Many international markets have struggled over the last few years, with China being the most recent.

But amidst all that, the Japanese market has quietly put up some solid numbers. In fact, the Nikkei index is up 37% in dollar terms since early 2013.

Some of this is due to a weaker yen, which has spurred exports and made foreign sales and profits more valuable in yen terms. Cost cutting and incremental increases in productivity are also contributing to the climb.

Here are the trends as well as the companies and markets that are on the up and up.

Big and Little

The sharp pullback in fuel and other commodity inputs has helped improve margins for many firms.

Japan has 3,400 listed companies led by the Nikkei index of 225 bellwether names. The Nikkei recently rose to almost 19-year highs recently, mainly due to gains in these big-name exporters.

But the broader TOPIX index, which consists of nearly 1,900 companies, hasn't reached its 2007 peak, as middle-market firms relying on domestic spending are struggling to ramp up earnings.

Both markets have posted big gains in absolute terms since Prime Minister Shinzo Abe launched his aggressive stimulus program, with the Nikkei getting a push from foreign inflows.

Meanwhile, a renewed focus on shareholder activism and value has driven a surge in return on equity over the last few years, from 5% to 8.5%. Still, that's below the global average of 12%.

The result is that about 40% of the shares for smaller companies in the TOPIX have a price-to-book ratio below one, meaning they trade below book value and have a market capitalization below their net worth. By contract, fewer than 20% of companies on the Nikkei trade below a price-to-book ratio of one.

Many smaller companies in Japan are taking actions to improve performance, such as increasing exports, buying back stock, and increasing dividends.

To take advantage of the large company-small company valuation gap, you could buy into the iShares MSCI Japan Small Cap (SCJ) exchange-traded fund.