An old Wall Street proverb says that the stock market “climbs a wall of worry” to march into bullish territory. The “wall of worry” phrase is cited in print from at least the 1950s.
 
An opposite proverb is “Bear markets slide down a slope of hope.” Another financial proverb about “worry” is “Worry is interest paid on trouble before it falls due.”
   
     
Investopedia
Wall of Worry
A phrase used to describe a bullish market trend occurring in the face of negative uncertainties. 
 
When stock prices are rising regardless of market uncertainties, the stock market is said to be climbing a wall of worry. These worries may include political or economic risks. Once the perceived risks have been resolved or have past, average market share prices tend to decline. 
 
16 September 1958, The Derrick (Oil City, PA), pg. 12, col. 3:
To illustrate: every basic bull market must have a Wall of Worry on which to climb. A bull market goes up in the face of intermediate bad news based on current facts that are very upsetting to the statisticians, who usually fight the move until it nears an intermediate top, when, as the news turns better, they finally give up and turn bullish.
 
21 November 1976, Galveston (TX) Daily News, pg. 5A, col. 7:
But, there is an old saying that “the market climbs on wall of worry.”.
   
27 July 1980, New York (NY) Times, “The Markets: Inflation Fears Build Again” by H. J. Maidenberg, pg. F19:
Anthony Ludovici, vice president and market analyst at Tucker, Anthony & R. L. Day Inc., agreed on the bullishness. “But as the old adage in the Street goes,‘every bull market must scale a wall of worry’,” he said. “Much of the worry today is traceable to the confusion among investors who follow Federal Reserve and other market indicators.”
 
Google Books
Is Inflation Ending?: Are You Ready?
By A. Gary Shilling, Kiril Sokoloff
Published by McGraw-Hill
1983
Pg. 69:
Those who are intimate with the securities markets often say that a “bull market climbs a wall of worry”— that is, the more skepticism there is about a change in trend, the more change should be believed.
   
Google Books
The Warning:
The Coming Great Crash in the Stock Market
By Joseph Ensign Granville
Published by Freundlich Books
1985
Pg. 201:
As bull markets climb a wall of worry, the great bear market now in force was crumbling on a wall of confidence.
 
New York (NY) Times
ARCHIVES OF BUSINESS:
THE DOW IN PERSPECTIVE
TRACING THE UPS AND DOWNS OF THE 20th CENTURY THROUGH THE EYES OF WALL STREET;
Most Experts Are Saying the Surge Will Continue
By ANISE C. WALLACE
Published: January 18, 1987
(...)
Even this kind of caution cheers investors. ‘‘The market does climb a wall of worry,’’ said Mr. Berg. Since the Dow hit 1,200 a year and a half ago, so-called value managers, who look for company stocks that are priced low in comparison with the value of company assets, have said that the market is overpriced. For instance, Leonard M. Heine, president of the Management Asset Corporation in Westport, Conn., has almost half of his clients’ $1 billion in cash. Much to the dismay of Mr. Heine and other investors, buyers continue to swarm into the market, driving prices ever higher.
 
Google Books
Buy the Rumor, Sell the Fact:
85 Maxims of Wall Street and What They Really Mean
By Michael Maiello
Published by McGraw-Hill Professional
2004
Pg. 19:
Bull Markets Climb a Wall of Worry
View the market as an amalgam of different and sometimes competing minds and it makes sense that though the overall sentiment might lead toward one outcome, powerful forces can temporarily pull it in another. The “Wall of Worry” behind every bull market is the group of bearish investors who are either shorting equities or constantly selling to take profits and who can cause severe dips during a long bull run.