Born in Lithuania in 1903, he came to the United States in 1907. The family lived in Brownsville and Flatbush, Brooklyn where his father worked as a paper and cordage wholesaler, though he also wrote articles on philosophical subjects.
Schapiro excelled in mathematics and Latin at school and at 16 he entered Columbia University on a Pulitzer Scholarship. He received an advanced degree from Columbia in engineering in 1925. He was a major donor to Columbia University including Schapiro Hall (a dormitory) and the Morris A. Schapiro Center for Engineering and Physical Science Research.
In addition to his intellectual exploits, Schapiro also excelled in chess. He led the Columbia University chess team to four national championships. In New York, he took 3rd, behind Dawid Janowski and Roy T. Black in 1920, twice won Manhattan CC championship (1921 and 1922). Schapiro won a match against Oscar Chajes (7.5-5.5) in 1923. He finished 5th at Lake Hopatcong 1923 (American Chess Congress). His career was before Elo ratings existed so he was never rated , but was one of several veteran players who, when the USCF first published rating lists, was awarded the title of Master Emeritus.
Schapiro served as head of his own investment banking firm, M. A. Schapiro and Company. He established new business techniques for the banking industry and in the course of his career he led some of the banking industry's largest mergers: Chase Bank and the Bank of Manhattan in 1955, then Chemical Bank and New York Trust in 1959.
"On both deals, Mr. Schapiro followed his traditional strategy. He recommended the two banks' stocks to affluent clients, then asked them to press the banks' managements to agree to a deal," the New York Times wrote in his obituary.
His strategy caused some of Schapiro's rivals to label him ''the bank liquidator,'' a nickname that was more an honor than a jab. Although he arranged some of the largest business deals in the 1950's, Schapiro never received a fee for his services; instead, he took his profits from the exchange of stock. ''It must be remembered that the bank stockholder is not wedded to banking as a business,'' Schapiro said during a speech in 1949. ''His sole concern is with the value of his investment.''
Schapiro married Alma Binion Cahn, a painter, who died in 1987 after 58 years of marriage. They had two children, Linda Schapiro Collins and Dr. Daniel Schapiro. His grandchildren include painter Jacob Collins. Schapiro died aged 93 at his New York City apartment in 1996, only a few months after his brother Meyer.
While disliked (feared) by some bankers, he was extremely well liked by his colleagues. Once, while vacationing in Maine, Schapiro telephoned his office and spoke with everyone there. Known for his small kindnesses, his 50 employees at his 2 firms received free lunches every day, a practice that is virtually unheard of along Wall Street...or anywhere else for that matter.
Schapiro died at his apartment on the Upper East Side of Manhattan at the age of 93.