Equities Markets

The Dow Jones Industrial Average is a price-weighted average of 30 significant stocks traded on the New York Stock Exchange and the Nasdaq. The old economy stocks are said to be represented by the Dow. The Dow tends to be the leading indicator for international investment.

While the Dow reflects the BIG money, S&P 500 reflects the broader view is the preferred gauge of equity markets due to its bread coverage of the market. Historically it has shown a negative correlation to the yen (even on an intraday basis). It is a market value weighted index made up of the prices of 500 large stocks traded in the US market, covering about 75% of US equities.

Nasdaq Composite is highly followed in the U.S. as an indicator of the performance of stocks of technology companies and growth companies. Since both U.S. and non-U.S. companies are listed on the NASDAQ stock market, the index is not exclusively a U.S. Index. The NASDAQ represents the speculative retail money.

Generally speaking, if the U.S. equity markets rise, they cause an increase in investors' risk appetite in which case foreign investment dollars will flock the U.S. equity market pumping the U.S. dollar higher.

The Nikkei is a stock market index for the Tokyo Stock Exchange (TSE). It has been calculated daily by the Nihon Keizai Shimbun (Nikkei) newspaper since 1950. It is a price-weighted average (the unit is yen), and the components are reviewed once a year. This market is close correlated with US 10-Year Treasury notes. It's also useful to spot risk appetite and gauge FX flows. 
Usually it's negatively correlated to the Yen. It can be explained as a reasonable decline in the yen usually lifts stocks of export-oriented companies (cheaper japanese products), which tends to boost the overall stock index. 
But the Nikkei-yen relationship is sometimes reversed (positive correlation): wherein a strong open market in the Nikkei tends to boost the yen (weighs on USD/JPY) as investors’ funds flow into yen-denominated stocks.