Contributions published at Quantitative Business Administration

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This paper presents an analysis of the higher-order dynamics of key financial quantities in asset-pricing models with recursive preferences. For this purpose, we first introduce a projection-based algorithm for solving such models. The method outperforms common methods like discretization and log-linearization in terms of efficiency and accuracy. Our algorithm allows us to document the presence of strong nonlinear effects in the modern long-run risks models which cannot be captured by the common methods. For example, for a prominent recent calibration of a long-run risks model, the log-linearization approach overstates the equity premium by 100 basis points or 22.5%. The increasing complexity of state-of-the-art asset-pricing models leads to complex nonlinear equilibrium functions with considerable curvature which in turn has sizable economic implications. Therefore, these models require numerical solution methods, such as the projection methods presented in this paper, that can adequately describe the higher-order equilibrium features.

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The first equity future was launced in 1982 on the S&P 500 index. The future market has grown enormously since then and in more liquid than the cash market in many countries. The analysis here proves that the future market is highly efficient in many perspectives. Transaction costs in futures are on average one third of those in the cash market. Arbitrage is hardly ever possible. As futures contain information about future dividends, they can be used to analyze the market estimation for dividends. Even this proves to be quite efficient, with an exception in 2008, where the market has either underestimated the subsequent dividends or increased risk aversion caused too low market values of future dividends. Withholding taxes cause a split between the future and cash market. For investors who cannot reclaim foreign withholding taxes, it is beneficiary for them to only invest in futures, as dividend earnings implied in the future price are not taxed.

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Most standard asset-pricing models in the finance literature assume that consumption growth is stationary, that is, the consumption process has a unit root. In contrast to this literature, we study the implications of aggregate consumption processes featuring short-run deviations from a long-run trend. We find that the implications of our model are dramatically different from those obtained in the existing literature. A representative-agent model with standard CRRA preferences can reproduce the equity premium, the volatility of stock prices, and the average risk-free rate with a coefficient of relative risk aversion below ten. This finding suggests that temporary deviations from trend can play an important role in explaining asset pricing puzzles.

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We document a curious feature of the German mutual fund industry. Unlike U.S. mutual funds, funds domiciled in Germany do not necessarily compute their net asset values (NAV) as of market close. Using a sample of German equity funds, we infer each fund's NAV closing time from the best-fit market model using both maximum likelihood and Bayesian estimation. The results of both approaches coincide perfectly and show that all but one of the funds domiciled in Germany report intraday NAVs. We show that using market returns computed at the end of the day instead of the best-fit time, usually leads to misleading inferences about mutual fund performance.

We document a curious feature of the German mutual fund industry. Unlike U.S. mutual funds, funds domiciled in Germany do not necessarily compute their net asset values (NAV) as of market close. Using a sample of German equity funds, we infer each fund's NAV closing time from the best-fit market model using both maximum likelihood and Bayesian estimation. The results of both approaches coincide perfectly and show that all but one of the funds domiciled in Germany report intraday NAVs. We show that using market returns computed at the end of the day instead of the best-fit time, usually leads to misleading inferences about mutual fund performance.

In this paper, we develop a method to efficiently estimate dynamic discrete choice models with AR(n) type serial correlation of the errors. First, to approximate the expected value function of the underlying dynamic problem, we use Gaussian quadrature, interpolation over an adaptively refined grid, and solve a potentially large non-linear system of equations. Second, to evaluate the likelihood function, we decompose the integral over the unobserved state variables in the likelihood function into a series of lower dimensional integrals, and successively approximate them using Gaussian quadrature rules. Finally, we solve the maximum likelihood problem using a nested fixed point algorithm. We then apply this method to obtain point estimates of the parameters of the bus engine replacement model of Rust [Econometrica, 55 (5): 999–1033, (1987)]: First, we verify the algorithm's ability to recover the parameters of an artificial data set, and second, we estimate the model using the original data, finding significant serial correlation for some subsamples.

This paper presents a new method for the analysis of moral hazard principal-agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first-order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to non-polynomial problems. Finally, the paper demonstrates that the polynomial optimization approach, unlike the classical approach, extends to principal-agent models with multi-dimensional action sets.

In this paper we examine the quantitative effects of margin regulation on volatility in asset markets. We consider a general equilibrium infinite-horizon economy with heterogeneous agents and collateral constraints. There are two assets in the economy which can be used as collateral for short-term loans. For the first asset the margin requirement is exogenously regulated while the margin requirement for the second asset is determined endogenously. In our calibrated economy, the presence of collateral constraints leads to strong excess volatility. Thus, a regulation of margin requirements may have stabilizing effects. However, in line with the empirical evidence on margin regulation in U.S. stock markets, we show that changes in the regulation of one class of assets may have only small effects on these assets' return volatility if investors have access to another (unregulated) class of collateralizable assets to take up leverage. In contrast, a countercyclical margin regulation of all asset classes in the economy has a very strong dampening effect on asset return volatility.

We show that the optimal asset allocation for an investor depends crucially on the theory with which the investor is modeled. For the same market data and the same client data different theories lead to different portfolios. The market data we consider is standard asset allocation data. The client data is determined by a standard risk profiling question and the theories we apply are mean-variance analysis, expected utility analysis and cumulative prospect theory.

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