Weak Form Tests of Efficient Market Hypothesis: Evidence from CEE-Countries and Russian Stock Markets

Tämän tutkielman tavoitteena on selvittää Venäjän, Slovakian, Tsekin, Romanian, Bulgarian, Unkarin ja Puolan osakemarkkinoiden heikkojen ehtojen tehokkuutta. Tämä tutkielma on kvantitatiivinen tutkimus ja päiväkohtaiset indeksin sulkemisarvot kerättiin Datastreamin tietokannasta. Data kerättiin pörssien ensimmäisestä kaupankäyntipäivästä aina vuoden 2006 elokuun loppuun saakka. Analysoinnin tehostamiseksi dataa tutkittiin koko aineistolla, sekä kahdella aliperiodilla. Osakemarkkinoiden tehokkuutta on testattu neljällä tilastollisella metodilla, mukaan lukien autokorrelaatiotesti ja epäparametrinen runs-testi. Tavoitteena on myös selvittääesiintyykö kyseisillä markkinoilla viikonpäiväanomalia. Viikonpäiväanomalian esiintymistä tutkitaan käyttämällä pienimmän neliösumman menetelmää (OLS). Viikonpäiväanomalia on löydettävissä kaikilta edellä mainituilta osakemarkkinoilta paitsi Tsekin markkinoilta. Merkittävää, positiivista tai negatiivista autokorrelaatiota, on löydettävissä kaikilta osakemarkkinoilta, myös Ljung-Box testi osoittaa kaikkien markkinoiden tehottomuutta täydellä periodilla. Osakemarkkinoiden satunnaiskulku hylätään runs-testin perusteella kaikilta muilta paitsi Slovakian osakemarkkinoilla, ainakin tarkastellessa koko aineistoa tai ensimmäistä aliperiodia. Aineisto ei myöskään ole normaalijakautunut minkään indeksin tai aikajakson kohdalla. Nämä havainnot osoittavat, että kyseessä olevat markkinat eivät ole heikkojen ehtojen mukaan tehokkaita

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

Monte Carlo Hypothesis Testing with The Sharpe Ratio

The purpose of this master thesis was to perform simulations that involve use of random number while testing hypotheses especially on two samples populations being compared weather by their means, variances or Sharpe ratios. Specifically, we simulated some well known distributions by Matlab and check out the accuracy of an hypothesis testing. Furthermore, we went deeper and check what could happen once the bootstrapping method as described by Effrons is applied on the simulated data. In addition to that, one well known RobustSharpe hypothesis testing stated in the paper of Ledoit and Wolf was applied to measure the statistical significance performance between two investment founds basing on testing weather there is a statistically significant difference between their Sharpe Ratios or not. We collected many literatures about our topic and perform by Matlab many simulated random numbers as possible to put out our purpose; As results we come out with a good understanding that testing are not always accurate; for instance while testing weather two normal distributed random vectors come from the same normal distribution. The Jacque-Berra test for normality showed that for the normal random vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal distribution in contrast 5,3% and 4,3% failed to shown the truth already known; but when we introduce the bootstrapping methods by Effrons while estimating pvalues where the hypothesis decision is based, the accuracy of the test was 100% successful. From the above results the reports showed that bootstrapping methods while testing or estimating some statistics should always considered because at most cases the outcome are accurate and errors are minimized in the computation. Also the RobustSharpe test which is known to use one of the bootstrapping methods, studentised one, were applied first on different simulated data including distribution of many kind and different shape secondly, on real data, Hedge and Mutual funds. The test performed quite well to agree with the existence of statistical significance difference between their Sharpe ratios as described in the paper of Ledoit andWolf.