2015. vol. 19. No. 4

We analyze optimal execution strategies when multiple traders are simultaneously in­volved in optimal execution. In this case, we obtain new trading strategies that follow from a direct extension of the mean variance approach of Grinold and Kahn, and Almgren and Chriss. However, as we show below, the proposed strategies can be quite different from the standard ones obtained in Grinold and Kahn, and Almgren and Chriss. This is because each trader (assu­med to be rational) is trying to minimize her trading cost or ‘implementation shortfall’ and therefore takes into account the price impacts caused by herself and all other traders. We also obtain a close form characterization for the dynamic Nash equilibrium in terms of the system of second-order ODEs, which can be solved explicitly. The resulting equilibrium strategies describe different types of predatory and defensive behavior, though aggregate order flow profile have some properties of standard Almgren, Chriss strategies, e.g. is monotoneous and convex. We show that the traders with smaller holdings are involved in predatory strategies, while traders with larger holdings tend to defend themselves against potential predators by following the de­layed trading strategies. We also show that depending on liquidity and volatility parameters, predatory traders may be frontrunners or contrarian traders.

At first, we discuss whether the concept of economic cycles is at all applicable to the rea­lities of the Russian economy. As for several subperiods during the last 35 years, it has been not only market but planned and transformed also, this issue is arguable. But in our opinion, all mid-term factors of total economic activity – positive as well as negative – may be divided into three groups: an exhaustion of old drivers for economic growth or an emergence of new ones; positive or negative external shocks; destructive or constructive decisions and actions made by monetary and non-monetary authorities. From this point on, mid-term fluctuations in the level of economic activity (and in the volume of output) may be described as a sequence of non-periodic expansions and contractions. In other words, as a phenomenon of cyclical economic movements with its peaks and troughs.

On these grounds, we established a reference chronology for the Russian economic cycle from the early 1980s to mid-2015. As there is no single monthly indicator available for the whole period, we used a set of indices. To be precise, six indices of industrial production and three indices of output by basic branches (official as well as non-official). We also tried two methods of seasonal adjustments (X-12-ARIMA and TRAMO/SEATS) and four methods for dating cyclical turning points (local min/max, Bry-Boschan, Harding-Pagan, and Markov-Switching model). As various combinations of initial data and various statistical methods usually led to different estimates of peaks and troughs, the final decision was made according to several additional qualitative criteria. The resulting set of turning points looks plausible and separates expansions and contractions in an explicable manner, but further investigations and discussions are needed to establish a consensus in the expert community.

In this paper we use standard methods and construct our own methodology of dating business cycle in the Russian economy in post-soviet era starting from the middle of 1990-ies. The main purpose of this paper is identification and dating of business cycles in the Russian eco­nomy during the last fifteen years. We use dating approaches of Harding – Pagan and Hamilton as a benchmark. This way we found turning points of the reference cycle starting from the second half of 1990-ies. It worth noting that both methods give very similar results. As a primary data in out analysis we used data on national accounts from Rosstat. We also use various data from Archive of Economic and Sociological Data of NRU-HSE. Our main finding is that during 1998–2014 the Russian economy went through two full business cycles with trough sin October, 1998 and May, 2009 and peaks in April, 2008 and September, 2012. Starting from that month the Russian economy stopped exhibiting growth and first went into stagnation period and then into deep recession from the beginning of 2015. In this paper we also date the growth cycles for the Russian economy. Our main finding is that in this case we found two more recessions in the growth cycle framework: from November, 2001 until June, 2002 and June, 2004 until January, 2005. The last recession in the growth cycle started in January, 2012.

The paper provides theoretical explanations of the influence of political institutions and economic inequality on barriers to entry on markets, a level of redistribution, technological progress and economic growth. The model combines two approaches of modern economic lite­rature, endogenous growth models of creative destruction and the approach of the political economy of development, according to which political institutions determine a social choice of economic institutions, which influence long-term growth rates. On the first step of the game agents differing in their incomes, skills and political power, make a social decision about the level of redistribution and the level of barriers to entry on markets. On the second step agents make economic decisions on investment, production and consumption. Political regimes differ in the distribution of votes between the members of elite and other citizens. The model explains the empirical evidence, suggesting that the transition to democracy in short and middle term reduces inequality in incomes, but does not always lead to the formation of institutions, favoring the equality of opportunities. In the model the influence of political regimes on barriers to entry on markets depends on the initial level of inequality in incomes and skills, and also on the average level of skills. In a society with a high level of inequality in incomes and skills, the existence of a majority coalition, which support a high level of barriers to entry on markets is more probable. This coalition will include the richest agents and the least skilled agents. The results of the model explain different outcomes of democratization process in terms of its effect on barriers to entry on markets and economic growth. The paper also considers four examples of third-wave democratization, which illustrates the results of the model.

One source of information for analyzing profitability of investments is the yields on go­vernment bonds with different maturities. However, the fact that bonds are rarely zero-coupon prevents the direct use of these yields. Since payments on bonds are done indifferent periods, the price of a bond is a sum of nonlinear components with interest rates corresponding to dif­ferent terms to maturity. The problem of obtaining zero-coupon yield data from bond prices is most acute for the markets such as Russian, where trade volumes are not as large and trans­actions do not happen very often.

The paper proposes a relatively easy-to-implement method for constructing parametric zero-coupon yield curve given price data, in which the parameters of the curve and volatility of the random disturbances are assumed to be time-varying, while the distribution of random disturbances is fat-tailed. The method modifies the classical Kalman filter and is based on the score vector of the measurement equation and the corresponding information matrix. The closest analogues of the proposed method are GAS (generalized autoregressive score) and DSC (dynamic conditional score) approaches . The method is not demanding to the quality of the data, since it is robust to outliers. Estimates of the interest rate curve are obtained adaptively and reflect the current market situation. Performance of the method is assessed against the data on the Russian government bond market for the period from January 2008 to April 2015. We obtain estimates of the parameters of the dynamic Nelson – Siegel curve for this period.

Issue about relevancy of usage of concepts of representative and aggregate agents inmo-dern economic science is very actual. In theoretical model [Malakhov, Pospelov, 2014]showed, that distribution of banks on shares of assets is stable over time. If this results is correct for real data, then it will another argument to usage of concept of aggregate agent in modeling of banking sector, which is an actual topic for macroeconomists. In this paper we provide an empirical test of this result using data from Russian banking system. We also analyze other key variables, such as households’ deposits, firm’s credits, interbank credits, etc., because if distributions of shares of these variables are stable too, then it will be additional argument to usage of concept of aggregate agents. Aim of this paper is selection of optimal (in some sense) functional forms of distribution of shares of key variable and validating stability of these distributions over time. Actuality of this topic is also confirmed by recent events in Russian economy and banking system in particular.

We show that using generalized versions of well-known distributions, we can accurately describe the distribution of Russian banks in terms of turnover balance sheet. In particular, the Pareto distribution of type IV and asymmetric generalized error distribution show a very high accuracy of approximation and these results are correct for all considered variables. Quality of approximation by these distribution is robust, both in time and in the cross-sectional dimension, however, individual banks can move in distribution. Thus, we can’t talk about the distribution of individual banks but of the distribution of banks of the entire Russian banking system.

Moreover, estimations of parameters of distribution of shares of assets have been minorly changing during observation period and these changes could be possibly connected with structural shifts in banking industry. Kolmogorov – Smirnov test shows, that differences between distributions of shares of assets become significant at 5% confidence level, only when differ ence between periods is more than 8 months. Thus theoretical model [Malakhov, Pospelov, 2014] mainly passes the empirical test.