Although the degree of the correlation tends to vary, generally you are correct, there is an inverse relationship. This is because Japanese Yen is considered a "Safe-Haven" currency, i.e. read more
The primary reason the yen and the Nikkei are inversely correlated is primarily because a weaker yen helps Japan's exports. A weaker yen means that a Japanese product can be sold for fewer Dollars (Euros, etc) abroad making it more attractive compared to the local competition. read more
The Japanese Yen and benchmark Nikkei 225 Index are highly correlated around 70%, and consistently demonstrate a stronger correlation than between the Japanese Yen and TOPIX Index. Upcoming events that may affect the Japanese Yen as well as the Nikkei 225 include the final French presidential election polls on 7 May, potential early Italian elections, and a tail-risk event where the North Korean crisis escalates. read more
The Japanese stock market is inversely correlated with the Yen. When Yen goes up, Nikkei goes down and vice versa. This is because the Japanese economy is highly dependent on exports. read more