Measuring Risk-Adjusted Performance and Product Attractiveness of a Life Annuity Portfolio

Abstract

The paper proposes a new methodological approach for the product performance analysis into the actuarial context. Two indexes are proposed as restyled versions of the corresponding most popular ones: They have been adapted into the actuarial assessment preserving the plainness in the interpretation of the numerical results. The paper offers a practical implementation of the new approach in the case of a specific contract, containing itself innovative profiles: It concerns a life annuity in which the installments are scaled by a demographic index and contains an embedded option linked to the financial profit participating quota. It is a new life product linked at the same time to the financial and demographic volatility. The product project is studied in its profitability performance assuming stochastic hypotheses for the financial and demographic systematic risks. The indexes are implemented in a conditional quantile simulated framework and tables and graphs illustrate their trends as function of time. The results give an example of the usefulness of the proposed indexes in the phase of decisions about the product design feasibility. Moreover some suggestions concerning the consumer’s perception of the contract profitability are obtained by means of a utility-equivalent fixed annuity.