Contributions published at Financial Economics (Felix Kübler)

We analyze complex bond portfolios within the framework of a dynamic general equilibrium asset-pricing model. Equilibrium bond portfolios are nonsensical and imply a trading volume that vastly exceeds observed trading volume on financial markets. Instead, portfolios that combine bond ladders with a market portfolio of equity assets are nearly optimal investment strategies. The welfare loss of these simple investment strategies, when compared to the equilibrium portfolio, converges to zero as the length of the bond ladder increases. This article, therefore, provides a rationale for naming bond ladders as a popular bond investment strategy.

Theoretically, collateral constraints have the potential to strongly amplify and propagate aggregate shocks. However, the quantitative literature tends to find rather weak and non-robust effects. This paper tries to improve on this by modeling the interaction between idiosyncratic risk and collateral constraints. To this aim, agents' productivities as workers and entrepreneurs are assumed to evolve stochastically. This leads to a perpetual mismatch between wealth and skills, which is the reason for collateralized borrowing. The advantage of this modeling strategy is threefold: First, the evolution of skills can be measured empirically. In contrast, the heterogeneity in patience that the previous literature assumes to excite collateralized borrowing is not even intended as a serious micro-foundation. Second, idiosyncratic risk creates a non-degenerate distribution of wealth. As a consequence, the percentage of constrained agents changes as shocks hit the economy. Among other things, this generates recessions that are much sharper than booms. Last but not least, the impact of collateral constraints turns out to be larger and more robust in the setup with idiosyncratic risk compared to models with heterogeneity in patience.

In this paper, I examine ε-equilibria of stationary dynamic economies with heterogeneous agents and possibly incomplete financial markets. I give a simple example to show that even for arbitrarily small ε > 0, allocation and prices can be far away from exact equilibrium allocations and prices. That is, errors in market clearing or individuals' optimality conditions do not provide enough information to assess the quality of an approximation. I derive a sufficient condition for an ε-equilibrium to be close to an exact equilibrium. If the economic fundamentals are semi-algebraic, one can verify computationally whether this condition holds. The condition can be interpreted economically as a robustness requirement on the set of ε-equilibria which form a neighbourhood of the computed approximation. I illustrate the main result and the computational method using an infinite horizon economy with overlapping generations and incomplete financial markets.

This paper reproduces the slope of the uncovered interest rate parity (UIP) regression for six different country pairs within one standard deviation under rational expectations. While standard theory predicts a slope of one, the empirically observed slope of the regression of currency returns on the interest rate differential between two countries is negative for most country pairs. This empirical fact that, on average, investors require higher returns on bonds denominated in a currency expected to appreciate, poses a strong challenge for economic models. In this paper, we propose a potential explanation within an infinite horizon dynamic stochastic general equilibrium model with incomplete markets. Heterogenous investors experience varying risk aversion as a result of habit formation. The underlying mechanism of the model relies on varying international diversification in the investors’ portfolio choice decision. In response to their changing habit levels, investors’ hedging desire varies over time, leading to adjustments in interest rates. The habit-induced investment decisions are negatively correlated with exchange rate movements. This leads to a negative correlation between interest rates and expected exchange rates, as implied by a negative UIP slope. Depending on the magnitude of habits, the model is capable of reproducing positive as well as negative UIP slopes, as seen empirically in the data.

In this paper we identify conditions under which the introduction of a pay-as-you-go social security system is ex-ante Pareto-improving in a stochastic overlapping generations economy with capital accumulation and land. We argue that these conditions are consistent with realistic specifications of the parameters of the economy. In our model, financial markets are complete and competitive equilibria are interim Pareto efficient. Therefore, a welfare improvement can only be obtained if agents' welfare is evaluated ex ante, and arises from an improvement in intergenerational risk sharing. We examine the various effects of social security, on the prices of long-lived assets and the stock of capital, and hence on output, wages and risky rates of returns, can be clearly identified. In addition, we analyze the optimal size of a given social security system as well as its optimal reform.

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Wealth Management besteht aus einer Reihe von Dienstleistungen zum Aufbau und der nachhaltigen Verwaltung von Vermögen. In diesem Artikel konzentriere ich mich auf den Aspekt des Portfolio Managements, vernachlässige dabei jedoch die wichtigen legalen und steuerlichen Aspekte. Die Finanzkrise von 1998 hat traditionelle Theorien über Investition, Risiko, Korrelation und Diversifikation in den Grundfesten erschüttert. Mittlerweile ist klar, dass die Standardabweichung alleine ein ungenügendes Mass des Risikos darstellt und dass traditionelle Investitionsstrategien, die sich auf die Annahmen und Vorhersagen des sogenannten Capital Asset Pricing Models stützen, überholt sind (sicherlich wird niemand mehr die Annahme von normalverteilten Renditen wirklich ernst nehmen). Alternative Ansätze, welche auf der Verhaltensökonomie aufbauen, scheinen einige der Probleme des traditionellen Ansatzes zu lösen - aber auch hier fehlt letztendlich der explizite Zusammenhang zwischen Preisen auf Finanzmärkten und gesamtwirtschaftlicher Aktivität. In Zeiten normaler öko‐nomischer Aktivität ist dies nicht allzu problematisch, aber es ist zu bezweifeln, dass wir uns (schon) wieder in solch „normalen“ Zeiten befinden. Um eine kohärente Theorie der optimalen Portfolio-Verwaltung zu entwickeln, muss man zunächst erklären, wie es regelmässig zu Finanzkrisen kommen kann.

In this paper we explore the computation and simulation of stochastic overlapping generation (OLG) models. To do so we compute all Markovian equilibria adopting a recently developed numerical algorithm. Among the models we studied, the indeterminacy in deterministic OLG model results in many different equilibrium paths corresponding to the initial condition that all asymptotically converge to the same steady state. The uncertainty introduces indeterminacy with infnite dimension due to the existence of numerous selections of transition and policy functions from the equilibrium set. Each selection correspondences a sequential competitive equilibrium that may present excessive volatile movements in asset price. It is possible to construct a continuum of recursive equilibrium. However our numerical simulations suggest that it is problematic to look at recursive equilibrium in which the volatility of asset price is solely determined by the distribution of the shock.

Core-collapse supernovae (CCSNe) are among the most energetic explosions in the universe, liberating the prodigious amount of ~ 1053 erg, the binding energy of their compact remnants, neutron stars or stellar mass black holes. While 99% of this energy is emitted in neutrinos, 1% goes into the internal and asymptotic kinetic energy of the ejecta, and it is reasonable to assume that a tiny fraction is radiated in gravitational waves (GWs). Ever since the first experimental efforts to detect GWs, CCSNe have been considered prime sources of gravitational waves for interferometric detectors. Besides neutrinos, which have already been observed in the context of stellar core collapse of SN1987A, GWs could provide us access to the electromagnetically hidden compact inner core of some such cataclysmic events, supplying us for example with valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. However, GW astronomy strongly depends on the extensive data processing of the detector output on the basis of reliable GW estimates, which only recently have become feasible with the emerging power of supercomputers. The work presented in this thesis is concerned with numerical CCSN models and their imprints in GWs. I performed an extensive series of more than 30 three-dimensional magnetohydrodynamical (MHD) core-collapse simulations. My models are based on a 15M [...] progenitor stemming from stellar evolution calculations, an effective general relativistic potential and either the Lattimer-Swesty (with three possible compressibilities) or the Shen equation of state (EoS) for hot, dense matter. Furthermore, the neutrino transport is tracked by computationally efficient algorithms for the radiative transfer of massless fermions. I systematically investigated the effects of the microphysical finite-temperature nuclear EoS, the initial rotation rate, both the toroidal and the poloidal magnetic fields, and multidimensional gravitational potentials on the GW signature. Based on the results of these calculations, I obtained the largest – and also one of the most realistic – catalogue of GW signatures from 3D MHD stellar core collapse simulations at present. I stress the importance of including postbounce neutrino physics, since it quantitatively alters the GW signature. Non- and slowly-rotating models show GW emission caused by prompt and protoneutron star (PNS) convection. Moreover, the signal stemming from prompt convection allows for the distinction between the two different nuclear EoS indirectly by different properties of the fluid instabilities. For simulations with moderate or even fast rotation rates, I only find the axisymmetric type I wave signature at core bounce. In line with recent results, I could confirm that the maximum GW amplitude scales roughly linearly with the ratio of rotational to gravitational energy (T/|W|) at core bounce below a threshold value of about 10%. Furthermore, I point out that PNS can become dynamically unstable to rotational instabilities at T/|W| values as low as ~ 2% at core bounce. Apart from these two points, I show that it is generally very difficult to discern the effects of the individual features of the input physics in a GW signal from a rotating CCSN that can be attributed unambiguously to a specific model. Weak magnetic fields do not notably influence the dynamical evolution of the core and thus the GW emission. However, for strong initial poloidal magnetic fields ≥ 1012G, the combined action of flux-freezing and field winding leads to conditions where the ratio of magnetic field pressure to matter pressure reaches about unity which leads to the onset of a jet-like supernova explosion. The collimated bipolar out-stream of matter is then reflected in the emission of a type IV GW signal. In contradiction to axisymmetric simulations, I find evidence that nonaxisymmetric fluid modes can counteract or even suppress jet formation for models with strong initial toroidal magnetic fields. I emphasize the importance of including multidimensional gravitational potentials in rapidly rotating 3D CCSN simulations: taking them into account can alter the resulting GW amplitudes up to a factor of 2 compared to simulations which encounter gravity only by a monopolar approximation. Moreover, I show that the postbounce dynamics occuring in the outer layers (at radii R ≥ 200km) of models run with 3D gravity deviates vastly from the ones run with a 1D or 2D gravitational potential. The latter finding implies that both spherically symmetric and axisymmetric treatments of gravity are too restrictive for a quantitative description of the overall postbounce evolution of rapidly rotating CCSN models. The results of models with continued neutrino emission show that including deleptonization during the postbounce phase is an indispensable issue for the quantitative prediction of GWs from core-collapse supernovae, because it can alter the GW amplitude up to a factor of 10 compared to a pure hydrodynamical treatment. My collapse simulations indicate that corresponding events in our Galaxy would be detectable either by LIGO, if the source is rotating, or at least by the advanced LIGO detector, if it is not or only slowly rotating.

We describe a sparse-grid collocation method to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method can be in applications by computing the non-linear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy, the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with up to 10 countries (i.e., up to 20 continuous-valued state variables).

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Multiplicity of equilibria is a prevalent problem in many economic models. Often equilibria are characterized as solutions to a system of polynomial equations. This paper gives an introduction to the application of GrÄobner basis methods for ¯nding all solutions of a polynomial system. The Shape Lemma, a key result from algebraic geometry, states under mild assumptions that a given equilibrium system has the same solution set as a much simpler triangular system. Essentially the computation of all solutions then reduces to ¯nding all roots of a single polynomial in a single unknown. The software package Singular computes the equivalent simple system. If all coeficients in the original equilibrium equations are rational numbers or parameters then the GrÄobner basis computations of Singular are exact. This fact implies that the GrÄobner basis methods cannot only be used for a numerical approximation of equilibria but in fact may allow the proof of theoretical results for the underlying economic model. Three economic applications illustrate that without much prior knowledge of algebraic geometry GrÄobner basis methods can be easily applied to gain interesting insights into many modern economic models.

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In this paper we examine the likelihood of multiple real steady states in deterministic exchange economies with overlapping generations. There is a single good and a single agent per generation with constant relative risk aversion expected utility. In order to test for multiple equilibria we employ methods from computational algebraic geometry. In our examples, we find that multiplicity becomes less likely as the life span of agents increases but becomes more likely as the coefficient of risk aversion increases. For moderate values of risk aversion, multiplicity is very unlikely when agents live for five or more periods. (JEL: C61, C63, D50, D58)

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