question 5&6

5. (4 points) Two accounts, X and Y, are each exposed to a risk that has five possible outcomes. The five outcomes, the probability of each, and the loss to each account are provided in the following table. Outcome Probability Loss to X Loss to Y P 0.80 0 0 0.07 200 100 R 0.02 400 200 S 0.09 500 1,500 T 0.02 1.000 700 The =-score corresponding to the acceptable probability that the actual result will require even more surplus than allocated is 1.5. The required return on marginal surplus is 10%. You are considering adding Account Y to the existing Account X. (a) (1.5 points) Calculate each of the following using the Marginal Surplus method: (i) The risk load multiplier (ii) The risk load charged to Account Y (b) (1.5 points) Calculate each of the following using the Marginal Variance method: (i) The risk load multiplier that produces the same risk load for the combined portfolio as that obtained using the Marginal Surplus method (ii) The risk load charged to Account Y (c) (/ point) Demonstrate that the Marginal Variance method is not renewal additive.6. (5 points) You are calculating a risk margin for premium liabilities as discussed in "A Framework for Assessing Risk Margins." The following information is provided: Premium Liabilities Score Potential Risk Indicators Motor Home Confidence in assessment of model goodness of fit 3 4 2. Ability to detect trends in key claim cost indicators 2 4 3. Extent, timeliness, consistency, and reliability of information 2 4. Extent of monitoring and review of model and assumption performance 4 5. Processes for obtaining and processing data are robust and replicable 6. Best predictors have been identified 6 Score from Balanced Scorecard Motor CoV Home CoV 2.0 to 3.0 15.0% 16.0% 3.0 to 4.0 10.0% 11.0% 4.0 to 5.0 8.5% 9.0% 5.0 to 6.0 5.0% 5.5% Proportion of Insurance Liabilities Outstanding Claim Premium Line of Business Liabilities Liabilities Motor 20% 10% Home 30% 10% Total 50% 50% The correlation between motor and home premium liabilities is 50%. Risk indicator weights are equal within each source of internal systemic risk. . Risk indicator weights for each source of internal systemic risk are: 30% for specification error; 50% for parameter selection error; and o 20% for data error. (a) (1.5 points) Define each of the following sources of internal systemic risk: Specification error Parameter selection error(b) (2.5 points) Calculate the internal systemic risk coefficient of variation for premium liabilities for both lines combined. A reasonable a priori assumption is that similar balanced scorecard scales can be used for both outstanding claim and premium liabilities. (c) (/ point) Provide a situation where this a priori assumption may not hold