When returns on assets display heavy tail or leptokurtosis, estimating value at risk (VaR) without considering distribution kurtosis can cause estimation bias. This study considered the kurtosis of distribution, utilizing various models to examine the conditional VaR of minimum variance portfolios (incorporating both the stock index and futures) and performing back-testing to compare individual model performance. Results demonstrate the improved accuracy of models using distribution kurtosis to estimate VaR. Furthermore, t distributed models outperformed both those with a normal distribution and symmetric volatility models in terms of the conditional VaR of minimum variance portfolios. These results suggest that in portfolio construction, investors should consider distribution kurtosis and volatility asymmetry.