headline risk
n. The risk associated with something or someone that has the potential to generate an excessive amount of negative publicity.
Examples
2003
In terms of "headline risk," this was a regrettable week for both Janus and Qwest — two Denver firms struggling mightily to regain the trust of the marketplace.

Public relations professionals tell their clients to avoid headline risk at all costs. Columnist Jonathan Blumm once defined it thusly: "Negative information appears in one news source, which puts the company on the defensive, which feeds other sources, who run other negative stories, which the original outlet picks up. Which starts the cycle all over again."
—Rob Reuteman, “Fallout for Janus and Qwest will likely linger,” Rocky Mountain News, September 06, 2003
2002
If you own a stock, or a business, you know a lot about risk — and how many varieties there are of it.

There's economic risk, which is what we've been having a whole lot of the last two years. There's interest rate risk — Alan Greenspan wakes up in a bad mood and decides to raise them. There's competitive risk — you own a store and Wal-Mart opens down the street. There's new-technology risk — you're the king of the eight-track tape industry, for example. …

And now we're hearing of yet another type of risk: headline risk.

The concept of headline risk apparently has been percolating in the background for a while, to judge from a quick scan of the term on Yahoo! But after seeing it used twice in one day last week, from two different sources about two different companies, one suspects "headline risk" is now climbing the best-seller list of popular business expressions.
—Bill Virgin, “Real risk in 'headline risk' is ignoring it,” The Seattle Post-Intelligencer, July 02, 2002
1993 (earliest)
We would not play stocks that are greatly affected by Clinton's programs. Such stocks will be whipsawed by unpredictable, fast changing events in Washington. February 17's speech was only a "policy skeleton." The meat goes on the bones over the next few months as the specifics of Clinton's budget are presented in late March, Hillary Clinton's health care plan is unveiled in early May, and the entire Clinton package is scrutinized by Congress.

We prefer to stand aside from the Washington guessing game and invest in companies benefiting from knowable themes that have been our focus—"niche plays, "Euro-industrials" and "destructuring" candidates. Investor's should avoid "daily headline risk" by steering clear of stock groups that will be subjected to vitriolic bashing by politicians.
—Gus Giviskos, “Brokers view the markets: A.G. Edwards Princeton,” Mercer Business, April 01, 1993
Notes
The real risk involved in headline risk isn't the initial negative publicity, but how the subject — usually a company or a politician — handles that publicity. Lying about it, trying to cover it up, or generally just appearing defensive and shifty, will activate the media's sensitive scandal antennae. The result will be stories with a negative slant or, worse, fresh revelations of wrongdoing; in short, more negative headlines. That is headline risk.