Duration, convexity and the optimal management of bond portfolios for insurance companies

Two Fong-Vasicek immunization results are discussed and applied in relation to asset portfolios of a sample of Italian insurance companies managing life insurance with-profit savings. Firstly, we analyzed the contribution of Fong and Vasicek (1984) providing a lower bound on the “shortfall” of an asset portfolio, managed with a duration-matching target, in the face of an arbitrary shock to the term structure of interest rates. A “passive” management strategy emerges, aimed at minimizing risk, such that the exposure to an arbitrary variation of the shape of the term structure is minimized with respect to a risk measure that is increasing with the cash-flows dispersion. Secondly, Fong and Vasicek (1983) approach is generalized, in line with the classical risk-return approach to portfolio management, in a model which overturns the “passive” perspective of minimum risk exposure and looks for only a partial risk minimization in exchange for more return potential. The empirical application shows that such a perspective may be proved useful to highlight which segregated funds can be re-positioned over the efficient frontier, at the chosen level of the firm’s risk appetite.