Optimal portfolio choice with wash sale constraints

We analytically solve the portfolio choice problem in the presence of wash sale constraints in a two-period model with one risky asset. Our results show that wash sale constraints can heavily affect portfolio choice of investors with unrealized losses. The trading behavior of such investors is to a large extent driven by the desire to realize those losses, either immediately by sharply decreasing the holding of assets carrying unrealized losses, or indirectly by increasing such holdings in order to prepare for a decrease in a future period to earn the tax rebate payment. Our findings are robust to increasing the number of trading dates and introducing a second risky asset and a correlation structure.     

Explicit solution of a general consumption/portfolio problem with subsistence consumption and bankruptcy

This paper solves a general continuous-time single-agent consumption and portfolio decision problem with subsistence consumption in closed form. The analysis allows for general continuously differentiable concave utility functions. The model takes into consideration that consumption must be no smaller than a given subsistence rate and that bankruptcy can occur. Thus the paper generalizes the results of Karatzas, Lehoczky, Sethi, and Shreve (1986).     

Optimal portfolio choice and consistent performance

Consistent financial performance is the key element to success in asset management. We use a dynamic wealth constraint to represent the consistent performance requirement, which takes into account the entire historical records as a benchmark so that the wealth always stays at or above the benchmark. The optimal policy under this wealth constraint is characterized, and several implications are presented in this paper. This consistent performance constraint could be an appealing tool to be implemented in a volatile market and have rich practical implications.     

Optimal production and portfolio investment decisions

This paper takes a further step towards the integration of the theories of production and finance under uncertainty. It sets up a continuous time-diffusion process model of production by firms and portfolio investment by individuals and provides a simultaneous solution to these two decisions. The derived equilibrium conditions, being in the stockholders' interest, are specific in form, and are determined by two factors: attitudes of investors towards risk and the systematic risks of the firm.     

Approximating exact expected utility via portfolio efficient frontiers

Expected utility theory is nowadays accepted as the standard for rational choice among risky assets. However, as Harry Markowitz recently pointed out, the problem of how the maximum expected utility along the risk–return portfolio efficient frontiers approximates the exact maximum expected utility is still open. This paper shows that some popular risk–return models are actually able to approximate expected utility maximization with respect to classical and new distance measures. It also analyzes the ability of the whole risk–return efficient frontiers to approximate the exact one. Our empirical analysis is based on recent publicly available real-world data sets.     

Reason rules...: the utility of rationality and the rationality of utility

Almost every theory of human behavior is based upon some assumption of rationalty. Such an assumption is commonly believed to be necessary in order to distinguish rational behavior, which is, from non-rational behavior, which is not amenable to scientific investigation. This article presents a thorough re-examination of this assumption, an inquiry which turns out to raise all the central issues of both the methodology and the theory of behavioral inquiry generally. It leads to the somewhat surprising conclusion that the notion of rationality does not have any meaningful role to play in behavioral inquiry, and that there is no sense in distinguishing rational from non-rational or irrational behavior. It also shows that the generalization of the utility notion in terms of information makes it into a much more powerful and subtle tool of analysis than it commonly appears to be taken for.     

Optimal investment for executive stockholders with exponential utility

The scope of this paper is to enhance the model for the own-company stockholder (Desmettre et?al. in Math Methods Oper Res 72(3):347?C378, 2010), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility setup. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility setup.     

On rankings and top choices in random utility models with dependent utilities

Different aggregate preference orders based on rankings and top choices have been defined in the literature to describe preferences among items in a fixed set of alternatives. A useful tool in this framework is constituted by random utility models, where the utility of each alternative, or object, is represented by a random variable, indexed by the object, which, for example, can capture the variability of preferences over a population. Applications are derived in diverse research fields, including computer science, management science and reliability. Recently, some stochastic ordering conditions have been provided for comparing alternatives by means of some aggregate preference orders in the case of independent random utility variables by Joe (Math Soc Sci 43:391–404, 2002). In this paper we provide new conditions, based on some joint stochastic orderings, for aggregate preference orders among the alternatives in the case of dependent random utilities. We also provide some examples of application in different research fields.      

Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models

We extend the recently introduced latent threshold dynamic models to include dependencies among the dynamic latent factors which underlie multivariate volatility. With an ability to induce time-varying sparsity in factor loadings, these models now also allow time-varying correlations among factors, which may be exploited in order to improve volatility forecasts. We couple multi-period, out-of-sample forecasting with portfolio analysis using standard and novel benchmark neutral portfolios. Detailed studies of stock index and FX time series include: multi-period, out-of-sample forecasting, statistical model comparisons, and portfolio performance testing using raw returns, risk-adjusted returns and portfolio volatility. We find uniform improvements on all measures relative to standard dynamic factor models. This is due to the parsimony of latent threshold models and their ability to exploit between-factor correlations so as to improve the characterization and prediction of volatility. These advances will be of interest to financial analysts, investors and practitioners, as well as to modeling researchers.     

Optimal prepayment and default rules for mortgage-backed securities

We study the optimal stopping problems embedded in a typical mortgage. Despite a possible non-rational behaviour of the typical borrower of a mortgage, such problems are worth to be solved for the lender to hedge against the prepayment risk, and because many mortgage-backed securities pricing models incorporate this suboptimality via a so-called prepayment function which can depend, at time t, on whether the prepayment is optimal or not. We state the prepayment problem in the context of the optimal stopping theory and present an algorithm to solve the problem via weak convergence of computationally simple trees. Numerical results in the case of the Vasicek model and of the CIR model are also presented. The procedure is extended to the case when both the prepayment as well as the default are possible: in this case, we present a new method of building two-dimensional computationally simple trees, and we apply it to the optimal stopping problem.     

Optimal consumption choice with intolerance for declining standard of living

We reconsider the optimal consumption choice of investors who do not tolerate any decline in their consumption rate. We connect the demand behavior of such agents to the behavior of standard time-additive agents. With consumption ratcheting, the investor demands the running maximum of the optimal plan a conventional time-additive investor with lower initial wealth would choose. The analysis is carried out for Lévy processes, in particular for jump-diffusions. We obtain explicit solutions for all Bernoulli utility functions, not only those of CRRA type.     

Optimal consumption and investment under partial information

We consider a stock market model where prices satisfy a stochastic differential equation with a stochastic drift process. The investor’s objective is to maximize the expected utility of consumption and terminal wealth under partial information; the latter meaning that investment decisions are based on the knowledge of the stock prices only. We derive explicit representations of optimal consumption and trading strategies using Malliavin calculus. The results apply to both classical models for the drift process, a mean reverting Ornstein-Uhlenbeck process and a continuous time Markov chain. The model can be transformed to a complete market model with full information. This allows to use results on optimization under convex constraints which are used in the numerical part for the implementation of more stable strategies. Supported by the Austrian Science Fund FWF, project P17947-N12. We thank two anonymous referees for their comments which led to a considerable improvement of the paper.     

Optimal interest-rate rules and inflation stabilization versus price-level stabilization

This paper compares the properties of interest-rate rules such as simple Taylor rules and rules that respond to price-level fluctuations (called Wicksellian rules) in a basic forward-looking model. By introducing appropriate history dependence in policy, Wicksellian rules perform better than optimal Taylor rules in terms of welfare, robustness to alternative shock processes, and are less prone to equilibrium indeterminacy. A simple Wicksellian rule augmented with a high degree of interest rate inertia resembles a robustly optimal rule, i.e., a monetary policy rule that implements the optimal plan and that is also completely robust to the specification of exogenous shock processes.     

Optimal rules and robust Bayes estimation of a Gamma scale parameter

For estimating an unknown scale parameter of Gamma distribution, we introduce the use of an asymmetric scale invariant loss function reflecting precision of estimation. This loss belongs to the class of precautionary loss functions. The problem of estimation of scale parameter of a Gamma distribution arises in several theoretical and applied problems. Explicit form of risk-unbiased, minimum risk scale-invariant, Bayes, generalized Bayes and minimax estimators are derived. We characterized the admissibility and inadmissibility of a class of linear estimators of the form $cX\,{+}\,d$ , when $X\sim \varGamma (\alpha ,\eta )$ . In the context of Bayesian statistical inference any statistical problem should be treated under a given loss function by specifying a prior distribution over the parameter space. Hence, arbitrariness of a unique prior distribution is a critical and permanent question. To overcome with this issue, we consider robust Bayesian analysis and deal with Gamma minimax, conditional Gamma minimax, the stable and characterize posterior regret Gamma minimax estimation of the unknown scale parameter under the asymmetric scale invariant loss function in detail.     

Optimal consumption and investment under time-varying relative risk aversion

We consider the continuous time consumption-investment problem originally formalized and solved by Merton in case of constant relative risk aversion. We present a complete solution for the case where relative risk aversion with respect to consumption varies with time, having in mind an investor with age-dependent risk aversion. This provides a new motivation for life-cycle investment rules. We study the optimal consumption and investment rules, in particular in the case where the relative risk aversion with respect to consumption is increasing with age.     

Optimal extended complete block designs for dependent observations

Optimal designs under general dependence structures are usually difficult to specify theoretically or find algorithmically. However, they can sometimes be found for a specific dependence structure and a particular parameter value. In this paper, a class of generalized binary block designs with t treatments and b blocks of size k>t is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k−ht (if k > ht). For a suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. Some constructions for a universally optimal design are described. A negative dependence parameter, and some other dependence structures, are also considered.     

Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection

In a mean variance framework, we analyse risk taking in the presence of a (possibly) dependent background risk, exemplified in a linear portfolio selection problem. We first characterise the comparative statics of changes in the distribution and dependence structure of the background risk. For unfair, undesirable and loss-aggravating increases in background risks (both dependent and independent), we then present necessary and sufficient restrictions on preferences such that greater background uncertainty leads to reduced risk taking. With mean-variance preferences, these restrictions boil down to simple conditions on the marginal rate of substitution between risk and return. They can be easily related to familiar notions such as risk vulnerability, properness or standardness.     

Optimal monetary policy rules,financial amplification,and uncertain business cycles

This paper studies optimal monetary policy in the presence of ‘uncertainty’, time-variation in cross-sectional dispersion of firms׳ productive performance. Using a model with financial market imperfections, the results suggest that (i) optimal policy is to dampen the strength of financial amplification by responding to uncertainty (at the expense of creating mild degree of fluctuations in inflation). (ii) Higher uncertainty makes the welfare-maximizing planner more willing to relax financial constraints. (iii) Credit spreads are a good proxy for uncertainty. Hence, a non-negligible response to credit spreads – together with a strong anti-inflationary policy stance – achieves the highest aggregate welfare possible.