Modeling asset allocation strategies and a new portfolio performance score
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We discuss a powerful, geometric representation of financial portfolios and stock markets, which identifies the space of portfolios with the points lying in a simplex convex polytope. The ambient space has dimension equal to the number of stocks, or assets. Although our statistical tools are quite general, in this paper we focus on the problem of portfolio scoring. Our contribution is to introduce an original computational framework to model portfolio allocation strategies, which is of independent interest for computational finance. To model asset allocation strategies, we employ log-concave distributions centered on portfolio benchmarks. Our approach addresses the crucial question of evaluating portfolio management, and is relevant to the individual private investors as well as financial organizations. We evaluate the performance of an allocation, in a certain time period, by providing a new portfolio score, based on the aforementioned framework and concepts. In particular, it relies on the expected proportion of actually invested portfolios that it outperforms when a certain set of strategies take place in that time period. We also discuss how this set of strategies – and the knowledge one may have about them – could vary in our framework, and we provide additional versions of our score in order to obtain a more complete picture of its performance. In all cases, we show that the score computations can be performed efficiently. Last but not least, we expect this framework to be useful in portfolio optimization and in automatically identifying extreme phenomena in a stock market.
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