Contrary to popular belief, the New York Stock Exchange was not founded under a buttonwood tree in 1792.
The leading stockbrokers of New York did sign an agreement in 1792, and this agreement is the oldest document in the NYSE archives, but it did not found a stock exchange. It was an informal agreement to charge a fixed commission on stock trades and to “trade preferentially.” There were no further rules for trading, no permanent organization or enforcement mechanism, and it’s unclear how long the agreement remained in force. The securities industry was secretive and left few records of its activity, in part to avoid falling afoul of laws against “stock-jobbing.” Although commission rates remained stable through this period, it’s hard to tell whether this was a continuing explicit arrangement or tacit agreement.
Oh, and although they often traded stocks under a buttonwood tree on Wall Street, they wouldn’t have signed any legal agreements there. That happened indoors.
The New York Stock & Exchange Board was actually founded on Saturday, March 8th, 1817, when the leading stockbrokers of New York (including a few who’d signed the so-called Buttonwood Agreement a quarter century earlier) adopted its first constitution. Here are the prices of stocks from their first trading day:

This from the March 11th issue of the New York Shipping and Commercial List, a semiweekly publication that reported shipping activity and prices of numerous commodities, as well as stock prices and other financial indicators. A few months later, the exchange would select the Shipping and Commercial List to publish its official prices, and this legend appeared on the price list beginning with the September 2nd issue:

(These are scans from microfilm, which after some difficulty I was able to obtain at the New York Public Library. The catalog also listed paper copies as extant, and they might be a bit more legible than the microfilm, though less easy to scan and embed.)
Several things stick out to me about these price lists. For starters, treasury and municipal bonds are listed alongside company shares; at the time, the word “stocks” included all of these, being only restricted to equity interests some time later. Another thing to note is some securities have pairs of prices. This indicates that these are price quotes, rather than reports of actual trades on the exchange. Two prices are a bid/offer pair, while I suppose a single price could be either a bid or an offer. Finally, note that most of the prices are near 100. Industry practice was to quote stocks, like bonds, as a percentage of par value rather than a price per share.
So what were these companies, and how would an early investor in NYSE-listed companies have done? The latter is hard to determine without a full history of dividends and stock splits, but there is information out there on how these companies performed in the years after 1817.
Banks
The (second) Bank of the United States appears alongside treasury bonds as a “national stock”, separate from the other banks. Unlike the modern Federal Reserve, but like other “central banks” of the time, it was a majority privately owned company that offered loans and accounts to private customers as well as its official government business. It was also the only bank that could open branches in more than one state. According to the 1817-18 city directory, its New York branch was located at 65 Broadway.
The bank was incorporated by Congress for a 20-year term in 1816. It became a target for populist outrage stoked by Andrew Jackson, who vetoed a renewal of its charter. The management tried to continue it in business as a local state-chartered bank in Philadelphia, but it failed in 1841, and the stock would’ve become worthless at that point.
As for the other banks listed, their institutional histories have been posted online by the New York Department of Financial Services (along with every other bank in the state) so it’s easy to track down what became of them.
The Bank of New York was organized as an unincorporated joint-stock company in 1784, just a few months after the evacuation of the British troops from New York at the end of the Revolutionary War. Alexander Hamilton was a co-founder and sat on its first board. Despite the backing of a prominent politician and war hero, the bank couldn’t obtain a charter from the state legislature until 1791 (chapter 37 of the session laws) and shareholders had unlimited liability until that point.
Its office was at 32 Wall Street in 1817. It still exists under the abbreviated brand of BNY, though it’s had a low profile outside the industry since selling its branch network to Chase in 2006.
The Manhattan Company was incorporated by the state legislature in 1799 (ch. 84) under false pretenses. It was chartered as a water company and given rights to construct dams and aqueducts to supply fresh water to Manhattan, with a stealthily inserted clause allowing it to operate any other lawful business once the waterworks were complete. Instead the company dug a well and laid a few pipes, and then almost immediately opened a bank to compete with BNY’s monopoly. (I should note that the founders were associates of Aaron Burr. Lots of bad blood there.)
In 1817 the Manhattan Company was at 23 Wall. Merged with Chase National Bank in 1955 and for almost 50 years afterwards the combined bank was officially “Chase Manhattan.” Today Chase sometimes claims a founding date of 1799 and it’s rumored that the Chase logo represents a water pipe.
Merchants’ Bank in the City of New York: Organized in 1803 and incorporated in 1805 (ch. 43). 35 Wall. Merged with the Manhattan Company in 1920, so now part of Chase.
Mechanics Bank in the City of New York: Incorporated in 1810 (ch. 87). 16 Wall. Merged with Chase in 1926.
Union Bank in the City of New York: Incorporated in 1811 (ch. 34). 17 Wall. Doesn’t appear in the DFS list, so I had to do some digging into old Banking Department reports to find that it closed circa 1867.
Bank of America: Incorporated in 1812 (ch. 78). Wall & William. No relation to the present-day Bank of America. Merged with Citibank in 1931.
New York Manufacturing Company: Incorporated in 1812 (ch. 167) and authorized to operate both a manufacturing business and a bank. In 1817 abandoned the manufacturing business and changed its name to Phenix Bank. 24 Wall. Went through a series of mergers in the 20th century, and its ultimate successor is Chase.
City Bank of New York: Incorporated in 1812 (ch. 175). 38 Wall. Started using the tweaked spelling “Citibank” as its telegraph address since I is much shorter than Y in Morse code. This became its official name in 1976. Still exists, of course.
Insurance companies
These are much harder to track down than the banks. The insurance business was mostly unregulated and quite unstable in the early 19th century, with companies opening and closing frequently, and lots of competition from private underwriters without corporate charters. New York in particular saw two devastating fires in 1835 and 1845 that bankrupted most of its insurers. In the absence of local insurance companies, insurers from neighboring states started serving the New York market; this was a big element in Hartford becoming the “insurance capital of the world.”
The first report of the Insurance Department shows only two of the early NYSE-listed companies as still existing in 1859; neither exists today. I found an 1880 article in the Insurance Times that shed some light on these businesses and their fates. Consulting the city directories and the session laws filled some more of the gaps.
The Mutual Insurance Company of the City of New York was organized in 1787 by Alexander Hamilton and associates as an unincorporated association. Incorporated in 1798 (ch. 46). Became a stock company in 1809 but kept the “Mutual” name. In 1817 their office was at 52 Wall. Became insolvent after the 1835 fire, but recapitalized and resumed business. In 1846 changed its name to the Knickerbocker Fire Insurance Company to avoid confused with numerous other mutual companies that had formed in the interim. Declined over the course of the 19th century and finally closed in 1890.
United Insurance Company in the City of New York: Established in 1796, incorporated in 1798 (ch. 41). 49 Wall. Closed in 1818.
New York Insurance Company: Incorporated in 1798 (ch. 71). Founded by Archibald Gracie - the one who built the mansion. Mainly a marine insurer. 34 Wall. Closed circa 1852.
Washington Insurance Company of the City of New York: Incorporated in 1802 (ch. 67) as a mutual insurer. Became a stock company in 1814. William & John. Failed in the 1835 fire.
Eagle Fire Company of New York: Incorporated in 1806 (ch. 152), also with the participation of Gracie. 59 Wall. Insolvent and recapitalized after the 1835 and 1845 fires, and like the Mutual/Knickerbocker survived until just after its 100th anniversary, closing in 1908.
Phenix Insurance Company of New York: Incorporated in 1807 (ch. 12). 47 Wall. Closed in 1820.
Ocean Insurance Company: Incorporated in 1810 (ch. 19). 45 Wall. Closed 1842.
New York Firemen Insurance Company: Incorporated in 1810 (ch. 20). Founded and initially owned by FDNY firefighters. 56 Wall. Closed 1825.
American Insurance Company of New York: Incorporated in 1812 (ch. 192) as a reorganization of the insolvent Marine Insurance Company. 51 Wall. Closed circa 1845.
Globe Insurance Company: Incorporated in 1814 (ch. 50). 55 Wall. Failed in the fire of 1835.
National Insurance Company: Incorporated in 1815 (ch. 173). 47 Wall. Closed 1835.
Pacific Insurance Company of New York: Incorporated in 1815 (ch. 179), though it didn’t open for business until 1818. 49 Wall. Closed 1831.
So this isn’t the most inspiring beginning of what would become a central engine of American capitalism. A handful of local banks - though a couple would eventually become major financial institutions, and only one completely failed - and a dozen small insurance companies, all of which would fail or be reorganized within 30 years. Plus a government-sponsored entity that collapsed soon after losing government sponsorship, and a few government bonds. This was long before any regulations requiring companies to publish financial reports, so a stock trader would have very little to go on. Dividend yields would be the clearest signal. But I imagine that these companies all being located within a few blocks of each other on Wall Street, word would get around pretty quickly as to which ones were thriving and struggling.
Remember, this was at the dawn of industrialization. New York was a city of about 100,000 residents, and still competing with Philadelphia to be the country’s financial center. It was only in the following decades that the Erie Canal would decisively make New York the main seaport of the East Coast, and its financial dominance followed from that. Then beginning in the 1830s, the railroads would become the first large businesses in America and their stocks would become the favored instruments for Wall Street speculators. The NYSE would grow from a sleepy club of brokers who transacted in local stocks to, well, the NYSE.
