Kazakhstan Stock Exchange (KASE) is established on November 17, 1993, with the participation of 23 leading Kazakh banks under the leadership of the National Bank of the Republic of Kazakhstan. KASE has had an important position in the country's economy since then. This study comparatively analyses the volatility structures of the return of the KASE Composite Index and the returns of the oil and energy companies traded in the KASE in the period between 5.01.2021 and 4.01.2023. The preliminary test (ARCH LM) showed that the volatility structure of the past period is effective on the current period in all four returns. Based on this finding, the structure of the series was evaluated with four different models. All four return series conformed with the GARCH-M (1, 1) model. Accordingly, the finding that oil and energy companies and the stock market composite index have the same volatility structure is important for investor decisions. Moreover, the finding that any past financial shock or volatility fluctuation affects the current return will positively affect the estimation of the future value of financial assets.