A Scalable Algorithm for Sparse Portfolio Selection

The sparse portfolio selection problem is one of the most famous and frequently studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities, and minimum investment constraints. Existing certifiably optimal approaches to this problem have not been shown to converge within a practical amount of time at real-world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic that supplies high-quality warm-starts, and a second heuristic for generating additional cuts that strengthens the root relaxation. We also study the problem’s continuous relaxation, establish that it is second-order cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that a conjunction of the imposition of ridge regularization and the use of the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.

Analysis of the distribution, rotation and scale characteristics of solar wind switchbacks: comparison between the first and second encounters of Parker Solar Probe

The S-shaped magnetic structure in the solar wind formed by the twisting of magnetic field lines is called a switchback, whose main characteristics are the reversal of the magnetic field and the significant increase in the solar wind radial velocity. We identify 242 switchbacks during the first two encounters of Parker Solar Probe (PSP). Statistics methods are applied to analyze the distribution and the rotation angle and direction of the magnetic field rotation of the switchbacks. The diameter of switchbacks is estimated with a minimum variance analysis (MVA) method based on the assumption of a cylindrical magnetic tube. We also make a comparison between switchbacks from inside and the boundary of coronal holes. The main conclusions are as follows: (1) the rotation angles of switchbacks observed during the first encounter seem larger than those of the switchbacks observed during the second encounter in general; (2) the tangential component of the velocity inside the switchbacks tends to be more positive (westward) than in the ambient solar wind; (3) switchbacks are more likely to rotate clockwise than anticlockwise, and the number of switchbacks with clockwise rotation is 1.48 and 2.65 times of those with anticlockwise rotation during the first and second encounters, respectively; (4) the diameter of switchbacks is about 10^5 km on average and across five orders of magnitude (10^3 – 10^7 km).

A comparison of minimum variance and maximum Sharpe ratio portfolios for mainstream investors

PurposeMotivated by the recent theoretical rehabilitation of mean-variance analysis, the authors revisit the question of whether minimum variance (MinVar) or maximum Sharpe ratio (MaxSR) investment weights are preferable in practical portfolio formation.Design/methodology/approachThe authors answer this question with a focus on mainstream investors which can be modeled by a preference for simple portfolio optimization techniques, a tendency to cling to past asset characteristics and a strong interest in index products. Specifically, in a rolling-window approach, the study compares the out-of-sample performance of MinVar and MaxSR portfolios in two asset universes covering multiple asset classes (via investable indices and their subindices) and for two popular input estimation methods (full covariance and single-index model).FindingsThe authors find that, regardless of the setting, there is no statistically significant difference between MinVar and MaxSR portfolio performance. Thus, the choice of approach does not matter for mainstream investors. In addition, the analysis reveals that, contrary to previous research, using a single-index model does not necessarily improve out-of-sample Sharpe ratios.Originality/valueThe study is the first to provide an in-depth comparison of MinVar and MaxSR returns which considers (1) multiple asset classes, (2) a single-index model and (3) state-of-the-art bootstrap performance tests.

Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution

The shape parameter estimation using the minimum-variance linear estimator with hyperparameter (MVLE-H) method is believed to be effective for a wear-out failure period in a small sample. In the process of the estimation, our method uses the hyperparameter and estimate shape parameters of the MVLE-H method. To obtain the optimal hyperparameter c, it takes a long time, even in the case of the small sample. The main purpose of this paper is to remove the restriction of small samples. We observed that if we set the shape parameters, for sample size n and c, we can use the regression equation to infer the optimal c from n. So we searched in five increments and complemented the hyperparameter for the remaining sample sizes with a linear regression line. We used Monte Carlo simulations (MCSs) to determine the optimal hyperparameter for various sample sizes and shape parameters of the MVLE-H method. Intrinsically, we showed that the MVLE-H method performs well by determining the hyperparameter. Further, we showed that the location and scale parameter estimations are improved using the shape parameter estimated by the MVLE-H method. We verified the validity of the MVLE-H method using MCSs and a numerical example.

Two-Time Procedure for Calculation of Carrier Frequency of Phasomodulated in Communication Systems

The use in radio communication systems of phase modulation of a signal intended for the transmission of useful information in a continuous mode creates the problem of frequency uncertainty of the received signal by frequency.In practice, it is not possible to implement frequency estimation in the conditions of chat uncertainty of the signal in the channel with low energy of the signal received in the continuous mode. Therefore, the estimation of the carrier frequency offset of the signal received relative to the nominal value is carried out before other synchronization procedures are included, namely: phase synchronization and clock synchronization. The paper generalizes the procedure and forms a two-step procedure for calculating the carrier frequency of the phase-modulated signal of a radio communication system for data transmission in a continuous mode, taking into account the condition of uncertainty of all signal parameters. Achieving the minimum observation interval in the given order of calculation of the carrier frequency is ensured by the use of the fast Fourier transform function. In order to analyze the effectiveness of this procedure, the process of estimating the carrier frequency of the phase-modulated signal of the radio communication system during data transmission in continuous mode and functional dependences of the maximum frequency in the signal spectrum and the minimum variance of carrier frequency estimation. This procedure allows a two-stage assessment of the carrier frequency according to the rule of maximum likelihood, taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in a continuous mode with a minimum observation interval. Achieving the minimum observation interval in the given order of carrier frequency estimation is ensured by using the fast Fourier transform function and two estimation steps. The analysis of the efficiency of the estimation of the specified order was carried out on the basis of comparison of a ratio of the received minimum variance of an estimation of a carrier frequency and theoretically possible border of the minimum variance.

Minimum Variance Algorithm-Based Correlation Analysis between Body Mass Index and the Malignant Degree of Prostate Cancer Mediated under Ultrasound Images

This study was to explore the correlation between the malignant degree of prostate cancer (PCa) and body mass index (BMI) mediated by ultrasound images under multioperator algorithm (MOA) based on minimum variance (MV) algorithm. MOA was established by optimizing the smoothing technique and diagonal loading algorithms of MV, and its quality and processing speed of ultrasound images were compared with other algorithms. Ninety two patients were selected as the subjects investigated, who had transrectal prostate biopsy mediated by ultrasound to be diagnosed as PCa in the hospital. Based on Gleason score and prostate specific antigen (PSA) value, all patients were divided into a high-risk PCa group (a high-risk group) and a non-high-risk PCa group (a non-high-risk group). The proportion of obese patients in the two groups was compared. The logistic regression analysis method was applied to analyze related factors of PCa development, and Pearson correlation was for analyzing the correlation between Gleason score and BMI of patients. The results showed that the number of patients in the high-risk group was greater than that of the non-high-risk group ( P < 0.05), while the proportion of nonobese patients in the non-high-risk group was markedly higher than that of the higher-risk group ( P < 0.01). Both PSA and BMI were obviously correlated with the development of high-risk PCa ( P < 0.05), and there was an extreme positive correlation between BMI and Gleason score (r = 0.661 and P = 0.007). It indicated that MOA was established based on conventional MV, which could increase the ultrasonic image quality and calculation speed. Besides, BMI was a risk factor of high-risk PCa and was positively correlated with malignant degree of PCa, which provided a referable evidence for clinical evaluation of malignant degree of PCa.