Multi-Factorized Semi-Covariance of Stock Markets and Gold Price

Yun Shi,Lin Yang,Jun Huang,Mei Huang

doi:10.3390/jrfm14040172

Abstract

Complex models have received significant interest in recent years and are being increasingly used to explain the stochastic phenomenon with upward and downward fluctuation such as the stock market. Different from existing semi-variance methods in traditional integer dimension construction for two variables, this paper proposes a simplified multi-factorized fractional dimension derivation with the exact Excel tool algorithm involving the fractional center moment extension to covariance, which is a complex parameter average that is a multi-factorized extension to Pearson covariance. By examining the peaks and troughs of gold price averages, the proposed algorithm provides more insight into revealing underlying stock market trends to see who is the financial market leader during good economic times. The calculation results demonstrate that the complex covariance is able to distinguish subtle differences among stock market performances and gold prices for the same field that the two variable covariance may overlook. We take London, Tokyo, Shanghai, Toronto, and Nasdaq as the representative examples.

Highlights

Complex algorithms are used in analyzing real-world implementations, as the trusted analytic solution, it typically tends to have challenges in software implementation, is costly, and requires time
This study constructed a complex covariance for fractional analysis of gold stock market fluctuations using fractional moment basis with a simple algorithm coded in Excel, other similar tools can be used
The results of the complex calculation show the difference between high frequency trading and low frequency trading that traditional covariance definition and calculation may overlook

Summary

Introduction

Complex algorithms are used in analyzing real-world implementations, as the trusted analytic solution, it typically tends to have challenges in software implementation, is costly, and requires time. There were significant cross effects between gold prices and stock prices on return and volatility (Mei and McNown 2019), while gold is a strong safe asset in most developed markets and can effectively reduce the profile risk, especially during the period of financial crisis in China (Arouri et al.2015). In this paper, a new method, semi-covariance, will be used to deepen the investigation of the inner nonlinear relationship between the price of gold and stock markets in China, Japan, the UK, Canada, and the USA from the beginning of 1999 to the end of 2019. We count the total numbers of the cross over days and divide the total days considered by the cross over times to obtain the average cycle of the active period This way we can observe which country has a normal gold to stock relationship and which countries do not

Excel Calculations of Semi-Covariances among the Price of Gold and Stock

Conclusions