We present a flexible and scalable method to compute global solutions of high-dimensional non-smooth dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximal problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of MPI and OpenMP. This parallelization enables us to efficiently use modern high-performance computing architectures. Our time iteration algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.
The demand for commodities in standard applications typically is increasing in in- come, whereas the demand for the risk free asset in the classic portfolio problem often decreases with income. The latter is shown to occur if and only if the consumer is uncertainty preferences over assets satisfy the condition that the risk free asset is more readily substituted for the risky asset as the quantity of the risky asset increases. In this case, the risky asset is said to be "urgently needed" following the terminology of Johnson in his classic 1913 certainty analysis [19]. The asset and certainty settings differ in critical ways which result in a much greater likelihood for the urgently needed preference property to be satisfied in the portfolio problem. We provide several sufficient conditions for when the risky asset will be urgently needed and a surprisingly simple, complete characterization for widely popular members of the HARA (hyperbolic absolute risk aversion) class. For more general preferences, two examples are given where it is possible to fully describe the region of asset space in which the risky asset is urgently needed. Finally, using a standard representative agent model we show that the risky asset being urgently needed is equivalent to the equilibrium (relative) price of the risky asset increasing with its own supply.
This paper evaluates individuals’ ability to avoid investment mistakes and analyzes how investment competence is related to the propensity to seek or rely on professional advice. To address these issues, we use novel survey data collected from a representative sample of Swiss households. We find that investment competence is characterized by significant age and gender gaps, and that individuals who rely less on price movements as a source of information about investments are more likely to show above-the-average investment competence. We also find that individuals with relatively extensive investment experience and those who rely relatively strongly on their own judgment in making investment decisions are more likely to make investment decisions autonomously. In addition, we find that investment competence is positively related to the demand for financial advice. Thus, it appears that the individuals who most need financial advice are those who are least likely to seek such advice and rely on it.
Several recent papers have studied the impact of macroeconomic shocks on the financial policies of firms. However, they only consider the case where these macroeconomic shocks affect the profitability of firms but not the financial markets conditions. We study the polar case where the profitability of firms is stationary, but interest rates and issuance costs are governed by an exogenous Markov chain. We characterize the optimal dividend policy and show that these two macroeconomic factors have opposing effects: all things being equal, firms distribute more dividends when interest rates are high and less when issuing costs are high.
We identify the effects of monetary policy on bank risk-taking with an exhaustive credit register containing loan contracts and applications since 1984. We separate the compositional changes in the credit supply from the demand, firm and bank balance-sheet channels by accounting for both observed and unobserved time-varying firm and bank heterogeneity through time*firm and time*bank fixed effects. A lower overnight interest rate induces lower capitalized banks to expand and prolong credit to riskier firms, and to lend to riskier new applicants, granting them loans that are larger and longer-term. A lower long-term rate, however, has smaller or no such effects.
The paper by Presbitero, Udell and Zazzaro (henceforth, PUZ) aims to investigate whether the financial crisis that in Italy really “hit” after Lehman Brothers in September 2008 actually led to a credit crunch there and which types of firms suffered most. PUZ start from the quarterly editions of a monthly survey of about 3,800 Italian manufacturing firms (by ISAE, now ISTAT) to analyze credit access by 3,623 firms between 2008:Q1 to 2009:Q3, i.e., 23,140 firm-quarter observations of which 12,734 came after Lehman. PUZ find suggestive evidence that there was a credit crunch in Italy post-Lehman, that firms in provinces with bank branches located further from their bank’s headquarter (i.e., with banks that are more functionally distant) suffered relatively more, and that in those provinces especially high-quality firms were affected. These findings are consistent with a home bias but not with a flight-to-quality interpretation. This nice paper by PUZ is truly thought-provoking as the home bias in banking that is documented is occurring within one country. But before pointing out a possible broader avenue for further investigation, I want to discuss a few limitations of this study (most of which the authors are also aware of and candidly highlight) and in this way also indicate more immediate directions for follow-up research.
This paper considers changes in market comovement of merging US firms. Comparing the expected to the actual post merger comovement, we find that the post merger beta exhibits excess comovement with the acquiring firm. This suggests that the firm’s comovement is at least partly determined by its investors. We find that the excess comovement is significantly greater in cash transactions, when target shareholders tender their entire stake, than in pure stock transactions. Additionally, we document that the excess comovement is greater when the target is included in the S&P 500 as a result of the merger.
We introduce a tractable class of non-ane price processes with multifrequency stochastic volatil- ity and jumps. The specications require few xed parameters and deliver fast option pricing. One key ingredient is a tight link between jumps and volatility regimes, as asset pricing theory suggests. Empirically, the model matches implied volatility surfaces and their dynamics with- out requiring parameter recalibration. A variety of metrics show improvements over traditional benchmarks in- and out-of-sample.
We compare asset allocations derived for cumulative prospect theory(CPT) based on two different methods: Maximizing CPT along the mean–variance efficient frontier and maximizing it without that restriction. We find that with normally distributed returns the difference is negligible. However, using standard asset allocation data of pension funds the difference is considerable. Moreover, with derivatives like call options the restriction to the mean-variance efficient frontier results in a sizable loss of e.g. expected return and expected utility.
We develop a new goodness-of-fit test for validating the performance of probability forecasts. Our test statistic is particularly powerful under sparseness and dependence in the observed data. To build our test statistic, we start from a formal definition of calibrated forecasts, which we operationalize by introducing two components. The first component tests the level of the estimated probabilities. The second component validates the shape, measuring the differentiation between high and low robability events. After constructing test statistics for both level and shape, we provide a global goodness-of-fit statistic, which is asymptotically x^2 distributed. In a simulation exercise, we find that our approach is correctly sized and more powerful than alternative statistics. In particular, our shape statistic is significantly more powerful than the Kolmogorov-Smirnov test. Under independence our global test has significantly greater power than the popular Hosmer and Lemeshow's x^2 test. Moreover, even under dependence our global test remains correctly sized and consistent. As a timely and important empirical application of our method, we study the validation of a forecasting model for credit default events.
