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On May 24th the DJIA dropped and the news has been attributing it to Donald Trump's cancelation of a talk with North Korea (see image below).

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My understanding is that the companies making up the DJIA haven't lost any substantial amount of money because of this decision-so why has the DJIA fallen?

In general,

How & Why does this news negatively effect the US economy when the overall value of companies haven't declined?

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There are likely two major (and closely related) reasons for this:

First- stock prices aren't purely reflective of what a company is worth today, instead, stock prices reflect the expected future prices as well. Events like this, which increase uncertainty and instability, might change expectations about future stock prices. This is then incorporated into current stock prices, which leads to a fall.

Second- a lot of automated trading algorithms incorporate news keywords into their pricing structures (for example), which can lead to reactions based on the headlines themselves. These can then create a feedback loop with other funds, like ETFs, which trade based on volatility indexes.

I'm sure there are other reasons as well, (perhaps the breakdown in the summit led some traders to reevaluate the relative bargaining power of the US and China in their upcoming summit, which in their mind might lead to an increased likelihood of a trade war, as a hypothetical), though those two can explain many large fluctuations!

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