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The US involvement was driven by a desire to prevent Japan from disruptively selling large amounts of US Treasuries, which would have caused volatility and upward pressure on US interest rates. The goal was to maintain stability in US markets, not just to aid an ally.

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The US-Japan yen intervention wasn't about establishing an unbreakable price cap. Instead, its primary goal was psychological: to make speculators nervous about shorting the yen near the 160 JPY/USD level, thereby restoring the Ministry of Finance's perceived threat.

For decades, the US has benefited from investors borrowing cheap Japanese yen to invest in higher-yield US assets (the carry trade). This has created a deep dependency, forcing the US to intervene and prevent Japan from raising its rates, which would cut off the vital flow of liquidity.

The US and Japan are not trying to fix the Japanese economy's fundamental problems. Instead, they are artificially propping up the yen to ensure the unwinding of the carry trade is a slow, managed decline rather than a sudden, catastrophic collapse that would devastate the global economy.

The Japanese yen's decline was much larger following a reported rate check by the New York Fed than after the Bank of Japan's own check. This indicates market participants see the prospect of coordinated U.S.-Japan intervention as a far more significant, though less likely, threat to yen weakness than unilateral action by Japan.

By selling Euros from the Exchange Stabilization Fund to buy Yen, the Treasury indirectly lowered the DXY without selling US Treasuries. This clever maneuver protected the fragile US bond market, which is crucial for financing the capital-intensive AI boom.

The US Treasury's intervention was not just about the Yen's exchange rate or trade balance. A primary motive was to prevent Japan from being forced to sell its vast US Treasury reserves to fund its own intervention, which could create significant pressure on the US bond market.

The Bank of Japan's intervention is a defensive measure, not an offensive one. It aims to prevent an explosive, out-of-control yen depreciation (the 'right tail' risk) and buy time, hoping the underlying macro picture (like U.S. yields) eventually changes in its favor.

The Bank of Japan's intervention was not just about the yen, but a strategic move to "punt for risk parity"—to reduce volatility and calm markets. By strengthening the yen, they stabilized US Treasury rates, which in turn supported equities, revealing a tug-of-war between central banks seeking stability and traders seeking volatility.

The US coordinated with Japan on currency intervention not just to support the yen, but as a strategic move to manage US long-term interest rates. The Treasury believes excessive dollar-yen volatility spills over into Japanese Government Bond (JGB) yields, which in turn significantly influences the long end of the US Treasury curve, making yen stability a tool for domestic rate management.

The Treasury's push to help Japan defend the yen is not altruism; it's a strategic move to protect the US bond market. By preventing Japan, the largest holder of US debt, from selling treasuries, the US maintains global demand for its own debt and keeps its borrowing costs low. The support for Japan is merely a convenient side effect.