Abstract
We develop an analytical solution to the dynamic multi-period portfolio choice problem of an investor with risky liabilities and time varying investment opportunities. We use the model to compare the asset allocation of investors who take liabilities into account, assuming time varying returns and a multi-period setting with the asset allocation of myopic ALM investors. In the absence of regulatory constraints on asset allocation weights, there are significant gains to investors who have access to a dynamic asset allocation model with liabilities. The gains are smaller under the typical funding ratio constraints faced by pension funds.
Highlights
It is known since the work of Samuelson (1969) and Merton (1969; 1971; 1973) that long– term investors might judge risks very differently from short–term investors and hold different portfolios
In this paper we develop an analytical solution to the dynamic multi–period portfolio choice problem of an investor under time–varying investment opportunities
Optimal portfolios can be obtained as exact analytical solutions for special cases of the multi–period portfolio choice problem in a continuous time setting (Kim and Omberg, 1996; Sorensen, 1999; Wachter, 2002; Brennan and Xia, 2002; Chacko and Viceira, 2005; Liu, 2007)
Summary
It is known since the work of Samuelson (1969) and Merton (1969; 1971; 1973) that long– term investors might judge risks very differently from short–term investors and hold different portfolios. Stochastic programming techniques for example face the cost of tractability; the traditional numerical methods cannot handle more than a few state variables, magnifying the effects of estimation risk even further; and the ALM models carried out under a continuous time context have been mostly studied under a constant investment opportunity set. Another strand of the ALM literature, closer in spirit to our paper, uses approximate analytical solutions and extends the asset–only models introduced by Campbell and Viceira (1999; 2001; 2002) and Campbell et al (2003) by incorporating liabilities. We provide a detailed derivation of all the analytical results in the paper
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