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Sun, 09 Feb 2014 10:54:10 +0200Sun, 09 Feb 2014 10:54:10 +0200Asset pricing and consumption-portfolio choice with recursive utility and unspanned risk : [version 4 august 2014]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34772
We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/ representative agent can be characterized by a specific semilinear partial differential equation. To date, the solution to this equation has mostly been approximated by Campbell-Shiller techniques, without addressing general issues of existence and uniqueness. We develop a novel approach that rigorously constructs the solution by a fixed point argument. We prove that under regularity conditions a solution exists and establish a fast and accurate numerical method to solve consumption-portfolio and asset pricing problems with recursive preferences and unspanned risk. Our setting is not restricted to affine asset price dynamics. Numerical examples illustrate our approach.Holger Kraft; Thomas Seiferling; Frank Thomas Seifriedreporthttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34772Tue, 02 Sep 2014 10:54:10 +0200Pricing two trees when mildew infests the orchard: how does contagion affect general equilibrium asset prices : [version: March 11, 2011)
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34701
This paper analyzes the equilibrium pricing implications of contagion risk in a two-tree Lucas economy with CRRA preferences. The dividends of both trees are subject to downward jumps. Some of these jumps are contagious and increase the risk of subsequent jumps in both trees for some time interval. We show that contagion risk leads to large price-dividend ratios for small assets, a joint movement of prices in the case of a regime change from the calm to the contagion state, significantly positive correlations between assets, and large positive betas for small assets. Whereas disparities between the assets with respect to their propensity to trigger contagion barely matter for pricing, the prices of robust assets that are hardly affected by contagion and excitable assets that are severely hit by contagion differ significantly. Both in absolute terms and relatively to the market, the price of a small safe haven increases if the economy reaches the contagion state. On the contrary, the price of a small, contagion-sensitive asset exhibits a pronounced downward jump.Nicole Branger; Holger Kraft; Christoph Meinerdingreporthttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34701Tue, 12 Aug 2014 15:46:21 +0200Consumption and wage humps in a life-cycle model with education : [version 11 june 2014]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34326
he observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. We explicitly solve a model with utility of both consumption and leisure and with educational decisions affecting future wages. We show optimal consumption is hump shaped and determine the peak age. The hump results from consumption and leisure being substitutes and from the implicit price of leisure being decreasing over time; more leisure means less education, which lowers future wages, and the present value of foregone wages decreases with age. Consumption is hump shaped whether the wage is hump shaped or increasing over life.Holger Kraft; Claus Munk; Frank Thomas Seifried; Mogens Steffensenworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34326Wed, 25 Jun 2014 17:05:32 +0200Asset pricing and consumption-portfolio choice with recursive utility and unspanned risk : [version 1 june 2014]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34180
We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/representative agent can be characterized by a specific semilinear partial differential equation. To date, the solution to this equation has mostly been approximated by Campbell-Shiller techniques, without addressing general issues of existence and uniqueness. We develop a novel approach that rigorously constructs the solution by a fixed point argument. We prove that under regularity conditions a solution exists and establish a fast and accurate numerical method to solve consumption-portfolio and asset pricing problems with recursive preferences and unspanned risk. Our setting is not restricted to affine asset price dynamics. Numerical examples illustrate our approach.Holger Kraft; Thomas Seiferling; Frank Thomas Seifriedworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/34180Tue, 17 Jun 2014 15:58:40 +0200Life insurance demand under health shock risk : [Version: 7 February 2014]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/33150
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.Holger Kraft; Lorenz S. Schendel; Mogens Steffensenworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/33150Tue, 04 Mar 2014 08:18:46 +0100Asset Pricing Under Uncertainty About Shock Propagation
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/32437
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.Nicole Branger; Patrick Grüning ; Holger Kraft; Christoph Meinerding; Christian Schlagworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/32437Tue, 10 Dec 2013 10:50:59 +0100Partial information about contagion risk, self-exciting processes and portfolio optimization
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/31551
This paper compares two classes of models that allow for additional channels of correlation between asset returns: regime switching models with jumps and models with contagious jumps. Both classes of models involve a hidden Markov chain that captures good and bad economic states. The distinctive feature of a model with contagious jumps is that large negative returns and unobservable transitions of the economy into a bad state can occur simultaneously. We show that in this framework the filtered loss intensities have dynamics similar to self-exciting processes. Besides, we study the impact of unobservable contagious jumps on optimal portfolio strategies and filtering.Nicole Branger; Holger Kraft; Christoph Meinerdingworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/31551Wed, 04 Sep 2013 10:40:33 +0200Financing asset growth
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/31412
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.Michael J. Brennan; Holger Kraftworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/31412Tue, 20 Aug 2013 14:47:49 +0200Systemic risk in the financial sector: what can we learn from option markets?
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/31409
In this paper, we propose a novel approach on how to estimate systemic risk and identify its key determinants. For all US financial companies with publicly traded equity options, we extract their option-implied value-at-risks (VaRs) and measure the spillover effects between individual company VaRs and the option-implied VaR of an US financial index. First, we study the spillover effect of increasing company risks on the financial sector. Second, we analyze which companies are most affected if the tail risk of the financial sector increases. We find that key accounting and market valuation metrics such as size, leverage, balance sheet composition, market-to-book ratio and earnings have a significant influence on the systemic risk profile of a financial institution. In contrast to earlier studies, the employed panel vector autoregression (PVAR) estimator allows for a causal interpretation of the results.Holger Kraft; Alexander Schmidtworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/31409Tue, 20 Aug 2013 14:39:49 +0200Stochastic differential utility as the continuous-time limit of recursive utility
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/30570
We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size.Holger Kraft; Frank Thomas Seifriedworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/30570Thu, 27 Jun 2013 16:09:30 +0200When do jumps matter for portfolio optimization? : [Version 29 April 2013]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/30569
We consider the continuous-time portfolio optimization problem of an investor with constant relative risk aversion who maximizes expected utility of terminal wealth. The risky asset follows a jump-diffusion model with a diffusion state variable. We propose an approximation method that replaces the jumps by a diffusion and solve the resulting problem analytically. Furthermore, we provide explicit bounds on the true optimal strategy and the relative wealth equivalent loss that do not rely on results from the true model. We apply our method to a calibrated affine model and fine that relative wealth equivalent losses are below 1.16% if the jump size is stochastic and below 1% if the jump size is constant and γ ≥ 5. We perform robustness checks for various levels of risk-aversion, expected jump size, and jump intensity.Marius Ascheberg; Nicole Branger; Holger Kraftworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/30569Thu, 27 Jun 2013 15:56:06 +0200Consumption habits and humps : [Version 23 June 2013]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/30568
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.Holger Kraft; Claus Munk; Frank Thomas Seifried; Sebastian Wagnerworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/30568Thu, 27 Jun 2013 15:22:20 +0200How does contagion affect general equilibrium asset prices? : [Version: March 13, 2013]
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/29381
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.Nicole Branger; Holger Kraft; Christoph Meinerdingworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/29381Fri, 19 Apr 2013 07:42:21 +0200Growth options and firm valuation
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/29376
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. Holger Kraft; Eduardo S. Schwartz; Farina Weissworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/29376Thu, 18 Apr 2013 07:56:32 +0200A dynamic programming approach to constrained portfolios
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/25656
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.Holger Kraft; Mogens Steffensenworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/25656Wed, 15 Aug 2012 17:39:52 +0200Investment, income, incompleteness
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6423
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: G11Björn Bick; Holger Kraft; Claus Munkworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6423Thu, 30 Apr 2009 14:54:25 +0200What is the impact of stock market contagion on an investor's portfolio choice?
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6245
Stocks are exposed to the risk of sudden downward jumps. Additionally, a crash in one stock (or index) can increase the risk of crashes in other stocks (or indices). Our paper explicitly takes this contagion risk into account and studies its impact on the portfolio decision of a CRRA investor both in complete and in incomplete market settings. We find that the investor significantly adjusts his portfolio when contagion is more likely to occur. Capturing the time dimension of contagion, i.e. the time span between jumps in two stocks or stock indices, is thus of first-order importance when analyzing portfolio decisions. Investors ignoring contagion completely or accounting for contagion while ignoring its time dimension suffer large and economically significant utility losses. These losses are larger in complete than in incomplete markets, and the investor might be better off if he does not trade derivatives. Furthermore, we emphasize that the risk of contagion has a crucial impact on investors' security demands, since it reduces their ability to diversify their portfolios. JEL-Classification: G12, G13Nicole Branger; Holger Kraft; Christoph Meinerdingworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6245Fri, 13 Mar 2009 11:20:38 +0100Optimal housing, consumption, and investment decisions over the life-cycle
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6244
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, C6Holger Kraft; Claus Munkworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6244Fri, 13 Mar 2009 11:16:47 +0100Foundations of continuous-time recursive utility : differentiability and normalization of certainty equivalents
http://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6243
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, C61Holger Kraft; Frank Thomas Seifriedworkingpaperhttp://publikationen.stub.uni-frankfurt.de/frontdoor/index/index/docId/6243Fri, 13 Mar 2009 11:12:36 +0100