Optimizing the Cash Reserve in a Portfolio of US Life Insurance Policies

Abstract: Hoarding a too large cash reserve is often unfavourable due to lost investment opportunities. Similarly, an insufficient cash reserve can be detrimental, as one might fail to meet payment obligations. Finding the optimal balance is nothing that is done in the blink of an eye, particularly when the underlying variable is stochastic, e.g., the life span of a human being. Resscapital is a fund manager investing in the secondary and tertiary markets for life insurance policies, also known as the life settlements market. They are currently on a mission to set up a closed-end fund where one of the main challenges is balancing the invested capital and the amount of capital set aside for payment obligations. The stochastic nature of life insurance policies entails the difficulty to foresee future premium payments and face value payouts. Without a model forecasting the cash flows, decisions regarding the cash reserve are based on nothing better than a guesstimate. Thus, with the aim to help determine the minimum cash reserve required to cover the payment obligations, this thesis was initiated. By developing a methodology based on general theory, the objective of this thesis is reached and the purpose fulfilled. The proposed model uses Monte Carlo simulation to generate scenarios that eventually creates a distribution of required cash reserves. Following the inversion principle, the remaining lifetime for each and every individual is simulated from their empirical distribution of survival probabilities, respectively. After simulating the occurrences of demise, an algorithm builds up the cash flows for the entire fund term for that specific scenario based on predetermined parameters. Since cash flows stem from both assets and management, the portfolio must be revalued continuously, demanding a gradual evaluation of the cash flows during the fund term. Repeated a large number of times, the quantile corresponding to any confidence level is attained by using a Value at Risk methodology. Analysis of the results and sensitivity analysis on the parameters provides a deeper understanding of the underlying factors, revealing, among other things, that longevity risk for policies with short life expectancy is a key driver of the required cash reserve. Furthermore, validation of the model shows that the results are sufficient and serve the purpose well.