The Causal Relationship Between Stocks, Gold, Crude Oil, and Bond Returns in Poland
Authors: Mamcarz Katarzyna 
Published: November 2024

Theoretical background: Capital investments involve taking risks to achieve a favourable rate of return. Investors are offered various options, including stocks, bonds, and commodities. The aforementioned investment opportunities are considered alternatives due to their varying price volatility and risk levels. Bonds and gold demonstrate a low or negative correlation with equities. On the other hand, crude oil and gold are positively correlated. An essential issue in analysing financial markets is to capture the dynamic behaviour of the financial time-series data, i.e. variables such as prices and returns on investments in assets mentioned above. In decision-making, investors should consider the causal relationship between asset classes, as some variables may contain important information about the future dynamics of other variables. The ability to predict future outcomes is crucial to reduce uncertainty. Vector autoregression (VAR) models are regarded as a useful modelling tool in investigating interrelations between financial instrument prices and returns. Purpose of the article: The paper aims to evaluate the linkages between stock, gold, crude oil, and bond returns in Poland. We focus on analysing both the long term equilibrium between logarithmic financial asset prices and the Granger causality between logarithmic returns in the short term. Research methods: The causal relationships between the stocks, gold, crude oil, and bond logarithmic returns are investigated based on the VAR/VECM estimates. The empirical data cover the period from December 2006 to January 2023. We use the following market data to measure the interrelations between the considered assets: WIG Index, gold and crude oil spot prices, and bond index reflecting the price movements on the Polish financial market. We carry out the test for stationarity employing the ADF and Phillips–Perron tests. The pre-estimation process also involves identifying the number of lags and conducting the Johansen cointegration test since variables are integrated of order one to examine the existence of the long-term equilibrium between the logarithmic prices of assets mentioned above. We use the Wald test for the models’ parameters to indicate the type of Granger causality between logarithmic returns. The forecast error variance decomposition (FEVD) and impulse response functions (IRF) analysis is also applied. Moreover, the post-estimation procedure includes a test for parameters stability and white noise of residuals. All calculations are performed using Stata’s standard software package. Main findings: The results suggest that the markets we examined in Poland are cointegrated, meaning a long-term relationship exists between the prices of financial assets. Additionally, we prove that gold logarithmic prices have a negative impact on the stock index, indicating an inverse relationship between their price developments. We also discover that crude oil and bonds’ effects on the stock market are positive. Although all β coefficients of the error correction equation are statistically significant, the short-term adjustment to equilibrium did not occur based on the α coefficients of the short-term equations. According to the Granger causality analysis related to the VAR in first differences, gold price changes have a short-term impact on stock returns. In contrast, stock returns cause crude oil returns. However, we find no causal linkages in the remaining cases, suggesting that the variables are independent. Changes in asset prices are mainly attributed to their shocks, while observed impacts described by IFR function patterns die out quite quickly. Overall, results confirm that investors can combine gold and stocks in their portfolios, as these interrelated assets have alternative investment properties. Additionally, it is worth noting that the correlation between stock returns and crude oil or bonds is undesirable when constructing portfolios.