. • Generate 120 equally spaced observations across the distribution. • Round each of these observations to the nearest integer. • Plot the frequency table of the observations to create the distributions for the experiment.

10. Experimental Design • Expected utility is increasing in the mean of the distribution. • Expected utility is decreasing in the “risk” of the distribution. • Create a preference order between two distributions by compensating for an increase in “risk” by increasing the mean. • The most risk averse will prefer lower mean and lower “risk” distributions. • The least risk averse will prefer higher mean and higher “risk” distributions.

11. Example Distribution • Mean = £103,000

12. Example Distribution 2 • Mean = £105,000

13. Distribution Comparisons – Example Using Exponential Risk Measures Mean = 103 Mean = 102 Mean = 104 Expected Utility Mean = 105 Mean = 106 Utility Parameter ()

14. Distribution Comparisons – Example Using Exponential Risk Measures Mean = 104 Expected Utility Mean = 103 Mean = 102 Mean = 105 Mean = 106 Utility Parameter ()

15. Distribution Comparisons – Example Using Exponential Risk Measures Mean = 103 Mean = 102 Expected Utility Mean = 104 Mean = 105 Mean = 106 Utility Parameter ()

16. Participants recruited through iPoints Participants paid in iPoints All participants reported either gross annual income above £50k or investable wealth above £100k Delivered through a non-branded external website Respondents had participated in previous surveys but had not participated within the past 6 months Over-sampling of the extreme risk profiles 6 section experiment Demographics Psychometric Risk Tolerance Training stage 9 Pairwise choice tasks between distributions Filler Task – maze 9 Pairwise choice tasks between distributions Experiment Procedures

17. Experimental Results • 108 Participants completed all parts of the survey • 1 participant removed for inconsistent responses • Over-sampling of the end points successful • Individuals in higher risk profiles tend to choose higher variance distributions more often • Use MLE to estimate the utility risk parameter for individuals - grouped by risk tolerance score

18. MLE Fit Results

19. Conclusions and Extensions • Our psychometric risk tolerance measure is consistent with risky choice • There is potential for a behavioural calibration of a risk measure for portfolio optimisation • Separate work on whether utility measures are better than variance, VaR or CVaR as risk measures for portfolio optimisation • Geographical calibration exercise – current ongoing work