I've read a couple of good blog posts in the last few days which, although apparently unrelated, have an interesting connection.
The first is Brian Romanchuk's piece in which he gives a nice, clear account of the role of stock-flow norms in economic modelling. He emphasises the importance of distinguishing between stock variables and flow variables. Stocks represent the state of affairs at a specific point in time; flows are what occur during a period of time, or simply between two specific points of time. Just as it is important to know what variables are stocks and what are flows, it is also important to distinguish different types of ratio: flows to flows, stocks to stocks, or stocks to flows.
The second is Scott Skrym's post on the "velocity of collateral" - a term used to highlight the way collateral is re-used in repo and other transactions, so that the same securities can be posted several times in so-called "collateral chains". Skrym provides a good description of the way this works and, as always, some useful context from current trends in the repo market.
People who use the term "velocity of collateral" like to present it as analogous to the velocity of circulation of money. We have a stock of eligible collateral, rather than a stock of money, and in each case we have a certain volume of transactions that the collateral, or money, is used in.
However, there is a confusion between stocks and flows that is creeping in here. When the velocity of circulation of money is considered it is in terms of comparing the stock of money with a measure of flow. Typically that flow is the monetary value of the transactions in a given period. So we take a period of, a year say, and add up the value of each transaction that has taken place within that year.
The unit of measurement for this value (being a flow) will be dollars per year. In comparison, the unit of measurement for the money supply will be just dollars. So when we divide the value of transactions by the stock of money, we get a measure of velocity of circulation which is expressed as number of times per year. We can interpret this as being the number of times each dollar changes hands per year, on average.
When calculating the "velocity of collateral", however, the stock of collateral is compared with the volume of collateralised transactions outstanding at any given time. This latter variable is a stock concept. It is measured as a pure dollar value, not a value per unit of time. This means that when we divide by the quantity of collateral, we get a number expressed as a pure ratio, not as a number per unit of time.
"Velocity of collateral" is a stock / stock ratio; velocity of money circulation is a stock / flow ratio. They are very different concepts. That is not to say that the thing that "velocity of collateral" measures does not matter; rather that we need to be wary of interpreting it as being comparable to the velocity of circulation of money.