For Berkshire’s Japanese stocks investment, why Buffett hedged the currency risk by borrowing yen?

A few thoughts

First, why not? Berkshire was able to borrow money for extremely long time horizons for negative real rates, much lower than the [real] dividend yields. It's almost like the float from a new insurance business turning an underwriting profit. You gather funds like that whenever you can. On its own, borrowing yen would be a risky move because of currency moves, but when paired with a stock investment it becomes risk free new float. Berkshire has a profitable long term $20bn investment that didn't use any of the cash pile...pretty cool.

I don't think he thinks of it primarily as a hedge, more as a funding mechanism. He may have a large pile of cash, true, but the time to maximize your pile of cash is when it's easy, not when you need it.

Lastly, an investment in Japan might deserve a hedge more than one in many other places in the world. There is a saying that there are four types of economies in the world: Industrialized, developing, Argentina, and Japan. The macro and investing rules for other places just don't seem to apply in Japan, so a gigantic move in the yen can never be ruled out, and nobody knows which way it might be.

As for your note about losing money on paper due the hedge, it's best to avoid that kind of thinking. The whole POINT of any hedge is that one side is going to lose while the other wins, along with the point that you don't know in advance which one is going to be which. Never look at the losing side of any hedge, it will drive you crazy. The only thing that matters is the bottom line on the combination, which is going very well indeed in this case, so focus on that.

Jim