“In the red” means that a business entity is experiencing losses; “in the black” means profits or gains. Accounting ledgers used red ink and black ink for accounting entries. “In the red ink” (the longer phrase of “in the red”) was the understood expression for losses by about the year 1920.
 
   
InvestorWords.com
red ink
Deficit, loss.
(...)
in the red
Losing money. opposite of in the black.
(...)
black ink
Profit. opposite of red ink.
(...)
in the black
Profitable. opposite of in the red.
   
Merriam-Webster Dictionary
Main Entry: red ink
Function: noun
Etymology: from the use of red ink in financial statements to indicate a loss
Date: 1926
1 : a business loss : deficit
2 : the condition of showing a business loss
     
(Oxford English Dictionary)
red , a. and n.
The colour conventionally (now less commonly) used to indicate debit items and balances in accounts, used esp. in phrases in the red: in debt, overdrawn, losing money (also fig.); out of the red: in credit, making a profit. Hence, debt, an overdraft. Cf. BLACK n. 2d.
1926 MAINES & GRANT Wise-Crack Dict. 10/1 In the red, losing money in show parlance. 1927 Scribner’s Mag. Apr. 380/2 ‘We’ve got to put forth our best efforts from now till the end of the month, or we’ll be in red on the books,’ he announced.
1928 Publisher’s Weekly 10 Nov. 1957/2 About 966 copies more and the title will be out of the red.
1931 F. L. ALLEN Only Yesterday viii. 212 The Philadelphia Sesquicentennial was sinking deeper and deeper into the red. 1949 Harper’s Mag. Mar. 62/2 The corporation was nearly a million dollars in the red.
1955 Times 28 June 3/3 With Tordoff and Saeed opening Somerset’s second innings with commendable vigour, Leicestershire went further into the red.
1960 Times 15 Feb. 11/6 The British Transport Commission is already in the red to the tune of at least £30m. 1966 O. NORTON School of Liars i. 5, I don’t think the manager at Barclays has ever heard of the Married Women’s Property Act,..my red is Andrew’s red.
1977 D. WILLIAMS Treasure by Degrees xviii. 169 A quarter of a million pounds..would be more than sufficient to keep the College out of the red for the foreseeable future.
1978 S. BRILL Teamsters vii. 268 CCC has never run in the red.
 
red ink
U.S. colloq. The debit side of an account: cf. RED n.1 1g. Also in extended use.
1929 Century Mar. 605/2 Red ink returns were as prolific as asparagus, which meant you..dug deep for the freight money.
1939 S. BENT Newspaper Crusaders ii. 35 The long-drawn crusade whereby St. Louis was taken out of political red ink and put on the credit side of the electoral ledger merits examination. 1948 Sun (Baltimore) 31 Jan. 1/3 We cannot play with red ink when we’re financing a great government.
1967 Boston Sunday Herald 7 May IV. 9/2 Give us enough red ink and make money plentiful enough and the economic skies will soon clear.
1977 Time 28 Feb. 26/1 Carter’s projected $57·4 billion deficit is an improvement over the $68 billion in red ink anticipated for fiscal 1977, which ends on Sept. 30.
1979 Financial Rev. 19 Oct. 27/1 The company would report a loss of more than $US 3 million for the third quarter, bringing the red-ink figure for nine months close to $US 6 million.
 
to be in the black: to show a profit; to have a credit balance. (From the practice of recording credit items and balances in black.) Cf. in the red (RED n.1). orig. U.S.
1928 N.Y. Times 11 Mar. VIII. 6/2 In the black, showing a profit.
1940 Jrnl. R. Aeronaut. Soc. XLIV. 734 With but few exceptions American air carriers are..operating ‘in the black’.
1955 Times 30 Aug. 9/5 On an overdraft, understandably, the banks charge their customers a percentage; but when we are ‘in the black’ nothing is ever added.
1958 Times 24 July 5/1 All the independent television companies are well in the black. A.T.V. made a profit of over £3,500,000 for the past year.
 
Google Books
Campbell’s Actual Accounting
By Thomas F. Campbell
Indianapolis, IN: The Bobbs-Merrill Company
1911 and 1912 (two copyrights)
Pg. 74:
Rule and foot the account; then transfer the gain to the credit side of the Loss & Gain account in black ink,...
Enter the $266.00 of loss in red ink,...
 
8 February 1920, San Antonio (TX) Light, pg. 12D, col. 1:
One of the more recent innovations that the incoming manager found was a bakery department; and the figures showed that the bakery, far from earning a good profit, was adding its share to the red ink on the company’s books.
   
3 May 1920, Anaconda (MT) Standard, pg. 4:
Uncle Sam was $12,217,638 in the red ink for the last month as a railroad operative.
 
2 April 1922, Anaconda (MT) Standard, pg. 2:
“Although the administration has done all possible to economize, we are still in the red ink,” said the mayor, commenting on the financial status of the city at the present time.
   
21 April 1922, Wall Street Journal, pg. 9:
Automatically, gas department ceased operating “in the red.”  Profits replaced losses and gas business again took up it proportionate burden of meeting divdend checks.
 
2 February 1923, Wall Street Journal, pg. 13:
Carter, Macy is now making satisfactory profits. Amsinck is operating in the black. So is Pacific Mail which will probably show some $250,000 earned in 1922.
 
6 February 1923, New York (NY) Times, pg. 23:
“The passing months have seen the records of brick manufacturers, as well as other business men, in the red ink of loss, and there is no indication that the coming months will see any change,” Mr. Bryan said.
 
20 September 1924, Wall Street Journal, pg. 1:
RED AND BLACK
Naturally the cold months of the year show red ink figures for the American Ice Co. It has been known in the history of the ice business that the company has been 10 months in the black and then again this has dwindled to six months. This year, owing to its unseasonal qualities, has probably seen a larger period in the red, but it has been pointed out that once the demand for ice reached summer proportions, profits instantly became very large, and so it has been this year, although it is not likely, owing to an unseaonable summer, that the company’s final earnings will be as high as they were last year, when $12.52 was earned on the common stock.