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- Contagion (3)
- Asset Allocation (2)
- General Equilibrium (2)
- labor income (2)
- recursive utility (2)
- welfare loss (2)
- Asset Pricing (1)
- Bellman Equations (1)
- Consumption hump (1)
- Consumption-investment Problems (1)

- A dynamic programming approach to constrained portfolios (2012)
- This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of inter¬mediate wealth and/or consumption.

- Asset Pricing Under Uncertainty About Shock Propagation (2013)
- We analyze the equilibrium in a two-tree (sector) economy with two regimes. The output of each tree is driven by a jump-diffusion process, and a downward jump in one sector of the economy can (but need not) trigger a shift to a regime where the likelihood of future jumps is generally higher. Furthermore, the true regime is unobservable, so that the representative Epstein-Zin investor has to extract the probability of being in a certain regime from the data. These two channels help us to match the stylized facts of countercyclical and excessive return volatilities and correlations between sectors. Moreover, the model reproduces the predictability of stock returns in the data without generating consumption growth predictability. The uncertainty about the state also reduces the slope of the term structure of equity. We document that heterogeneity between the two sectors with respect to shock propagation risk can lead to highly persistent aggregate price-dividend ratios. Finally, the possibility of jumps in one sector triggering higher overall jump probabilities boosts jump risk premia while uncertainty about the regime is the reason for sizeable diffusive risk premia.

- Consumption habits and humps (2013)
- We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing consumption path over life. However, because of habit formation, a high initial consumption would lead to high required consumption in the future. To cover the future required consumption, wealth is set aside, but the necessary amount decreases with age which allows consumption to increase in the early part of life. At some age, the impatience outweighs the habit concerns so that consumption starts to decrease. We derive the optimal consumption strategy in closed form, deduce sufficient conditions for the presence of a consumption hump, and characterize the age at which the hump occurs. Numerical examples illustrate our findings. We show that our model calibrates well to U.S. consumption data from the Consumer Expenditure Survey.

- Financing asset growth (2013)
- In this paper we provide new evidence that corporate financing decisions are associated with managerial incentives to report high equity earnings. Managers rely most heavily on debt to finance their asset growth when their future earnings prospects are poor, when they are under pressure due to past declines in earnings, negative past stock returns, and excessively optimistic analyst earnings forecasts, and when the earnings yield is high relative to bond yields so that from an accounting perspective equity is ‘expensive’. Managers of high debt issuing firms are more likely to be newly appointed and also more likely to be replaced in subsequent years. Abnormal returns on portfolios formed on the basis of asset growth and debt issuance are strongly positively associated with the contemporaneous changes in returns on assets and on equity as well as with earnings surprises. This may account for the finding that debt issuance forecasts negative abnormal returns, since debt issuance also forecasts negative changes in returns on assets and on equity and negative earnings surprises. Different mechanisms appear to be at work for firms that retire debt.

- Foundations of continuous-time recursive utility : differentiability and normalization of certainty equivalents (2009)
- This paper relates recursive utility in continuous time to its discrete-time origins and provides a rigorous and intuitive alternative to a heuristic approach presented in [Duffie, Epstein 1992], who formally define recursive utility in continuous time via backward stochastic differential equations (stochastic differential utility). Furthermore, we show that the notion of Gâteaux differentiability of certainty equivalents used in their paper has to be replaced by a different concept. Our approach allows us to address the important issue of normalization of aggregators in non-Brownian settings. We show that normalization is always feasible if the certainty equivalent of the aggregator is of expected utility type. Conversely, we prove that in general L´evy frameworks this is essentially also necessary, i.e. aggregators that are not of expected utility type cannot be normalized in general. Besides, for these settings we clarify the relationship of our approach to stochastic differential utility and, finally, establish dynamic programming results. JEL Classifications: D81, D91, C61

- Growth options and firm valuation (2013)
- This paper studies the relation between firm value and a firm's growth options. We find strong empirical evidence that (average) Tobin's Q increases with firm-level volatility. However, the significance mainly comes from R&D firms, which have more growth options than non-R&D firms. By decomposing firm-level volatility into its systematic and unsystematic part, we also document that only idiosyncratic volatility (ivol) has a significant effect on valuation. Second, we analyze the relation of stock returns to realized contemporaneous idiosyncratic volatility and R&D expenses. Single sorting according to the size of idiosyncratic volatility, we only find a significant ivol anomaly for non-R&D portfolios, whereas in a four-factor model the portfolio alphas of R&D portfolios are all positive. Double sorting on idiosyncratic volatility and R&D expenses also reveals these differences between R&D and non-R&D firms. To simultaneously control for several explanatory variables, we also run panel regressions of portfolio alphas which confirm the relative importance of idiosyncratic volatility that is amplified by R&D expenses.

- How does contagion affect general equilibrium asset prices? (2013)
- This paper analyzes the equilibrium pricing implications of contagion risk in a Lucas-tree economy with recursive preferences and jumps. We introduce a new economic channel allowing for the possibility that endowment shocks simultaneously trigger a regime shift to a bad economic state. We document that these contagious jumps have far-reaching asset pricing implications. The risk premium for such shocks is superadditive, i.e. it is 2.5\% larger than the sum of the risk premia for pure endowment shocks and regime switches. Moreover, contagion risk reduces the risk-free rate by around 0.5\%. We also derive semiclosed-form solutions for the wealth-consumption ratio and the price-dividend ratios in an economy with two Lucas trees and analyze cross-sectional effects of contagion risk qualitatively. We find that heterogeneity among the assets with respect to contagion risk can increase risk premia disproportionately. In particular, big assets with a large exposure to contagious shocks carry significantly higher risk premia.

- Investment, income, incompleteness (2009)
- The utility-maximizing consumption and investment strategy of an individual investor receiving an unspanned labor income stream seems impossible to find in closed form and very dificult to find using numerical solution techniques. We suggest an easy procedure for finding a specific, simple, and admissible consumption and investment strategy, which is near-optimal in the sense that the wealthequivalent loss compared to the unknown optimal strategy is very small. We first explain and implement the strategy in a simple setting with constant interest rates, a single risky asset, and an exogenously given income stream, but we also show that the success of the strategy is robust to changes in parameter values, to the introduction of stochastic interest rates, and to endogenous labor supply decisions. JEL-Classification: G11

- Life insurance demand under health shock risk (2014)
- This paper studies the life cycle consumption-investment-insurance problem of a family. The wage earner faces the risk of a health shock that significantly increases his probability of dying. The family can buy term life insurance with realistic features. In particular, the available contracts are long term so that decisions are sticky and can only be revised at significant costs. Furthermore, a revision is only possible as long as the insured person is healthy. A second important and realistic feature of our model is that the labor income of the wage earner is unspanned. We document that the combination of unspanned labor income and the stickiness of insurance decisions reduces the insurance demand significantly. This is because an income shock induces the need to reduce the insurance coverage, since premia become less affordable. Since such a reduction is costly and families anticipate these potential costs, they buy less protection at all ages. In particular, young families stay away from life insurance markets altogether.

- Optimal housing, consumption, and investment decisions over the life-cycle (2009)
- We provide explicit solutions to life-cycle utility maximization problems simultaneously involving dynamic decisions on investments in stocks and bonds, consumption of perishable goods, and the rental and the ownership of residential real estate. House prices, stock prices, interest rates, and the labor income of the decision-maker follow correlated stochastic processes. The preferences of the individual are of the Epstein-Zin recursive structure and depend on consumption of both perishable goods and housing services. The explicit consumption and investment strategies are simple and intuitive and are thoroughly discussed and illustrated in the paper. For a calibrated version of the model we find, among other things, that the fairly high correlation between labor income and house prices imply much larger life-cycle variations in the desired exposure to house price risks than in the exposure to the stock and bond markets. We demonstrate that the derived closed-form strategies are still very useful if the housing positions are only reset infrequently and if the investor is restricted from borrowing against future income. Our results suggest that markets for REITs or other financial contracts facilitating the hedging of house price risks will lead to non-negligible but moderate improvements of welfare. JEL-Classification: G11, D14, D91, C6