In the increasingly frequent global financial turmoil, investors prefer to invest in stable assets to hedge risks. Crude oil naturally has dual use value as a general commodity and as a financial asset, which has attracted wide attention. In this paper, we adopt a wavelet coherence analysis to study the standard of crude oil as a hedging asset and analyze the dynamic correlation of crude oil and stock market price fluctuations in the four economies of the United States, Japan, China and Hong Kong at different frequencies. The empirical evidence shows that crude oil can be conditionally used as a hedging asset for underlying securities. From the perspective of space, crude oil is suitable for investors in China’s stock market as a hedging asset, while for stock markets in the US, Japan and Hong Kong, the ability of crude oil to hedge risk has been greatly weakened. From the perspective of investment term, although crude oil cannot be regarded as a hedging asset for long-term investment, it can still play a hedging role in the short term. When the market is in a state of panic, the ability of oil to hedge risk is stronger.