What's behind the Japanese stock rally when the economy itself is as moribund as ever? People piling into assets that offer at least a hope of returns, instead of a guaranteed loss if they stick to fixed deposits etc in an era of high inflation?
Imagine that in 2012, $1.00 = 100 JPY and this buys the same tube of toothpaste in both countries. Then ten years later in 2022, that toothpaste still costs 100 yen in Japan, but costs $2.00 in the USA. Naively, you'd expect therefore that the yen has gotten more expensive, and the exchange rate to be around $2 = 100 yen, or else there's a major arbitrage opportunity for North Americans to buy Japanese toothpaste. (Imagine this is not just toothpaste, but virtually all consumer goods).
Then you find out that in fact, the exchange rate has gone the other way, where $1 USD buys something like 150 yen. Despite this, toothpaste is still 100 JPY in Japan, and $2 in the USA. How do you square this difference?
This doesn't necessarily bode well for the Japanese family or consumer (as their low prices may be a result of their low wages), but in terms of international competitiveness, it's a strong sign. It means that Japanese companies can make a killing on exports and tourism. From a mathematical standpoint, there are only two ways to balance this price difference: either Japanese productivity is much better than was previously priced-in, or else they have huge inflation coming shortly down the line. The former will be good for Japanese stocks and the latter case will be good for the yen (as the central bank would have to increase interest rates and/or sell US treasuries to protect the currency).
For example, Japan was also getting more competitive in the 1970s-1980s, but at that time it happened alongside a population boom, young workforce, economic growth, inflation, and a strengthening Japanese consumer. This time, it's more like Japanese companies getting internationally competitive while their economy declines and their workers accept lower wages and lower standards of living, with high rates of industrial production amidst shrinking domestic demand. Again, not so good for Japanese families perhaps, but that's not what competitiveness is necessarily about.
2. Supposedly the Japanese government is trying to get them to 'return' it to shareholders
3. Some people believe the currency will go up making these bags of cash more valuable in dollar terms
4. Warren Buffet figured out he could borrow money in yen at a lower interest rate than their stocks pay out, use it to buy yen denominated stocks, and basically print free money. You can't do that but a lot of people are buying what he's buying.