[Paper Review] Comparison of gain-loss asymmetry behavior for stocks and indexes

Magdalena A. Załuska–Kotur, K. Karpio+1 more|ArXiv.org|Aug 22, 2006

Complex Systems and Time Series Analysis3 references3 citations

TL;DR

This study applies investment horizon analysis to Polish stock market data, using first-passage time distributions to quantify gain-loss asymmetry. It finds that emerging market indices like WIG exhibit reversed asymmetry—gains are faster than losses—contrasting with developed markets like DJIA, and that this behavior is not explained by individual stocks, which show symmetric return dynamics.

ABSTRACT

Investment horizon approach has been used to analyze indexes of Polish stock market.Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain-loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and for most of individual companies stocks. The gain-loss asymmetry for these data, measured by the coefficient, that we postulated before \cite{karpio}, has opposite sign to this for WIG index.

Motivation & Objective

• To investigate gain-loss asymmetry in Polish stock market indices and individual stocks using investment horizon analysis.
• To determine whether the asymmetry observed in broad indices like WIG is a result of aggregated individual stock behavior.
• To compare the asymmetry patterns in emerging markets (e.g., Poland) with those in developed markets (e.g., DJIA).
• To quantify asymmetry using a coefficient κ derived from slope differences in gain and loss curves.
• To explore whether correlations among index constituents explain the observed asymmetry in emerging market indices.

Proposed method

• Transformed price data using logarithmic returns and removed trend via 100-point moving average to isolate fluctuations.
• Constructed investment horizon distributions by measuring first-passage times to reach specific return levels (ρ) from each point in time.
• Fitted the generalized inverse Gaussian distribution (Eq. 2) to the horizon distributions to estimate t_max, the time of maximum probability.
• Plotted t_max against |ρ| for positive (gains) and negative (losses) returns to assess asymmetry in time dynamics.
• Fitted linear models to gain and loss curves to compute the asymmetry coefficient κ = γ − γ′, where γ and γ′ are slopes of gain and loss curves.
• Compared results across WIG, WIG20, individual stocks (e.g., Best, Budimex), and international benchmarks like DJIA to identify structural differences.

Experimental results

Research questions

• RQ1 Does the gain-loss asymmetry in the Polish WIG index differ from that observed in developed market indices like DJIA?
• RQ2 To what extent is the WIG index's asymmetry explained by the aggregated behavior of its constituent stocks?
• RQ3 How does the asymmetry coefficient κ vary across individual stocks versus broad market indices in emerging markets?
• RQ4 What role do cross-asset correlations among index constituents play in generating the observed asymmetry in emerging market indices?
• RQ5 Is the inverse statistics approach using first-passage time distributions effective in capturing non-Gaussian dynamics in emerging market returns?

Key findings

• The WIG index exhibits strong gain-loss asymmetry with gains achieved faster than losses, as indicated by t_max curves lying above for gains.
• The asymmetry coefficient κ for WIG is negative (implying faster gains), contrasting with positive κ in developed markets like DJIA.
• Individual stocks such as Best, Budimex, DzBank, and Eldorado show symmetric gain-loss dynamics, with κ values of 0.42, 0.1, 0, and 0.3 respectively.
• WIG20 index dynamics closely resemble a simple sum of its constituent stocks, with κ = 0.1, indicating minimal asymmetry.
• The observed asymmetry in WIG is not a result of individual stock behavior but likely stems from correlated dynamics among its constituents.
• The generalized inverse Gaussian distribution (Eq. 2) provides a better fit to investment horizon data than the classical first-passage time distribution (Eq. 1).