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This paper studies how long-run cointegration between house prices, rents and labor income affects lifecycle portfolio choice. Labor income is central to lifecycle models, and previous studies suggest that income, house prices and rents are cointegrated. In this model, cointegration implies that residential real estate investment can hedge future regional income changes in addition to rents. Regional income is closely linked to the cost of labor intensive services such as elderly care, health care or education, which together with housing, account for a substantial share of household expenditures. Residential real estate may therefore be attractive to hedge both future rents and the labor cost of these other consumption expenses.

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This paper explicitly solves a flexible class of quadratic dynamic portfolio and consumption choice problems with a common state vector process embedded across investment asset prices, labor income and product consumption prices. The solution to the lifecycle problem, asset prices and welfare changes under alternative investment policies are characterized by a class of semilinear Partial Differential Equations (PDEs). The main methodological contribution is a separation result for semilinear PDEs that accommodates specified interactions between across state variables. If coefficients are quadratic functions of the state, the framework reduces the PDE to coupled Riccati equations and provides explicit solutions under additional restrictions. Explicit solutions cover models featuring cointegration, interactions across state variables, stochastic market price of risk and stochastic volatility. Many portfolio investment problems in the literature are included as special cases and I outline new applications to multivariate cointegration models. The paper also analyzes conditions leading to a translation invariant distribution of lifecycle variables, such as the investment fraction, the wealth-to-income and the consumption-to-income ratios, establishing a basis to compare them across cohorts.

with Anne Balter and Nikolaus Schweizer
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This paper explores the potential of leveraged Exchange Traded Funds (LETFs) for long-term investors and lifecycle portfolios. Leverage can increase welfare by enabling strategies that match the risk appetite of risk-tolerant investors, or by increasing financial wealth exposure to compensate for the illiquidity of human capital. We find LETFs to be suitable for both purposes with a caveat: risks associated to LETFs make it worthwhile typically only if the investor is sufficiently risk-tolerant. We also solve a dynamic portfolio optimization problem taking leverage costs and limits into account. We find that the optimal leverage target is fairly insensitive to typical leverage costs, and that welfare gains of relaxing leverage constraints are sizeable for risk tolerant investors. In our suitability analysis we study the risks of modelling discretely leveraged returns with geometric Brownian motion, as well as the probability of LETFs crashing over horizons of up to 40 years derived from extreme value theory and historical data.

with Anne Balter and Nikolaus Schweizer
Revise and resubmit at Annals of Operations Research
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When heterogeneous agents apply the same collective strategy to invest in a financial market, their individual risk preferences and labor market prospects need to be aggregated to come up with a strategy that properly accounts for heterogeneity. In this paper, we consider this collective investment problem for a planner who seeks to minimize the maximal certainty-equivalent regret across agents, thus bringing all agents as closely as possible to their individual optimum. The motivating application is the investment problem of a pension provider in a defined-contribution pension system who needs to account for heterogeneity among participants. To our knowledge, our paper is the first to address the joint problem of clustering participants into groups with similar characteristics while optimizing lifecycle strategies within each cluster.

For the financial investment problem, we assume leverage constraints, discrete trading and a restriction to deterministic lifecycle strategies. In order to compute the regret-minimizing investment strategy for a given group of agents, we apply a recent technique based on evolutionary dynamics and population games. This gives an efficient algorithm for finding optimal dynamic compromises between hundreds of agents. We find that even with relatively few clusters – say, four or five – near-optimal welfare can be achieved for all agents in our setting. Moreover, it turns out that the optimal clustering is mostly a clustering by the coefficient of risk aversion which does not depend strongly on heterogeneity in wage trajectories.