TOKYO -- The yen is trading at its lowest level against the dollar in 12 and a half years, but contrary to popular belief, shorting the Japanese currency -- and going long on the greenback -- is linked to Japanese stocks, not U.S. interest rates.

Shorting the yen and buying Japanese stocks is a bet called the "Abe trade," popular among foreign investors buying into Abenomics, a set of economic policies promoted by Prime Minister Shinzo Abe.

The yen's decline accelerated May 22, when Federal Reserve Chair Janet Yellen hinted at a rate hike if the U.S. economy continues to improve. "I think it will be appropriate at some point this year to take the initial step to raise the federal funds rate target and begin the process of normalizing monetary policy," she said in a speech.

The Japanese currency has since dropped to the 124 range against the dollar. But the U.S. Treasury market's reaction has been tepid. The two-year Treasury yield, which is sensitive to monetary policy, edged up after Yellen's remarks but still stands at just over 0.6%, short of the 0.7% level in March. The 10-year yield, the harbinger of long-run inflation, has been slowly losing ground.

The Chicago Mercantile Exchange's FedWatch, which gauges the market's expectation of changes to U.S. interest rates, gives a probability of around 20% for a rate hike in September, and just under 60% for one within the year. Both figures declined from a month ago.

Currency market participants misconstrued Yellen's remarks, which were intended to keep expectations of a rate hike near the front burner amid not-so-strong economic data, according to Izuru Kato of Totan Research.

"The Fed must have been perplexed by the way the currency market reacted," Kato said.

Until the interest rate gap between Japan and the U.S. broadens as anticipated, the yen's value should bounce back for a correction. But while the euro and some other currencies have rebounded somewhat, the yen has continued its decline. The currency market's focus is shifting from the dollar's strength to the yen's weakness.

"Expectations of the U.S. lifting interest rates are an excuse. The Abe trade is likely the cause of a weak yen," said Minoru Uchida of the Bank of Tokyo-Mitsubishi UFJ. On the currency market, the yen is increasingly linked to Japanese stocks. Investors bullish on them detest a drop in dollar value caused by a softer yen. To minimize such risk, they reportedly are engaged in Abe trades.

Speculative investors sold more yen against the dollar, with net yen short positions showing the largest uptick since Abe took office in December 2012, a market report issued Friday by the U.S. Commodity Futures Trading Commission found.

The Nikkei Stock Average closed Monday at 20,569.87, up 0.03%, extending its winning streak to 12 trading days, the longest in 27 years. The market rally is fueled by an influx of foreign money, attracted by Japanese companies with strong earnings.

How far will the yen fall and stocks rise? In the short run, investors may be ready to take profit. The yen could return half the gains to around 120 to the dollar, Daisuke Karakama of Mizuho Bank said.

But with the world awash in easy money, the stock rally could continue. In that case, the yen's value could erode further. Eventual corrections are in order, but many predict the yen will remain soft at least until summer.