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17
16
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.
16 [Version 2015]
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 quantities known only in the true model. We apply our method to a calibrated affine model. Our findings are threefold: Jumps matter more, i.e. our approximation is less accurate, if (i) the expected jump size or (ii) the jump intensity is large. Fixing the average impact of jumps, we find that (iii) rare, but severe jumps matter more than frequent, but small jumps.
15
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.
14
The efficacy of monetary authority actions depends primarily on the ability of the monetary authority to affect inflation expectations, which ultimately depend on agents' trust. We propose a model embedding trust cycles, as emerging from sequential coordination games between atomistic agents and the policy maker, in a monetary model. Trust affects agents' stochastic discount factor, namely the price of future risk, and their expectation formation process: these effects in turn interact with the monetary transmission mechanism. Using data from the Eurobarometer survey we analyze the link between trust on the one side and the transmission mechanism of shocks and of the policy rate on the other: data show that the two interact significantly and in a way comparable to the obtained in our model.
13
This paper investigates risk-taking in the liquid portfolios held by a large panel of Swedish twins. We document that the portfolio share invested in risky assets is an increasing and concave function of financial wealth, leading to different risk sensitivities across investors. Human capital, which we estimate directly from individual labor income, also drives risk-taking positively, while internal habit and expenditure commitments tend to reduce it. Our micro findings lend strong support to decreasing relative risk aversion and habit formation preferences. Furthermore, heterogeneous risk sensitivities across investors help reconcile individual preferences with representative-agent models.
12
We develop a dynamic network model whose links are governed by banks' optmizing decisions and by an endogenous tâtonnement market adjustment. Banks in our model can default and engage in firesales: risk is transmitted through direct and cascading counterparty defaults as well as through indirect pecuniary externalities triggered by firesales. We use the model to assess the evolution of the network configuration under various prudential policy regimes, to measure banks' contribution to systemic risk (through Shapley values) in response to shocks and to analyze the effects of systemic risk charges. We complement the analysis by introducing the possibility of central bank liquidity provision.
11
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.
11 [neue Version]
There has been a considerable debate about whether disaster models can rationalize the equity premium puzzle. This is because empirically disasters are not single extreme events, but long-lasting periods in which moderate negative consumption growth realizations cluster. Our paper proposes a novel way to explain this stylized fact. By allowing for consumption drops that can spark an economic crisis, we introduce a new economic channel that combines long-run and short-run risk. First, we document that our model can match consumption data of several countries. Second, it generates a large equity risk premium even if consumption drops are of moderate size.
10
This paper presents a theory that explains why it is beneficial for banks to engage in circular lending activities on the interbank market. Using a simple network structure, it shows that if there is a non-zero bailout probability, banks can significantly increase the expected repayment of uninsured creditors by entering into cyclical liabilities on the interbank market before investing in loan portfolios. Therefore, banks are better able to attract funds from uninsured creditors. Our results show that implicit government guarantees incentivize banks to have large interbank exposures, to be highly interconnected, and to invest in highly correlated, risky portfolios. This can serve as an explanation for the observed high interconnectedness between banks and their investment behavior in the run-up to the subprime mortgage crisis.