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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.
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.
We propose a novel approach on how to estimate systemic risk and identify its key determinants. For US financial companies with publicly traded equity options, we extract option-implied value-at-risks and measure the spillover effects between individual company value-at-risks and the option-implied value-at-risk of a financial index. First, we study the spillover effect of increasing company risks on the financial sector. Second, we analyze which companies are mostly affected if the tail risk of the financial sector increases. Key metrics such as size, leverage, market-to-book ratio and earnings have a significant influence on the systemic risk profiles of financial institutions.
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.
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.
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 long-term life insurance that can only be revised at significant costs, which makes insurance decisions sticky. Furthermore, a revision is only possible as long as the insured person is healthy. A second important 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 long-term 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 long-term life insurance markets altogether. Our results are robust to adding short-term life insurance, annuities and health insurance.
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.
This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence.
This paper studies a dynamic stochastic general equilibrium model involving climate change. Our model allows for damages on economic growth resulting from global warming. In the calibration, we capture effects from climate change and feedback effects on the temperature dynamics. We solve for the optimal state-dependent abatement policy. In our simulations, the costs of this policy measured in terms of lost GDP growth are moderate. On the other hand, postponing abatement action could reduce the probability that the climate can be stabilized. For instance, waiting for 10 years reduces this probability from 60% to 30%. Waiting for another 10 years leads to a probability that is less than 10%. Finally, doing nothing opens the risk that temperatures might explode and economic growth decreases significantly.
This paper studies a household’s optimal demand for a reverse mortgage. These contracts allow homeowners to tap their home equity to finance consumption needs. In stylized frameworks, we show that the decision to enter a reverse mortgage is mainly driven by the dierential between the aggregate appreciation of the house price and principal limiting factor on the one hand and the funding costs of a household on the other hand. We also study a rich life-cycle model that can explain the low demand for reverse mortgages as observed in US data. In this model, we analyze the optimal response of a household that is confronted with a health shock or financial disaster. If an agent suers from an unexpected health shock, she reduces the risky portfolio share and is more likely to enter a reverse mortgage. On the other hand, if there is a large drop in the stock market, she keeps the risky portfolio share almost constant by buying additional shares of stock. Besides, the probability to take out a reverse mortgage is hardly aected.
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.
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.
Financing asset growth
(2012)
We document the existence of a debt anomaly that is in addition to the asset growth anomaly: for a given asset growth rate, firms that issue more debt, as well as firms that retire more debt, have lower stock returns in the 12 months starting 6 months after the calendar year of asset growth. Exploring the reasons for debt issuance, we find that managers of firms for which analyst expectations are more over-optimistic, which suffer from declining investment profitability, and whose earnings-price ratios are relatively high are inclined to rely more heavily on debt financing. On the other hand, firms that retire more debt for a given asset growth rate tend to have improving profitability but to be over-priced. We also find that the financing decision is influenced by the prior debt ratio, the asset growth rate, profitability, and CEO pay sensitivity. We interpret our results in terms of managerial incentives, signaling, and market timing.
This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence.
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.
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.
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