Patrizia Stucchi

Su Una Estensione Bidimensionale del Teorema di Scomposizione di Peccati

Facendo ricorso all’introduzione di una opportuna condizione di sincronia fra due coppie di tassi (i, j), esterna, e (i*, j*), interna, si dimostra che condizione necessaria e sufficiente per la validità finanzíaria di una estensione hidimensionale del teorema di scomposizione di Peccati è che le due coppie (i, j) e (i*, j*) soddisfino tale proprietà di sincronia.SummaryThis paper keeps as starting poing the Peccati’s decomposition of the d.c.f. of an enterpreneural project seen as a present value of single-period results, recently given by the author in an unidimensional framework. The goal of the paper is twofold: the first is to provide a bidimensional extension of the decomposition in order to keep account of mixed projects, that is projects that according to any internal couple (i*, j*) reveal alternance of investment and respectively collection periods. A straightforward extension is given on the basis of a simple analogic argument. But a more careful evaluation of the problem suggests that if we require that the decomposition be meaningful from a financial point of view. things are no more simple either in one or in two dimensions.To solve the problem we introduce a proper synchrony condition: precisely, the pair of couples (i, j) and (i*, j*) are said to satisfy the synchrony condition if and only if the sequences of the signs of the partial balancesMt(i, j) andMt(i*, j*) are the same. After that we are able to show that, with reference to a couple (i, j) of external rates, a bidimensional decomposition centered on an internal couple (i*, j*) is meaningful if and only if the pair (i, j) and (i*, j*) satisfy the synchrony condition. Formally, the result comes as a nice byproduct of a rule on the factorization of particular bivariate polynomials recently given by Stucchi. In particular going back to a one-dimensional world, it turns out that for pure investment (Soper) projects the synchrony condition works as a condition of applicability of the Peccati’s decomposition.

Synthetic portfolio insurance on the Italian stock index: From theory to practice

Abstract We claim here that a practical way to create synthetic portfolio insurance on the Italian stock market index (not currently traded) should be to select a portfolio of a small number of Italian blue chips properly composed so as to be a good proxy of the market index, and to revise proportions between the proxy and the risk-free asset only if the difference between the current composition and the theoretically optimal one exceeds some fixed bound so as to squeeze transaction costs. With reference to a three-year weekly data base of the Milan Stock Exchange, this paper reports results of a test of efficiency of strategies of this type in granting synthetic portfolio insurance.

A Comparison of Ranking Criteria: an Application to Asset Class Indices of Europe, US, Russia and China

The main purpose of this work is the ex post comparison of the performances of three macro asset class indices for Europe, United States, Russia and China during the period 2003-2015. The analysis is based on six different ranking criteria, starting with the well-known Sharpe index and its VaR and CVaR modifications, then considering the Omega and Sortino ratios which employ higher partial moments, and at last the Rachev ratio which changes the profitability index. All the previous performance indices give substantially the same ranking; they all show supremacy of Chinese fixed income and both European and American real estate in the years 2003-2008; they indicate US and European stock indices as the worst performers in 2008, and American, Russian and Chinese fixed income indices from 2012 to 2015 again as the worst performers. A visual display of the six different rankings is also provided, highlighting the adequacy of the Sharpe ratio against its more refined alternatives.