Catálogo de publicaciones - libros

We use principal component analysis (PCA) for extracting principal components having larger-power in cross correlation from risky assets (Elton and Gruber 1973), and random matrix theory (RMT) for removing noise in the correlation and for choosing statistically significant components (Laloux et al 1999, Plerou et al 1999) in order to estimate expected correlation in portfolio optimization problem. In addition to correlation between every pairs of asset returns, the standard mean-variance model of optimal asset allocation requires estimation of expected return and risk for each assets. Asset allocation is, in practice, quite sensitive to how to estimate the expected return. We applied estimation based on “beta” (following the idea of Black and Litterman 1992) to portfolio optimization for 658 stocks in Tokyo Stock Exchange (TSE). By using daily returns in TSE and verifying that TSE has qualitatively similar principal components as NYSE (Plerou et al 1999), we show (i) that the error in estimation of correlation matrix via RMT is more stable and smaller than either historical, single-index model or constant-correlation model, (ii) that the realized risk-return in TSE based on our method outperforms that of index-fund with respect to Sharpe ratio, and (iii) that the optimization gives a practically reasonable asset allocation.

As the two noise reduction methods are conceptually different, they also produce different results. Our preliminary studies cannot serve as a basis to make schematic suggestions as to which method ought to be preferred in which situation. This will always be difficult. But further and systematic studies extending the ones presented here might yield some guidelines.

Time changes of noise level at Warsaw Stock Market are analyzed using a recently developed method basing on properties of the coarse grained entropy. The condition of the minimal noise level is used to build an efficient portfolio. Our noise level approach seems to be a much better tool for risk estimations than standard volatility parameters. Implementation of a corresponding threshold investment strategy gives positive returns for historical data.

We examined the effectiveness of long-range weather forecasts applied to analyze weather derivatives. We carried out 651 back tests for different historical periods and confirmed that the accuracy of evaluating the risk of weather derivatives could be drastically improved by using long-range weather forecasts.

We review a resent performance measure for economical time series — the (optimal) investment horizon approach. For stock indices, the approach shows a pronounced gain-loss asymmetry that is observed for the individual stocks that comprise the index. This difference may hint towards an synchronize of the draw downs of the stocks.

We analyze the shares aggregated into the Dow Jones Industrial Average (DJIA) index in order to recognize groups of stocks sharing synchronous time evolutions. To this purpose, a pairwise version of the Chaotic Map Clustering algorithm is applied: a map is associated to each share and the correlation coefficients of the daily price series provide the coupling strengths among maps. A natural partition of the data arises by simulating a chaotic map dynamics. The detection of clusters of similar stocks can be exploited in portfolio optimization.

A so called Zipf analysis portofolio management technique is introduced in order to comprehend the risk and returns. Two portofoios are built each from a well known financial index. The portofolio management is based on two approaches: one called the “equally weighted portofolio”, the other the “confidence parametrized portofolio”. A discussion of the (yearly) expected return, variance, Sharpe ratio and follows. Optimization levels of high returns or low risks are found.

It is usually assumed that stock prices reflect a balance between large numbers of small individual sellers and buyers. However, over the past fifty years mutual funds and other institutional shareholders have assumed an ever increasing part of stock transactions: their assets, as a percentage of GDP, have been multiplied by more than one hundred. The paper presents evidence which shows that reactions to major shocks are often dominated by a small number of institutional players. Most often the market gets a wrong perception and inadequate understanding of such events because the relevant information (e.g. the fact that one mutual fund has sold several million shares) only becomes available weeks or months after the event, through reports to the Securities and Exchange Commission (SEC). Our observations suggest that there is a radical difference between small (< 0.5%) day-to-day price variations which may be due to the interplay of many agents and large (> 5%) price changes which, on the contrary, may be caused by massive sales (or purchases) by a few players. This suggests that the mechanisms which account for large returns are markedly different from those ruling small returns.

The risk of a credit portfolio depends crucially on correlations between the probability of default (PD) in different economic sectors. We present statistical evidence that a (one-) factorial model is sufficient to describe PD correlations, and suggest a method of parameter estimation which avoids in a controlled way the underestimation of correlation risk.

Anecdotal evidences suggest that a small number of firms continue to win until they finally acquire a big presence and monopolistic power in a market. To see whether such “winner-take-all” story is true or not, we look at the persistence of growth rates for Japanese small firms. Using a unique dataset covering half a million firms in each year of 1995–2003, we find the following. First, scale variables, such as total asset and sales, exhibit a divergence property: firms that have experienced positive growth in the preceding years are more likely to achieve positive growth again. Second, other variables that are more or less related to firm profitability exhibit a convergence property: firms with positive growth in the past are less likely to achieve positive growth again. These two evidences indicate that firm growth rates are not random but history dependent.