Abstract
This paper studies the optimal mortgage choice of an investor in a simple bond market with a stochastic interest rate and access to term life insurance. The study is based on advances in stochastic control theory, which provides analytical solutions to portfolio problems with a stochastic interest rate. We derive the optimal portfolio of a mortgagor in a simple framework and formulate stylized versions of mortgage products offered in the market today. This allows us to analyze the optimal investment strategy in terms of optimal mortgage choice. We conclude that certain extreme investors optimally choose either a traditional fixed rate mortgage or an adjustable rate mortgage, while investors with moderate risk aversion and income prefer a mix of the two. By matching specific investor characteristics to existing mortgage products, our study provides a better understanding of the complex and yet restricted mortgage choice faced by many household investors. In addition, the simple analytical framework enables a detailed analysis of how changes to market, income and preference parameters affect the optimal mortgage choice.
Highlights
This paper studies optimal investment and consumption in relation to mortgage choice as viewed from the perspective of a household investor
It has been demonstrated that in the case where labor income is assumed to behave like an annuity bond, i.e., dY(t) = 0, the optimal mortgage is entirely funded by an Fixed Rate Mortgage (FRM) if the investor at the same time is infinitely risk averse and without mortality risk
This study has provided a closed-form solution to a simple optimal mortgage choice problem
Summary
This paper studies optimal investment and consumption in relation to mortgage choice as viewed from the perspective of a household investor. The strand of mortgage choice literature (see [5] and the references therein) often studies particular mortgage products, seeks to capture more realistic (incomplete) market settings, includes complex borrowing constraints and discrete actions, such as prepayment and default, and requires numerical solutions The downfall of these studies is that they can only evaluate the performance and optimality of the products in the specific market setting and preferences chosen for the study, but do not immediately provide insight to the mixed effects of market and preference parameters and their influence on the optimal portfolio mix and repayments over time. Our setup provides a simple benchmark where significant relations regarding optimal mortgage choice are captured, providing an initial intuition behind the choice of FRMs
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