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Dynamic Asset Allocation with Stochastic Income and Interest Rates

The household participation in financial markets creates a demand and a need for competent investment advice. The optimal investment strategy for a given individual will depend both on market characteristics, such as the dynamics of asset prices and interest rates, and on personal characteristics, such as risk aversion, time preference, and labor income. In this paper we will study the optimal strategies when both interest rates and the labor income rate of the individual are stochastic.

Stochastic interest rates is the main source of shifts in the investment opportunity set, and the effect of interest rate uncertainty on the optimal strategies of an investor without labor income is by now relatively well-studied in the literature. There are also a number of studies of the effects of labor income uncertainty on the optimal strategies, but they all assume constant investment opportunities. (References are given below.) We argue and demonstrate in this paper that allowing jointly for stochastic interest rates and labor income will affect the optimal investment strategy beyond the separate effects of stochastic income and stochastic interest rates.

Why is it important to combine stochastic interest rates and labor income? Intuitively, a main determinant of the optimal strategy is the human wealth of the individual, i.e. the present value of the future labor income. This present value involves the discounting of a stream of uncertain income rates.

An increase in interest rates can imply a substantial decrease in human wealth and a long-term, non-myopic investor will want to hedge against this misfortune. In addition, the expected income rate in the near future is likely to depend on the interest rate level, which serves as a good proxy of the overall well-being of the economy. High interest rates typically reflect high growth rates of the economy which may lead to an upward pressure on wages.

Dynamic Asset Allocation with Stochastic Income and Interest Rates