Though id post as just one example, perhaps the most obvious, that shows how heavily the JPY is considered a risk-off asset and to show the clearly, since the SPX is a risk-on asset, that the JPY is negatively correlated with the SPX.
In times of market fear/ uncertainty, YEN is sought out, just like bonds and gold, as a safe heaven asset. The theory behind this is that the JPY offers stability through the nation being one of the only developed nation with a net credit balance sheet.
Clearly, in the financial crisis, one with a hypothesis as the above, should see the SPX fall and the YEN risk.. Indeed, the chart shows exacty that, almost 1:1 correlation.
Now, the JPY SPX correlation DOES change, in times of extreme fear or extreme exuberance, the YEN will be proportionately more correlated with the SPX and other risk assets.
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In "Normal" or non heavily trending markets, the correlation is less obvious - since it is the extremes that cause investors to seek difference assets and change their strategy in masses.
In times of fear, investors move their liquidity to risk-off YEN, hence we see USDJPY fall during the crisis. We also see SPX fall in a correlated manner, this is because investors pull their liquidity OUT of SPX and apply it in some proportion to YEN.