【正文】
Many households have large financial positions that are exposed to interest ate risk. To finance the purchase of a house, households typically take out a mortgage loan, with monthly payments either fixed in nominal terms or tied to the shortterm interest rate. In addition, many households hold bonds, both directly and indirectly in a pension account. This article addresses the question of how to optimally invest in financial assets, including the mortgage and bond portfolio choice. To this end I study a dynamic lifecycle model where investors optimize over the housing and portfolio choice. I bine the main model features of two recent strands in the portfolio choice literature. First, I follow Cocco (2020) and Yao and Zhang (2020a,b) by explicitly modeling the housing decision and incorporating a stochastic labor ine stream Households derive utility from both housing and other goods consumption. They acquire housing services by either renting or owning the house they live in. Investors can change their housing tenure and size only at a transaction cost, resulting in infrequent, endogenously generated house moves. Both the house and human capital have a major impact on the investor’s willingness and ability to take risk in his or her financial portfolio. Cocco (2020) and Yao and Zhang (2020a,b) assume constant interest rates, do not consider bonds and do not allow for a choice between different mortgage types. Consequently these papers do not address a household’s interest rate risk management. Second, this article follows Campbell and Viceira (2020) and Brennan and Xia (2020) by incorporating bonds in the financial portfolio. Nominal bonds are priced by a twofactor model for the term structure of interest rates with expected inflation and real interest rate as factors. Unlike Campbell and Viceira (2020) and Brennan and Xia (2020), I model labor ine, housing and mortgages, and I am therefore able to study the lifecycle pattern in households’ interest rate risk management and the optimal mortgage choice. Renters choose how to allocate financial wealth to stocks, 3year bonds, 10year bonds and cash. Negative positions are precluded. Homeowners also choose the mortgage type and size. A homeowner may take out a mortgage loan up to the market value of the house minus a down payme nt. I allow for an adjust able rate mortgage (ARM), a fixedrate mortgage (FRM) and a bination of the two (hybrid mortgage). A homeowner can adjust his or her mortgage type and size at zero cost. The ARM is modeled as a negative cash position. The FRM is modeled as a negative position in the 10year bond. While this is a simplification from actual FRMs offered in the United States, it captures the essence that the present value of the FRM payments is subject to interest rate risk. To keep the model tractable, I abstract from a prepayment option and declining maturity for FRMs. The parameter values for the asset price dynamics are calibrated to . data and partially based on estimates by De Jong, Driessen and Van Hemert (2020). In accordance with Brennan and Xia (2020) and Campbell and Viceira (2020), the mean reversion in the real interest rate is found to be faster than the mean reversion in the expected inflation rate. I show that this implies that a portfolio consisting of a positive position in a shortterm bond and a negative position in a longterm bond can be constructed with the property that it has a negative exposure to real interest rate shocks and a zero exposure to expected inflation rate shocks. The most novel insights e from the optimal portfolio choice over the life cycle. I