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

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  Expected Utility 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

5 Optimal Portfolio Mixes with Cash  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.  Asset Allocation % Equities Bonds Cash 5 Year Investment Horizon

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 Utility Parameter (  ) Expected Utility Mean = 106 Mean = 105 Mean = 104 Mean = 103 Mean = 102

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

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

16 Experiment Procedures  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

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