A multi-horizon scale for volatility

We decompose volatility of a stock market index both in time and scale using wavelet filters and design a probabilistic indicator for valatilities, analogous to the Richter scale in geophysics. The peak-over-threshold method is used to fit the generalized Pareto probability distribution for the extreme values in the realized variances of wavelet coefficients. The indicator is computed for the daily Dow Jones Industrial Averages index data from 1986 to 2007 and for the intraday CAC 40 data from 1995 to 2006. The results are used for comparison and structural multi-resolution analysis of extreme events on the stock market and for the detection of financial crises.Stock market, volatility, wavelets, multi-resolution analysis, financial crisis.

Asymptotic and bootstrap properties of rank regressions

The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^{-1/6}. The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^{-1/2}. The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.Rank Estimators, Bootstrap, M-Estimators, U-Statistics, U-Processes

Tax reform in the oil sector of Russia - a positive assessment

I analyze the system of taxes imposed on the Russian oil sector before and after the tax reform of 2002. I first establish a price parity relation explaining the gap between the world and domestic prices through export duties and alternative transportation costs. Based on it, I argue that the indirect taxes (VAT, the sales and excise taxes) do not decrease the net profits of oil producers, but are mostly shifted onto consumers. The tax burden on producers, on the other hand, consists of the export duties, resource payments, the profit tax and the property tax. I show that the tax reform had little effect on the total amount of taxes imposed on producers, but changed its structure across the types of taxes. After the reform the share of efficiently collected taxes, most importantly the extraction tax (ET), increased, explaining higher tax revenues. Finally, I estimate the extent to which the extraction tax is economically inefficient. By showing that the deadweight loss associated with ET is only a small fraction of the generated tax revenues, I argue that ET is a better choice for capturing the natural rent in the Russian oil sector than the poorly controlled profit tax. On the whole, this evidence depicts the reform of oil taxation in 2002 as a big step forward of the Russian fiscal system. This report is a shorter English version of the paper "Estimating the tax burden in the Russian oil sector under the price parity hypothesis" (Ekonomika i Matematicheskie Metody (2005), 41, 3).Russian oil sector; price parity; tax reforms in Russia

On the Equivalence of Dual Theories

We discuss the equivalence of two dual scalar field theories in 2 dimensions. The models are derived though the elimination of different fields in the same Freedman--Townsend model. It is shown that tree $S$-matrices of these models do not coincide. The 2-loop counterterms are calculated. It turns out that while one of these models is single-charged, the other theory is multi-charged. Thus the dual models considered are non-equivalent on classical and quantum levels. It indicates the possibility of the anomaly leading to non-equivalence of dual models.Comment: 14 pages, LaTeX; 2 figures, encapsulated PostScrip

Investigating value and growth : what labels hide ?

Value and growth investment styles are a concept which has gained extreme popularity over the past two decades, probably due to its practical efficiency and relative simplicity. We study the mechanics of different factors' impact on excess returns in a multivariate setting. We use a panel of stock returns and accounting data from 1979 to 2007 for the companies listed on NYSE without survivor bias for clustering, regression analysis and constructing style based portfolios. Our findings suggest that value and growth labels often hide important heterogeneity of the underlying sources of risks. Many variables, conventionally used for style definitions, cannot be used jointly, because they affect returns in opposite directions. A simple truth that more variables does not necessarily mean better model nicely summaries our results. We advocate a more flexible approach to analyzing accounting-based factors of outperformance treating them separately before or instead of aggregating.Style analysis, value puzzle, pricing anomalies, equity.

Predicting Stock Returns in a Cross-Section : Do Individual Firm chatacteristics Matter ?

It is a common wisdom that individual stocks' returns are difficult to predict, though in many situations it is important to have such estimates at our disposal. In particular, they are needed to determine the cost of capital. Market equilibrium models posit that expected returns are proportional to the sensitivities to systematic risk factors. Fama and French (1993) three-factor model explains the stock returns premium as a sum of three components due to different risk factors : the traditional CAPM market beta, and the betas to the returns on two portfolios, "Small Minus Big" (the differential in the stock returns for small and big companies) and "High Minus Low" (the differential in the stock returns for the companies with high and low book-to-price ratio). The authors argue that this model is sufficient to capture the impact on returns of companies' accounting fundamentals, such as earnings-to-price, cash flow-to-price, past sales growth, long term and short-term past earnings. Using a panel of stock returns and accounting data from 1979 to 2008 for the companies listed on NYSE, we show that this is not the case, at least at individual stocks' level. According to our findings, fundamental characteristics of companies' performance are of higher importance to predict future expected returns than sensitivities to the Fama and French risk factors. We explain this finding within the rational pricing paradigm : contemporaneous accounting fundamentals may be better proxies for the future sensitivity to risk factors, than the historical covariance estimates.Accounting fundamentals, equity performance, style analysis, value and growth, cost of capital.

Price Dynamics in Market with Heterogeneous Investment Horizons and Boundedly Rational Traders

This paper studies the effects of multiple investment horizons and investors' bounded rationality on the price dynamics. We consider a pure exchange economy with one risky asset, populated with agents maximizing CRRA-type expected utility of wealth over discrete investment periods. An investor's demand for the risky asset may depend on the historical returns, so that our model encompasses a wide range of behaviorist patterns. The necessary conditions, under which the risky return can be a stationary iid process, are established. The compatibility of these conditions with different types of demand functions in the heterogeneous agents' framework are explored. We find that conditional volatility of returns cannot be constant in many generic situations, especially if agents with different investment horizons operate on the market. In the latter case the return process can display conditional heteroscedasticity, even if all investors are so-called "fundamentalists" and their demand for the risky asset is subject to exogenous iid shocks. We show that the heterogeneity of investment horizons can be a possible explanation of different stylized patterns in stock returns, in particular, mean-reversion and volatility clustering.Asset pricing, heterogeneous agents, multiple investment scales, volatility clustering.