Asset Allocation in the light of Liability Cash Flows

Asset allocation is one of the most important investment decisions that financial institutions have to make. Modern portfolio theory suggests that an optimal asset portfolio is one which maximises the return of the portfolio at a certain level of risk which is defined as the variance of the portfolio. In the light of liability cash flows, modern portfolio theory can be extended by regarding a liability as a negative asset. However, non-normal features of both asset return and liability features are always witnessed in reality and the appropriateness of defining risk as the variance of the ultimate surplus that assets have over liability is always questionable. In this paper, instead of defining risk as the variance of portfolio, the authors define risk as the probability of insolvency and derive the optimal asset portfolios thereafter. Both assets and liabilities are assumed to follow certain stochastic process. Four different stochastic investment models are examined and compared. Asset portfolios based on different approaches are also contrasted.