Forecasting portfolio returns with skew‐geometric Brownian motions

Bufalo, Michele; Liseo, Brunero; Orlando, Giuseppe

doi:10.1002/asmb.2678

Cited by 13 publications

(3 citation statements)

References 45 publications

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“…For the analysis, we have considered both real data and a simulated Brownian motion for comparison (for a connection between macroeconomic business cycles, determinism, and financial stochastic Ornstein-Uhlenbeck process, see Orlando et al [59]). The former refers to USA equities, and the latter is a signal commonly used in finance to model a stochastic process y t such as the Ornstein-Uhlenbeck process [60] dy t = −ϕ y t dt + σ dB t where ϕ > 0 and σ > 0 are some parameters and B t denotes a standard Brownian motion [61][62][63][64].…”

Section: Datamentioning

confidence: 99%

Expecting the Unexpected: Entropy and Multifractal Systems in Finance

Orlando,

Lampart

2023

Entropy

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Entropy serves as a measure of chaos in systems by representing the average rate of information loss about a phase point’s position on the attractor. When dealing with a multifractal system, a single exponent cannot fully describe its dynamics, necessitating a continuous spectrum of exponents, known as the singularity spectrum. From an investor’s point of view, a rise in entropy is a signal of abnormal and possibly negative returns. This means he has to expect the unexpected and prepare for it. To explore this, we analyse the New York Stock Exchange (NYSE) U.S. Index as well as its constituents. Through this examination, we assess their multifractal characteristics and identify market conditions (bearish/bullish markets) using entropy, an effective method for recognizing fluctuating fractal markets. Our findings challenge conventional beliefs by demonstrating that price declines lead to increased entropy, contrary to some studies in the literature that suggest that reduced entropy in market crises implies more determinism. Instead, we propose that bear markets are likely to exhibit higher entropy, indicating a greater chance of unexpected extreme events. Moreover, our study reveals a power-law behaviour and indicates the absence of variance.

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Section: Datamentioning

confidence: 99%

Expecting the Unexpected: Entropy and Multifractal Systems in Finance

Orlando,

Lampart

2023

Entropy

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“…In particular, the inclusion of the normal law and the shape parameter regulating the skewness, allows for a continuous variation from normality to non-normality (see Azzalini, 2021). Recently, Bufalo et al (2022) described an application to forecasting portfolio returns with skew-geometric Brownian motions in presence of cross dependency between assets.…”

Section: On Skewed Distributions Of Returnsmentioning

confidence: 99%

Straightening skewed markets with an index tracking optimizationless portfolio

Bufalo¹,

Bufalo²,

Cesarone³

et al. 2022

Preprint

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Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, assuming that the returns follow skew geometric Brownian motions and that they are correlated, we describe some statistical properties for the ex-post, the ex-ante tracking errors, and the forecasted tracking portfolio. To this end, we develop an innovative statistical methodology, based on a benchmark-asset principal component factorization, to determine a tracking portfolio that replicates the performance of a benchmark by investing in a subset of the investable universe. This strategy, named hybrid Principal Component Analysis (hPCA), is applied both on normal and skew distributions. In the case of skew-normal returns, we propose a framework for calibrating the model parameters, based on the maximum likelihood estimation method. For testing and validation, we compare four alternative models for index tracking. The first two are based on the hPCA when returns are assumed to be normal or skew-normal. The third model adopts a standard optimizationbased approach and the last one is used in the financial sector by some practitioners. For validation and testing, we present a thorough comparison of these strategies on real-world data, both in terms of performance and computational efficiency. A noticeable result is that, not only, the suggested lean PCA-based portfolio selection approach compares well versus cumbersome algorithms for optimization-based portfolios, but, also, it could provide a better service to the asset management industry.

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“…Mandelbrot (Mandelbrot & Van Ness, 1968) was the first to apply fractional Brownian motion to natural time series for modeling strong interdependence between distant samples. A more recent approach can be found in Bufalo et al (2022). In the case of natural disasters, however, it has been experimentally found that the Hurst exponent is around 0.24 which “indicates that these time series are fractal and relatively long‐term” antipersistent (Jin et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes

Orlando

Bufalo

2022

Journal of Forecasting

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This work aims to forecast (over 1, 5, and 15 years) the extremes, the expected value, and the volatility of natural disasters occurrences. To achieve this objective, we adopt a generalized two‐factor square‐root model linking together occurrences and volatility through stochastic correlation (Brownian motion). We use a generalized Pareto distribution (GPD) to forecast the maximum number of occurrences as a measure of value at risk (VaR). The results are checked in terms of accuracy, compared versus some baseline models (i.e., the Poisson process and the extreme value model) and backtested.

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Forecasting portfolio returns with skew‐geometric Brownian motions

Cited by 13 publications

References 45 publications

Expecting the Unexpected: Entropy and Multifractal Systems in Finance

Expecting the Unexpected: Entropy and Multifractal Systems in Finance

Straightening skewed markets with an index tracking optimizationless portfolio

A generalized two‐factor square‐root framework for modeling occurrences of natural catastrophes

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