Miroslav Čulík, Ph. Dana Dluhošová doc. Jozef Fecenko, CSc.
Václav Jurečka, CSc. Eva Kislingerová, CSc. University of Economics Prague, Czech Republic doc. Martin Macháček, Ph. Anna Majtánová, Ventosa baňkování technika proti stárnutí. Dušan Marček, CSc. Miloš Mařík, CSc. University of Economics Prague, Czech Republic prof. Petr Musílek, Ph. Karol Vlachynský, CSc. Dana Dluhošová prof. In these problems, we try to find the optimal portfolio with respect to some objective function among all portfolios that dominate a given benchmark by a stochastic dominance relation.
We consider two orders of stochastic dominance the first and the second order stochastic dominance and the mean return criterion. Moreover, we employ three risk measures variance, Value at Risk and conditional Value at Risk as the objectives. Hence we find 9 optimal portfolios that minimize risk under mean return or stochastic dominance constraints.
Financial Management of Firms and Financial Institutions 9 th International Scientific Conference
We use 30 years long history data from US stock market. Moreover, we apply the cross-validation techniques and we compare the evolution of the optimal portfolios during the last 5 years.
Introduction Mathematical formulations of decision making problems under risk lead to stochastic programming models which search for the optimal solution with respect to a given objective criterion nejlepší taktika proti stárnutí feasibility constraints. In financial applications, they turn out to so called portfolio selection problems.
The first portfolio selection problem was introduced by Markowitz The model jointly focuses on maximizing expected return and minimizing variance of the portfolio, where variance serves as a measure of risk. It was the first example of bi-objective portfolio optimization problems which are called mean-risk models. Later on, the meanrisk models were enriched by stochastic dominance relations.
Dentcheva and Ruszczyńskiintroduced portfolio selection models that minimize an objective on the set of portfolios that dominates a benchmark with respect to the second order stochastic dominance. Similarly, Dentcheva and Ruszczyński and Noyan and Ruszczyński analyzed optimization models with the first order stochastic dominance.
The notion of stochastic dominance was introduced in statistics more than 50 years ago and it was firstly applied to economics and finance in Quirk and SaposnikHadar and Ventosa baňkování technika proti stárnutí and Hanoch and Levy Portfolios that dominate a benchmark by the first order stochastic dominance FSD are preferred to the benchmark by all non-satiated decision makers.
In the case when only risk averse decision makers are of interest, they prefer a portfolio to the benchmark if the portfolio dominates the benchmark by the second order stochastic dominance SSD.
Miloš Kopa, Ph. Ventosa baňkování technika proti stárnutí the empirical application, we consider US stock market data from year We firstly find nine optimal portfolios three objectives and three types of constraints using annual data from to Then we compare an out-of-sample performance of these nine portfolios.
The reminder of the paper is structured as follows. Section 2 introduces a basic notation and definitions of the portfolio selection theory and stochastic dominance relations. It is followed by formulations of nine considered optimization problems. Section 4 introduces data and presents results of the empirical study. Finally, the paper is concluded in Section Preliminaries Let us consider a random vector of returns of n base assets.
We assume that the returns have discrete probability distribution given by T equiprobable scenarios. We will use for the vectors Ventosa baňkování technika proti stárnutí portfolio weights and for a compact convex set of portfolio weights.
Definition 1: We say that a portfolio dominates another portfolio with respect to the first order stochastic dominance if and only if for all utility functions u provided the expected values above are finite. Definition 2: We say that a portfolio dominates another portfolio with respect to the second order stochastic dominance if and only if for all concave utility functions u provided the expected Ventosa baňkování technika proti stárnutí above are finite.
The second order stochastic dominance relation can be verified by comparing either twice cumulative distribution functions or second quantile functions or conditional values at risk, see for example Kopa and Chovanec The only difference is in the specification of matrix elements. While matrix allows only binary elements permutation matrixa double stochastic matrix may consist of any positive elements.
Of course, in both cases, all row sums and all column sums has to equal one. Now we can combine three risk objectives with three types of constraints. We consider a standard set of 10 active benchmark stock portfolios as the base assets. They are formed, and annually rebalanced, based Ventosa baňkování technika proti stárnutí individual stocks market capitalization of 18 equity, each representing a decile of Ventosa baňkování technika proti stárnutí cross-section of stocks in a given year.
The first decile stocks the smallest size are called small and the last decile stocks are called large. We use data on annual excess returns from to 30 observations. Hence we have base assets and scenarios. First, we present descriptive Ventosa baňkování technika proti stárnutí of considered base assets in Table 1. Table 1: Base assets : descriptive statistics mean st.
If it is the case, then the only dominating portfolio is the benchmark. Hence the optimal portfolio of the corresponding model is the benchmark and one need not to solve the optimization problems from Section Ventosa baňkování technika proti stárnutí.
Poté přiloţíme těsnící krouţky a šroubky přitáhneme. Pro správné fungování přístroje je nutné, aby odkládací deska byla dobře upevněna. Horní desku připevníme tak, ţe umělohmotný čep nasadíme do dráţek na horní části přístroje viz detail B a lehkým zatlačením ji upevníme tak, aby nám ohnutý okraj desky zapadl do dráţky na zadní části přístroje.
We find that the benchmark is inefficient in both cases. Now we proceed with computing of nine optimal portfolios for three considered risk measures and three types of constraints.
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Table 2 summarizes the compositions of the optimal portfolios. Since the SSD constraints always imply the mean return constraints, they identify the smaller feasibility set than the mean return constraints. Perhaps surprisingly, in this study, we show that the differences between the optimal portfolios of the problems with mean return constraints and the optimal portfolios of the problems with SSD constraints are very small, no matter which measure of risk is considered.
Taking FSD constraints, the feasibility set Ventosa baňkování technika proti stárnutí even smaller than in the SSD case, however, in this case, the difference is substantial, because the corresponding optimal portfolios consist of different base assets with different weights.
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We can see all these differences between the optimal portfolios also in the Table 3 which present in-sample descriptive statistics. It is accompanied by the higher mean returns and smaller minimal returns of optimal portfolios of the FSD constraint problems related to other optimal portfolios when considering the same risk measure in the objective. We have analyzed their in-sample and out-of sample performance and compared them Ventosa baňkování technika proti stárnutí each other.
The considered optimization problems were formulated combining three risk measures variance, VaR and CVaR with three types 20 of constraints mean return constraints, FSD constraints and SSD constraints. For a Ventosa baňkování technika proti stárnutí risk measure, FSD constraint problems give a portfolio with the highest mean, variance and minimal return, no matter which risk measure is considered.
Moreover, this finding holds true also for the out-of-sample data.
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The optimal portfolios of FSD constraint problems significantly differ from the others. Finally we have shown that the optimal portfolios of CVaR constraint problems are very similar to the optimal portfolios of the mean return constraint problems, when taking the same risk objective. This analysis could be enriched by the optimization problems with higher order Ventosa baňkování technika proti stárnutí dominance constraints, see e.
Post and Kopa a or other risk measures or with other relations, for example coming from the Data envelopment analysis, see e. Branda and Kopa Finally, one can employ the bootstrap technique as e. Dentcheva and RuszczyńskiKopa and Dupačová and Kopa Unfortunately, all these modifications would either significantly increase the computational burden or lead to non-tractable formulations.
A second-order stochastic dominance portfolio efficiency measure. A portfolio optimality test based on the first order stochastic dominance criterion. Efficient Ventosa baňkování technika proti stárnutí according to stochastic dominance criteria. Stochastic dominance: Investment decision making under uncertainty. Second edition.
Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements, Annals of Operations Research. Portfolio Selection. Portfolio Selection: Efficient Diversification of Investments. Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints, Mathematical Programming,  PFLUG, G.
Some remarks on the value at risk and the conditional value-at-risk. Uryasev, ed. Empirical tests for stochastic dominance efficiency. Conditional value-at-risk for general loss distributions.
The aim of this paper is to describe and to appraise the pension reform and the contemporary situation and try to predict the future development. Key words Pension reform, pension funds, 2 nd funds.
Introduction The pension reform in the Czech Republic officially started January From this date it was possible to enter the new 2nd pillar but the number of participants in the 2nd pillar is still very small.
It is evident especially considering the reality that it was only possible till June to Ventosa baňkování technika proti stárnutí this reform for older participants. This means that it was not allowed for those who were older than 35 to enter the 2nd pillar after Ventosa baňkování technika proti stárnutí date. This paper is focused on the new 2nd pillar and on the changes of the 3rd pillar.
Characteristics of the Pension Reform in the Czech Republic Originally the Czech pension system was defined as a two-pillar system. The 1st and by far thickest pillar is the state pension system, which is paid into by all employed citizens - people pay their pensions for 28 percent of gross salary.
It is termed pay-as-you-go; it means that the demands of the present pension system draw on those funds in the same time. The 1st pillar is compulsory and nowadays it is the main source of retirement funds.
On the contrary the 3rd pillar is voluntary and it is based on investing into pension funds. This was the situation before the pension reform. The 2nd pillar is the new possibility of investing. It entered into force January and allows carrying on the part of compulsory contributions in the 1st pillar to private accounts.
The state will do 25 percent of participants gross wages, and it will be able to transfer 3 percent to the pension fund.
All participants must add other 2 percent Ventosa baňkování technika proti stárnutí their gross monthly salary.
The entry to this pillar is voluntary but when you decide to join the 2nd pillar you are not allowed to get out. Kateřina Kořená, Ph.
Participants can invest Ventosa baňkování technika proti stárnutí the dynamic, balanced or conservative fund or into the government bonds fund. There were radical changes of the existing 3rd pillar, too.
Nowadays 2 types of funds are registered: the old transformed funds and the new participation funds. The most important is that from the January you can enter only the new registered type of pension fund.
Your advantage is you can choose a more dynamic investment strategy, on the contrary the Nejlepší proti stárnutí pod očním korektorem from this fund depends on this strategy and it is not guaranteed as it is in the old transformed funds.
Another important change in this pension scheme is a change of the state contribution. Till this change you could receive the state subsidy even you save only CZK monthly, now you must save at least CZK monthly.
On the other hand the value of the state contribution can be higher than before in case you save CZK monthly, the state contribution is CZK. Beginning of the Pension Reform in the Czech Republic Officially marie veronique olej proti stárnutí plus recenze pension reform started January ; the laws were accepted one year Ventosa baňkování technika proti stárnutí at the end of This time should have been given to preparations and explanations of the necessity of the pension reform but the situation was different.
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It is necessary to say that neither the pension reform was prepared nor the potential participants and funds. The prevailing mood in society was against the pension reform because of the bad position of that time government.
It is clear that the political risk connected to this reform had become the most important issue. We could see it during the whole half of the year when the pension reform was criticized and questioned by the opposition parties.
This was shown by the proclamation of the chairman of the strongest opposition political party The Social Democrats Bohuslav Sobotka - he advised the participants and funds not to enter the 2nd pillar.
He proclaimed that after elections that time the regular in his party would cancel the 2nd pillar. After this proclamation many potential participants thought they might lose their money in this case and that their money might be confiscated although this had never been said.
Government officials were not able to find an adequate respond to this situation. This means that the government was no longer able to explain the indispensability of the pension reform because of the demographic and economic situation.
The MIXA krem na vrásky s mistake was allowing the perception of the reform as the political issue. The result was that the majority of Czech citizens were not persuaded about the necessity of the pension reform.
Contemporary Situation The beginning of the pension reform was very slow and complicated. The implementing regulations were accepted at the end of after a nontransparent vote in the Chamber of Deputies of the Czech Parliament. Because of this confused situation it was not totally clear even in January how many funds would take part in the reform and which types of funds would Ventosa baňkování technika proti stárnutí offered.