FRED graph called Velocity of M2 Money Stock shows that the money stock M2 does not hold a constant ratio to flow of nominal GDP:
https://fred.stlouisfed.org/series/M2V
This article Money, Credit, and Velocity (May 1982) makes statements concerning velocity of money that may be inaccurate when considered over long periods of time, however, it accurately describes some realistic features of money and credit markets:
https://files.stlouisfed.org/files/htdocs/publications/review/82/05/Money_May1982.pdf
In contemporary market economies, the money supply grows through two types of credit transactions: the central bank creating deposits (money) and bank reserves by buying government securities, and depository institutions creating deposits (money) from increased reserves by granting loans.
Of course, not all credit extensions entail monetary expansion. There are three distinct sources of credit extension: (1) bank and non-bank depository institution’s (commercial banks, savings and loans, credit unions, mutual savings banks); (2)non-depository financial intermediaries (finance companies, investment banks, brokerages, insurance companies); and (3) sellers of goods (retail and trade credit).
In the first case, a depository institution lends money to a borrower who in turn uses these funds to purchase goods or repay debts; the credit extension entails monetary expansion of purchasing power because it consists of checkable deposit expansion. During the last three decades, loans by such depository institutions have accounted for between 35 and 50 percent of the annual total of credit market funds extended to the non—financial sector. Alternatively put, more than half of the credit extended annually in U.S. financial markets does not entail deposit expansion.
In the second case, a non—depository institution (e.g., a consumer finance company) issues the credit or buys the accounts receivable of a credit—issuing seller. The latter method of credit extension is called factoring, and non—depository institutions fund this activity by either selling debentures directly or by acting as an agent for a depository institution. Under either method, the extension of credit does not entail an expansion of deposits but a reallocation of existing deposit holdings.
Finally, in case three, credit may be extended directly by the seller of goods and held as accounts receivable. Often this credit is financed by the sale of commercial paper issued by the seller/credit—issuer (e.g.,firms with their own financial subsidiaries such as Sears or General Motors). In these instances, whether the firm holds its own accounts receivable, factors its accounts receivable or sells commercial paper, the extended credit represents an increase in purchasing power not created by checkable deposit expansion.
This article argues that capital gains transactions, for assets that were produced in the past and not measured as part of current nominal GDP, should not count as income and do not count in nominal GDP:
https://taxfoundation.org/should-capital-gain-be-considered-income/
The Bureau of Economic Analysis (BEA), one of the principle statistics reporting agencies for the U.S. economy, does not include capital gains or losses in their National Income and Products Accounts (NIPA), from which GDP is calculated. The BEA reasons: “Capital gains and losses are not included in NIPA measures, because they result from the revaluation and sale of existing assets rather than from current production.” In other words, a change in the sale price of an asset does not add or subtract from the goods and services produced in the United States today.
When banks offer credit to purchase assets in the secondary market these transactions would tend to increase bank credit, and M2 money stock, but would have no impact on the income NIPA describes as the nominal GDP. There are many transactions that would tend to increase or decrease M2 that are not coupled in any way to the current flow called the nominal GDP.
If aggregate demand is driven at the margin by market credit and government policies then inflation or deflation are caused by complex credit and money market activities, in primary and secondary markets, also coupled with central bank policies and fiscal policies. Then the Velocity of M2 Money Stock would simply be a ratio V = GDP/M2 calculated as a residual outcome of the complex financial system.