Modeling asset allocations and a new portfolio performance score

Abstract

We discuss and extend a powerful, geometric framework to represent the set of portfolios, which identifies the space of asset allocations with the points lying in a convex polytope. Based on this viewpoint, we survey certain state-of-the-art tools from geometric and statistical computing to handle important and difficult problems in digital finance. Although our tools are quite general, in this paper, we focus on two specific questions. The first concerns crisis detection, which is of prime interest for the public in general and for policy makers in particular because of the significant impact that crises have on the economy. Certain features in stock markets lead to this type of anomaly detection: Given the assets' returns, we describe the relationship between portfolios' return and volatility by means of a copula, without making any assumption on investors' strategies. We examine a recent method relying on copulae to construct an appropriate indicator that allows us to automate crisis detection. On real data the indicator detects all past crashes in the cryptocurrency market and from the DJ600-Europe index, from 1990 to 2008, the indicator identifies correctly 4 crises and issues one false positive for which we offer an explanation. Our second contribution is to introduce an original computational framework to model asset allocation strategies, which is of independent interest for digital finance and its applications. Our approach addresses the crucial question of evaluating portfolio management, and is relevant the individual managers as well as financial institutions. To evaluate portfolio performance, we provide a new portfolio score, based on the aforementioned framework and concepts. In particular, it relies on statistical properties of portfolios, and we show how they can be computed efficiently.

Testing of Portfolio Optimization by Timor-Leste Portfolio Investment Strategy on the Stock Market

“…This framework describes a portfolio in terms of returns, allowing investors to efficiently avoid risk according to expected returns and the variance of portfolio returns (Mukherji and Jeong 2021;van Staden et al 2021). Therefore, investors build portfolios intending to increase returns, with the expectation of minimal risk when optimizing the portfolio (Chalkis et al 2021). Moreover, the key problem of the optimal portfolio is the inversion of the covariance matrix, so the relationship between the assets in the portfolio and the correlation of returns contribute to the portfolio risk (Olmo 2021).…”

CHRRT: boosting coordinate hit-and-run with rounding by thinning

“…Convex polytopes are geometrical objects that constrain the parameter space in many applied modeling contexts, including operations research (Ciomek and Kadziński, 2021), ecological modeling (Drouineau et al, 2021), computational finance (Chalkis et al, 2021a), astronomy (Lubini and Coles, 2012), physics (Leake et al, 2020), and systems biology (Herrmann et al, 2019). Uniform convex polytope sampling (UCPS), i.e., drawing representative random numbers from a truncated uniform distribution defined over a bounded polytope, has become a standard tool for model analysis, parameter space exploration/characterization, and volume approximation.…”