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181
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.
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52
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.
6
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.
25
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.
40
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.
139
We show that the net corporate payout yield predicts both the stock market index and house prices and that the log home rent-price ratio predicts both house prices and labor income growth. We incorporate the predictability in a rich life-cycle model of household decisions involving consumption of both perishable goods and housing services, stochastic and unspanned labor income, stochastic house prices, home renting and owning, stock investments, and portfolio constraints. We find that households can significantly improve their welfare by optimally conditioning decisions on the predictors. For a modestly risk-averse agent with a 35-year working period and a 15-year retirement period, the present value of the higher average life-time consumption amounts to roughly $179,000 (assuming both an initial wealth and an initial annual income of $20,000), and the certainty equivalent gain is around 5.5% of total wealth (financial wealth plus human capital). Furthermore, every cohort of agents in our model would have benefited from applying predictor-conditional strategies along the realized time series over our 1960-2010 data period.
85
We set up and solve a rich life-cycle model of household decisions involving consumption of both perishable goods and housing services, stochastic and unspanned labor income, stochastic house prices, home renting and owning, stock investments, and portfolio constraints. The model features habit formation for housing consumption, which leads to optimal decisions closer in line with empirical observations. Our model can explain (i) that stock investments are low or zero for many young agents and then gradually increasing over life, (ii) that the housing expenditure share is age- and wealth-dependent, (iii) that perishable consumption is more sensitive to wealth and income shocks than housing consumption, and (iv) that non-housing consumption is hump-shaped over life.
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.
53
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.