“Aunt Jane” is Wall Street’s term for the average, unsophisticated investor. Personifying someone with an “aunt” or an “uncle” name is commonplace and is often difficult to trace to a specific date.
 
“Aunt Jane” is cited in print by at least 1954. The name “Aunt Jane” was probably either coined or popularized by Robert R. Young (see below), in his corporate struggle with the New York Central Railroad..
 
Another name for an unsophisticated investor is “Aunt Millie.”
       
 
11 February 1954, New York (NY) Times, pg. 46:
Bob Young is a specialist in rallying the support of small stockholders (“Aunt Janes,” he calls them). Presumably, it is the more than 40,000 “Aunt Janes” among the Central’s stockholders to whom he will make his appeal in the proxy fight.
 
17 February 1954, Abilene (TX) Reporter-News, “Business Outlook” by J. A. Livingston, pg. 3B, col. 1:
Robert Young Assumes Knightly Role
In Struggle for New York Central
Robert R. Young, former chairman of the Chesapeake & Ohio Railway, is a remarkable man. On Wednesday, Feb. 10, the board of directors of the New York Central Railroad, second largest in the United States, decided to reject Young’s offer to become chairman of the Central.
(...)
The inference Young wants drawn is that Young has no selfish interest. His is the voice of the little stockholders—the Aunt Janes, as he is wont to say—and they are on his side.
     
Google Books
Dividends and Democracy
By Lewis D. Gilbert
Published by American Research Council
1956
Pg. 99:
... but most I would say are from “Aunt Jane,” that legendary shareholder figure who typifies the small investor and who is said to live in Kankakee, Illinois, or Kokomo, Indiana, or Oshkosh, Wisconsin, or Dubuque, Iowa.
   
5 November 1956, Washington (DC) Post, “Small Investor Gripped by Indecisions, What With Wars and a Major Election” by Malvina Lindsay, pg. A23:
These dubious days find many an Aunt Jane (small stockholder) bogged down in financial indecision.
   
9 July 1958, Washington (DC) Post, “‘Aunt Jane’ Investor Service Progresses” by Frank C. Porter, pg. A27:
Investor Service, a Washington agency offering the small investor syndicated loan and real estate opportunities, expects to top the million-dollar mark in volume this year, according to its founder, Samuel J. Gorlitz. 
 
10 April 1961, Fresno (CA) Bee, “Most Stock Owners Are In Middle Income Group” by Sylvia Porter, pg. 11A, col. 4:
Joe and Aunt Jane, in short, are way in the minority.
 
Google Books
Mutual funds—Legal Pickpockets?
By Dean Palance
New York, NY: Vantage Press
1963
Pg. 320:
Aunt Jane: Wall Street’s nickname for the mutual fund investor.
     
Google Books
The Executive
By Baker Library
Published by The Library
1963
Pg. 26:
These studies say plainly that Aunt Jane—the mythical lady who owns the stock but can’t be bothered to read or understand anything pertaining to it—is dying.
 
29 November 1965, New York (NY) Times, “Small Investors Being Faithful To AT & T. Despite Stock Dip” by Edward T. O’Toole, pg. 53:
Does the persistent weakness in American Telephone—the biggest stock on the Big Board and the most widely held issue in the nation—reflect a loss of confidence by Aunt Jane and some 2.6 million other individual investors?
 
3 December 1965, Fresno (CA) Bee, “Soaring Stock Mart Trade Stirs Unease” by Sylvia Porter, pg. 4C, col. 1:
BUT THE SMALL speculator is not the same character as in 1961, say informed Wall Streeters. (“Aunt Jane isn’t in.”)
 
14 June 1968, Appleton (WI) Post-Crescent, “Today’s Speculator in Stocks Not ‘Aunt Jane’” by Sylvia Porter, pg. B4, col. 1:
The woman who is speculating in glamour stocks on an unprescedented scale today is NOT “Aunt Jane,” the little old spinster of folklore who can least afford to risk her pittance in stocks.
     
Google Books
Robert R. Young, the Populist of Wall Street
By Joseph Borkin
Published by Harper & Row
1969
Pg. 175:
“Aunt Jane” was Young’s reference to the small stockholders, many of them middle-aged women, who looked on their stock as part of a ... 
 
30 April 1970, New York (NY) Times, “Market Place: Dutch Boy Plugs Wall Street Dike” by Robert Metz, pg. 56:
Call it the Aunt Jane Society—champion of the small shareholder. 
     
Google Books
A View from the Street
By Donald T. Regan
New York, NY: New American Library
1972
Pg. 180:
Second, the securities industry serves millions of customers, from the mythical Aunt Jane with five shares of AT&T to the Prudential Life Insurance Company…
 
Market Place: Analysts’ Efforts Termed Sketchy
$3.95 - New York Times - Oct 13, 1972
Aunt Jane, the ubiquitious small investor who everyone is so worried about, has been reading her brokerage house’s research reports very carefully of late, ...
   
Google Books
The Encyclopedia of Management
By Carl Heyel
Published by Van Nostrand Reinhold Co.
1982
Pg. 37:
“Aunt Jane” — a stockholder with no financial background.
 
22 July 1988, USA Today, “The kind of street slang you could use” by Michelle Osborn, Money section, pg. 5B:
Wall Street Slang : High Steppers, Fallen Angels, & Lollipops
By Kathleen Odean
Dodd, Mead & Co. 212 pp. $16.95
(...)
It’s fun and instructive - unless you’re a lobby rat (tape-watcher in from the streets), dead duck (speculator who lost everything), Aunt Jane (small shareholder) or barefoot pilgrim (someone whom a broker can talk into any trade), of course.