## Friday, 12 September 2014

### Stock Flow Ratios and the "Velocity of Collateral"

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[1].

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.

[1] Although, as I have written previously, we should be careful with this interpretation.

1. I think you broke the wonk-meter on this one.

Interesting investigation about the asymmetries of stock flow relationships.

Being symmetry-obsessive, I’d look at it a bit differently.

This is pretty quick and dirty:

Suppose M = 100 and velocity = 2.

Assume GDP transactions.

So GDP = 200.

And there is a money flow of 200.

But there may also be a real stock record of what has happened.

That stock may have disappeared due to consumption, but there is still a real stock record, at least in the case of goods if not services.

So the idea that there is no stock outstanding is really a function of consumption (possibility some depreciation as well).

Conversely, it is possible to construct an example where velocity of money acts on original GDP investment that remains at full nominal value, in which case there is an outstanding stock of 200.

Now assume non-GDP transactions in the case of money.

Such as the use of the same stock of M to acquire financial assets.

Then there is clearly a mapping of velocity into outstanding stock.

Turning to collateral:

Suppose C = 100 and velocity = 2.

Similar to the second case for M, the same collateral will be associated with several different accounting entries (for monetary stocks).

But the actual collateral only exists once as a spot position in its original quantity.

So yes there is outstanding stock which is a multiple of the actual collateral.

But this is not much different than the non-GDP case for money above, is it?

So I think there is a flow in both cases.

The outstanding stock may disappear in the in the case of money acting on GDP transactions that are subject to consumption or depreciation or in the case of GDP services.

But beyond that I’d be cautious about generalizing an asymmetry.

1. "I think you broke the wonk-meter on this one." Ha-ha! It struck me when I was writing it that it was a bit niche, but - hey - I write what interests me, not what I think lots of people want to read.

I'm not sure I entirely follow you, but I suspect I disagree.

I don't think there is a useful stock measure of GDP. You could propose some measure that starts the period at zero and is then added to by all the GDP to date. This would then be measured simply in dollars, rather than dollars per period. But I don't think that's valid, because the value of your "stock" at any time depends critically on the point in time at which you take the "stock" to be zero, and therefore a time period is implicit.

Looking at non-GDP transactions, we either have the stock of financial assets or we have some flow measure. For money velocity measures, the flow measure would be the gross volume of transactions. For a given stock of assets, the gross volume of transactions could be anything.

Looking at collateral, to get something closer to money velocity, we would have to look, not at the volume of outstanding positions, but rather the turnover. This would mean that if we had mainly six-month repos say, the velocity would be much less than if we had mainly overnight repos, even if the amount of repos outstanding was the same (ignoring susbtitution here). This sort of measure might be described as the number of times there was a change in title for each security, on average (and this would actually be more accurate a description than the money velocity interpretation). However, this is not what collateral velocity (as generally described) measures.

2. Vice versa, the concept of collateral velocity, as I understand it from your post, would translate into something like a leverage ratio between different types of monetary assets, i.e some measure of base vs. broad monies.

But then I'm not sure, such an analogy makes much sense, because an important distinction between monetary and non-monetary financial assets is lost. That might be what JKH is getting at (?), namely that monetary assets are best thought of as mapping onto a stock of goods or services that can be bought with it, as opposed to other types of money it can be exchanged for.

As for GDP and non-GDP transactions, this distinction seems to get lost under both concepts of velocity.

3. As to translating to a leverage ratio, I think that is certainly a better way of looking at it. A leverage ratio is clearly a stock / stock ratio. However. I would say that I don't actually think that rehypothecation achieves anything like leverage in a balance sheet sense. You sometimes hear about a collateral equivalent of the money multiplier and I like that idea any better than I do collateral velocity.

I agree on the GDP and non-GDP distinction. I'm not sure that it makes sense to try and factor that in anyway.