An application : A Client Financial Risk Tolerance Model

1. An application: A ClientFinancial Risk Tolerance Model

2. A ClientFinancial Risk Tolerance Model Financial service institutions face a difficult task in evaluating clientsrisk tolerance. It is a major component for the design of an investmentpolicy and understanding the implication of possible investment optionsin terms of safety and suitability.Here we present a simple model of client's risk tolerance abilitywhichdepends on his/hers annual income (AI) and total networth(TNW).The control objective of the client financial risk tolerancepolicymodel is for any given pair of input variables (annual income, totalnetworth) to and a corresponding output, a risk tolerance (RT) level.

3. A ClientFinancial Risk Tolerance Model Suppose the financial experts agree to describe the input variablesannual income and total networth and theoutput variable risk tolerance by the sets,

4. A ClientFinancial Risk Tolerance Model The terms of the linguistic variables annual income, total networth,and risk tolerance described by triangular and part of trapezoidal numbers formally have the same membership functions presented analytically below,

5. A ClientFinancial Risk Tolerance Model Terms of the input annual income Terms of the input total networth Terms of the output risk tolerance

6. A ClientFinancial Risk Tolerance Model If : : : and : : : then Rules Assume that the financial expertsselected the rulespresented on the decision table

7. A ClientFinancial Risk Tolerance Model If : : : and : : : then Rules Rule 1: If client's annual income (CAI) is low (L) and client's totalnetworth (CTN) is low (L), then client's risk tolerance (CRT) is low (L); Rule 2: If CAI is L and CTN is medium (M), then CRT is L; Rule 3: If CAI is L and CTN is high (H), then CRT is moderate (MO); Rule 4: If CAI is M and CTN is L, then CRT is L; Rule 5: If CAI is M and CTN is M, then CRT is MO; Rule 6: If CAI is M and CTN is H, then CRT is H; Rule 7: If CAI is H and CTN is L, then CRT is MO; Rule 8: If CAI is H and CTN is M, then CRT is H; Rule 9: If CAI is H and CTN is H, then CRT is H.

8. A ClientFinancial Risk Tolerance Model Fuzzification assuming readings: x0 = 40 in thousands (annual income) and y0 = 25 in ten of thousands (totalnetworth). They are matched against the appropriate terms. The fuzzy inputs are calculated. Note that x = 40 and y = 25 are substituted for v insteadof 40,000 and 250,000 since x and y are measured in thousands and tenof thousands. The result is

9. A ClientFinancial Risk Tolerance Model Fuzzificaiton Fuzzy reading inputs for the clients financial risk tolerancemodel. Readings: x0 = 40 and y0 = 25

10. A ClientFinancial Risk Tolerance Model Fuzzy Operations Induced decision table for the clients financial risk tolerance model. There are four active rules, 1,2,4,5 Rule 1: If client's annual income (CAI) is low (L) and client's totalnetworth (CTN) is low (L), then client's risk tolerance (CRT) is low (L); Rule 2: If CAI is L and CTN is medium (M), then CRT is L; Rule 4: If CAI is M and CTN is L, then CRT is L; Rule 5: If CAI is M and CTN is M, then CRT is MO;

11. A ClientFinancial Risk Tolerance Model Multiple conjuctive antecedents The strength of these rules or level of firing (the and part) is calculated as follows

12. A ClientFinancial Risk Tolerance Model Firing of rules for the client nancial risk tolerance model

13. A ClientFinancial Risk Tolerance Model Aggregation of Fuzzy Rules Geometrically this means that we have to superimposetrapezoids on top of one another in the same coordinate system. Aggregated output for the client financial risk tolerance model

14. A ClientFinancial Risk Tolerance Model Defuzzificaton The aggregated output for the client financial risktolerance model can be defuzzified by the defuzzification methods.