## 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.

## Wednesday, 3 September 2014

### Own Rates of Interest and Real Rates of Interest

David Glasner had a couple of posts recently (here and here) considering real rates of interest in a barter economy.  I'm not sure I quite agree with him even in his last post on the topic, so I thought it was interesting to look at further.  I'm going to use the numbers from his example.

The issue he is looking at is the pricing of loans in a barter economy.  In this economy, loans have to be constructed with commodities.  So I might lend you 100 onions at 5% interest, which would mean that at the end of the loan you would pay me back 105 onions.  We are assuming this is a proper loan, like a loan of money, so onions are simply the denomination and the settlement medium.  In other words, you do not have to return to me the same onions I loaned you, plus five more.  You simply deliver to me 105 onions of the required type.

We can say that 5% is then the "own rate" for loans of onions.  We then consider what own rates might apply to loans of other commodities, like tomatoes or cucumbers.  For this, we assume that normally onions, tomatoes and cucumbers all trade at par with one another, but currently there is lower demand for tomatoes and higher demand for cucumbers.  So, at the current prices, 100 tomatoes exchange for 90 onions and 100 cucumbers exchange for 110 onions.

Simple arbitrage then dictates what the own rates of interest must be for tomatoes and cucumbers.  For example, someone might borrow 900 onions and exchange them for 1,000 tomatoes.  To repay their onion loan they need 945 onions (principal plus 5% interest), which they can get at the end of the loan by exchanging 945 tomatoes at the then par rate.  So a loan of 1,000 tomatoes will require repayment of 945 tomatoes, an interest rate of -5.5%.  Anything else will allow endless profits from borrowing in one commodity and lending in the other.  A similar argument shows that the own rate on loans in cucumbers must be 10.5%.

We need to ask how there can ever be a negative own rate of interest, such as we have here on tomatoes.  Does this not mean that someone can borrow 1,000 tomatoes, repay 945 and walk away with 55 tomatoes in profit?  The answer relates to the time aspect of the loan and the implications for storage.  If tomatoes are perishable, it may not be possible to store them from one period to the next at all, so this arbitrage may not be available.  Even if we take a non-perishable commodity, such as a precious metal, there may be storage costs such as security and these may eliminate the potential profits.

It is worth considering what would happen if there were no storage costs.   People would then want to borrow more tomatoes in order to simply hold them and take the profit.  This would tend to bid up the own rate on loans of tomatoes, which would prompt other people to exchange cucumbers and onions for tomatoes to be able to make more tomato loans.  This in turn would increase the current price of tomatoes in terms of these other commodities.  So both the own rate on tomato loans and the current price of tomatoes increases.  This continues until the arbitrage is eliminated.

So we have a different own rate for each commodity, but the relationship between all the rates is tied to the price structure.  With prices given, if one rate changes, they must all change.

If we introduce money to this economy, it must fit the same structure.  There will be a money price for each commodity.  We can work out the appropriate rate for money loans by reference to the current and future price of onions and the own rate on onions in order to meet the no arbitrage condition.  If we do the same exercise using tomatoes or cucumbers, we will get the same rate.

The question now is what the real rate of interest is here.  We have a different own rate of interest on each commodity.  Which if any is the actual real rate of interest?  In fact, we cannot say what the real rate of interest is without specifying the commodity in which we are expressing it.  There is no absolute real rate of interest that can be expressed purely in terms of time value.

That is not to say that time value does not matter.  If the time preference for consumption of vegetables changes, all of the own rates will change.  It is simply that we cannot point to a single own rate and say that this is the one that reflects pure time value, abstracted away from relative price movements.

In practice, we determine real rates of interest by reference to baskets of commodities.  We often calculate a real rate of interest using a consumer price index.  If we were to use a different index we would get a different result.

We can also use baskets of commodities in our imaginary economy.  For example, we could calculate the own rate on a basket of 10,000 onions, 20,000 tomatoes and 30,000 cucumbers.  In this case, the own rate works out at 6.75% (i.e. you get back 10,675 onions, 21,350 tomatoes and 32,025 cucumbers).  This means that we would be indifferent between lending the basket at 6.75%, or lending in any of the individual commodities alone at their respective own rates.

As with the individual commodities, the appropriate rate depends on the basket we choose - there is no true rate that is independent of that choice.  However, whatever basket we choose to reference, the arbitrage free rate required on money loans will always be the same.