A “relief rally” (or a “sigh-of-relief rally”) is when a market picks up after a period of bad or uncertain news. For example, at the end of 2012, the federal government in Washington was occupied in creating a bipartisan agreement to avoid the “fiscal cliff.” When an agreement was in place, the stock market had a “relief rally.”
 
“Relief rally” has been cited in print since at least 1985, “sigh-of-relief rally” has been cited in print since at least 1988.
 
   
The Free Dictionary
Relief Rally
A general increase in stock or other security prices because an expected negative situation did not materialize or began to reverse itself.
 
23 September 1985, Syracuse (NY) Herald-Journal, “The investors,” pg. D2, col. 1:
Mike Strauss
Prudential-Bache
On Wall Street last week the post-Labor Day drift turned into a late summer, full scale retreat. At this time the only hope appears to be the lack of hope. Everything is becoming so universally dismal that there has got to be a relief rally lurking around.
 
30 July 1988, The Plain Dealer (Cleveland, OH), “Biggest gain in month posted: Higher bond prices fuel rally,” pg. 11-A, col. 1:
“We’re having a sigh-of-relief rally…in reaction to (Fed Chairman Alan) Greenspan’s speech yesterday,” says Jon Groveman, chief trader at Landenburg Thalman.
 
8 February 1990, Miami (FL) Herald, “Treasury auction results send stocks up 33 points,” pg. 1C:
Positive results from the Treasury Department’s auction of 10-year notes sparked a “sigh-of-relief” rally on Wall Street Wednesday that propelled blue-chip issues sharply higher.
   
New York (NY) Times
Blue-Chip Stocks Advance on U.S.-Japan Trade Agreement
Published: June 29, 1995
(...)
Bob Walberg, an analyst at MMS International, said he had expected a stronger “relief” rally on the news of a trade accord.
 
OCLC WorldCat record
Back to basics : moving beyond the relief rally in Asia.
Author: HSBC Securities.
Publisher: London : HSBC Securities, 1998.
Edition/Format:   Book : English
 
OCLC WorldCat record
READY FOR THE WAR DIVIDEND? Wall Street is betting on a short but sharp “relief rally” once an Iraqi invasion begins
Edition/Format:   Article : English
Publication: BUSINESS WEEK -NEW YORK- no. 3824, (March 17, 2003): 42-43
Database: British Library Serials
 
Google Books
Wall Street Lingo:
Thousands of Investment Terms Explained Simply
By Nora Peterson
Ocala, FL: Atlantic Pub. Group
2007
Pg. 110:
RELIEF RALLY A sharply upward spike in prices following a period of investor uncertainty.
 
FOX Business
Relief Rally: Dow Zooms 300 Points Higher on Fiscal Cliff Fix
By Adam Samson
Published January 02, 2013
Wall Street stormed into 2013 with a euphoric rally on Wednesday as traders enthusiastically cheered a short-term compromise in Washington that clawed the U.S. back from the recession-inducing fiscal cliff.
   
Seeking Alpha
S&P 500 Snapshot: ‘Cliff’ Relief Rally Fades With Help From The Fed
By Doug Short
January 4, 2013
The Cliff-avoidance relief rally fizzled at the open, trumped by the unexpected increase in initial unemployment claims. Some halfhearted buying took the S&P 500 into the shallow green, but the 2PM FOMC press release halted the buyers. Fed’s forecast that QE3 would end this year was not what the market expected. The index closed the day with a loss of 0.21%.