Kimball's prudence and two-fund separation as determinants of mutual fund performance evaluation

We consider investors with mean-variance-skewness preferences who aim at selecting one out of F different funds and combining it optimally with the riskless asset and direct stock holdings. Direct stock holdings are either exogenously or endogenously determined. In our theoretical section, we derive and discuss several performance measures for the investor's decision problems with a central role of Kimball's (1990) prudence and of several variants of Sharpe and Treynor measures. In our empirical section, we show that the distinction between exogenous and endogenous stock holding is less important than the issue of skewness preferences. The latter are most relevant for fund rankings, when an investor's skewness preferences are not derived from cubic HARA utility so that the two-fund separation theorem is not valid. Keywords: investor specific performance measure, performance evaluation, prudence, skewness preferences --

Two-Fund separation and positive marginal utility

The requirement of positive marginal utility only makes it possible to derive a restricted twofund separation theorem for portfolio selection problems replacing the original separation theorem of Cass and Stiglitz (1970). We use our findings for a re-examination of the bias-in-beta problem in mutual funds performance evaluation and of the relevance of the standard CAPM without borrowing restrictions. We also present empirical evidence for the only limited validity of the separation theorem when explicitly recognizing positive marginal utility. Moreover, quadratic utility functions are not apt to approximate the admissible range of risk preferences in the case of higher-order utility functions. --two-fund separation,HARA utility,positive marginal utility,borrowing restrictions,Capital Asset Pricing Model, bias in beta, performance evaluation

Performance evaluation, portfolio selection, and HARA utility

Our main goal is the generalization of the approach of Jobson and Korkie(1984) for funds performance evaluation. Therefore, we consider the portfolio selection problem of an investor who faces short sales restrictions when choosing among F different investment funds and assume the investor's utility function to be of the HARA type. We develop a performance measure and discuss its relationships to Treynor(1965), Sharpe(1966), Jensen(1968), Prakash and Bear(1986), and Grinblatt and Titman(1989). Particular attention is given to the special case of cubic utility implying skewness preferences. Our findings are illustrated by an empirical example. --HARA utility,performance evaluation,portfolio selection,skewness

Implied rates of return, the discount rate effect, and market risk premia

We show analytically under quite general conditions that implied rates of return based on analysts' earnings forecasts are only a downward biased estimator for future expected one-period returns and therefore not suited for computing market risk premia. The extent of this bias is substantial as verified by a bootstrap approach. We present an alternative estimation equation for future expected one-period returns based on current and past implied rates of return that is superior to simple estimators based on historical returns. The reason for this superiority is a lower variance of estimation results and not the circumvention of the discount rate effect typically stated as a major problem of estimators based on historical return realizations. The superiority of this new approach for portfolio selection purposes is verified numerically for our bootstrap environment and empirically for real capital market data. --analysts' earnings forecasts,discount rate effect,equity premium puzzle,implied rate of return

Coherent banking capital and optimal credit portfolio structure

Coherent measures of a bank's whole risk capital imply a structure of a bank's optimal credit portfolio that is independent of its deposits and the expected deposit rate, of expected bankruptcy costs and of expected costs of regulatory capital. --Basel II,Regulatory Capital,Coherent Risk Capital,Separation

Investors' direct stock holdings and performance evaluation for mutual funds

Investors need performance measures particularly as a means for funds selection in the process of exante portfolio optimization. Unfortunately, there are various performance measures recommended for different decision situations. Since an investor may be uncertain which kind of decision problem is best apt to describe his personal situation the question arises up to which extent funds rankings react sensitive with respect to changes in performance measurement. To be more precise, an investor with mean-variance preferences is considered who is trying to identify the best fund f* out of a set consisting of F funds and to combine this one optimally with the direct holding of a broadly diversified (reference) portfolio P of stocks as well as riskless lending or borrowing. For an investor just starting to acquire risky securities all three fractions of the various assets in question as part of his overall portfolio can be considered variable, while there also might be investors with already given direct holdings of stocks amounting to a certain fraction of their total wealth which cannot or shall not be altered. For both situations different adequate performance measures have been suggested by Breuer/Gürtler (1999, 2000) and Scholz/Wilkens (2003). We analyze theoretically as well as empirically possible deviations in resulting funds rankings for the two decision situations described previously. While there are indeed only loose theoretical relationships between the performance measures under consideration, empirical evidence suggests almost identical funds rankings. As a consequence, potential investors need not bother much about whether their situation is best described by an already fixed or a still variable amount of direct stock holdings. Moreover, traditional performance measures like the Sharpe ratio or the Treynor ratio will in general lead to reasonable funds selection in both situations. -- Performancemaße werden von Investoren insbesondere als Mittel zur Selektion von Investmentfonds im Rahmen von Ex-ante-Optimierungen verwandt. Unglücklicherweise existieren verschiedene Performancemaße für unterschiedliche Entscheidungsprobleme. Da ein Anleger im Unklaren darüber sein mag, welches Entscheidungsproblem am besten seine persönliche Situation beschreibt, drängt sich die Frage auf, in welchem Ausmaß Fondsrankings auf einen Wechsel des Performancemaßes reagieren. Präziser formuliert, wird ein Investor mit u-o-Präferenzen betrachtet, der versucht, den besten Fonds f* aus einer Menge von F zur Auswahl stehenden zu bestimmen und diesen in optimaler Weise mit dem direkten Halten eines breit diversifizierten (Referenz-) Portfolios P aus Aktien sowie risikoloser Anlage bzw. Verschuldung zu kombinieren. Aus Sicht eines Investors, der gerade beginnt, seine Mittel in riskanten Aktiva anzulegen, können alle Anteile der verschiedenen Aktivaklassen an seinem Gesamtvermögen als variabel aufgefasst werden, während auch Anleger mit bereits vor Fondsselektion gegebenem positiven Aktienengagement existieren mögen, das nicht ohne weiteres geändert werden kann oder soll. Für beide Situationen wurden geeignete Performancemaße vorgeschlagen, und zwar von Breuer/Gürtler (1999, 2000) und Scholz/Wilkens (2003). Mögliche Unterschiede in den jeweiligen Fondsreihungen für die beiden genannten Entscheidungssituationen werden theoretisch wie empirisch untersucht. Während sich nur lockere theoretische Zusammenhänge belegen lassen, weist der empirische Befund auf tatsächlich fast identische Reihungen hin. Als Konsequenz hieraus müssen sich potentielle Anleger nicht allzu viele Gedanken darüber machen, ob ihre Situation besser durch ein fixes oder ein variables Aktienengagement beschrieben wird. Ferner führen traditionelle Performancemaße wie die Sharpe Ratio oder die Treynor Ratio in beiden Entscheidungssituationen zu akzeptablen Reihungen.Performance measurement,Sharpe ratio,Treynor ratio,optimal portaolio selection,Performancemessung,Sharpe-Maß,Treynor-Maß,optimale Portfolioselektion

Statistical physics of neural systems with non-additive dendritic coupling

How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such non-additive dendritic processing on single neuron responses and the performance of associative memory tasks in artificial neural networks. First, we compute the effect of random input to a neuron incorporating nonlinear dendrites. This approach is independent of the details of the neuronal dynamics. Second, we use those results to study the impact of dendritic nonlinearities on the network dynamics in a paradigmatic model for associative memory, both numerically and analytically. We find that dendritic nonlinearities maintain network convergence and increase the robustness of memory performance against noise. Interestingly, an intermediate number of dendritic branches is optimal for memory functionality

Analysts' dividend forecasts, portfolio selection, and market risk premia

The most relevant practical impediment to an application of the Markowitz portfolio selection approach is the problem of estimating return moments, in particular return expectations. We analyze the consequences of using return estimates implied by analysts' dividend forecasts under the explicit notion of taxes and non-flat term structures of interest rates and achieve quite good performance results. As a by-product, these results cast some doubt upon the adequacy of estimating market risk premia with implied returns, because estimation techniques with good performance results are hardly suited to describe market expectations. --analysts' forecasts,CAPM,implied returns,market risk premium,portfolio optimization,return estimation

Stochastic simulation algorithm for the quantum linear Boltzmann equation

We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The algorithm leads to a numerically efficient stochastic simulation procedure for the most general form of this integro-differential equation, which involves a five-dimensional integral over microscopically defined scattering amplitudes that account for the gas interactions in a non-perturbative fashion. The simulation technique is used to assess various limiting forms of the quantum linear Boltzmann equation, such as the limits of pure collisional decoherence and quantum Brownian motion, the Born approximation and the classical limit. Moreover, we extend the method to allow for the simulation of the dissipative and decohering dynamics of superpositions of spatially localized wave packets, which enables the study of many physically relevant quantum phenomena, occurring e.g. in the interferometry of massive particles.Comment: 21 pages, 9 figures; v2: corresponds to published versio

Стохастическое моделирование физико-механических полей

В статье предлагаются конструктивные методы и алгоритмы стохастического моделирования физико-механических полей на основе теории R-функций и нечёткой логики, позволяющие учитывать технические и технологические допуски на геометрическую и физическую информацию, погрешности измерений, ошибки округления, и на основе анализа их комплексного влияния на решение делать экспертное заключение.The constructive methods and algorithms for simulation of physical-mechanical fields based on the Rfunctions theory and fuzzy logics are elaborated which allow us take into account technical and technological assumptions on geometrical and physical informations, meassuring errors, rounding errors, and draw expert conclusions