An Evolution of Index Futures Convertibility

Scott Sumner is the leading advocate of index futures targeting.    I favor a very similar proposal, index futures convertibility.   Both are really sets of proposals, and over time, there has been substantial convergence.

I have used the term "index futures convertibility" to refer to Sumner's proposals.   To some degree, it is a matter of framing rather than substantive difference.    My interest in this approach developed from something Leland Yeager mentioned in correspondence.   We were discussing issues with "indirect convertibility." (Update:  Kevin Dowd has made key contributions to the literature on futures targeting and I believe that his thinking on the matter developed in a way very similar to mine--modifications of indirect convertibility.)

Consider a gold standard.   Paper money is redeemable with gold.   Gold can be deposited in exchange  for paper money.    Add a central bank and a slightly different framing, and the central bank is obligated to buy and sell gold at a fixed price.

Of course, it is possible to make money out of gold--full bodied gold coins.   It is possible that gold can be exchanged by weight.   With a well-developed gold standard, some interbank settlements can be made with gold bars.  And, of course, there is a long history of encouraging central (or commercial) banks to hold ample gold reserves.   On the other hand, it is possible that no one would be interested in using gold coins and there are alternatives to settling payments by transferring gold bars.

 Further, only minimal gold reserves are necessary for a gold standard.   The obligation of a central bank to buy and sell gold at a fixed price requires it to adjust the quantity of money, most probably by open market operations with government bonds or other securities, so that the equilibrium price level results in a relative price of gold that clears the gold market.   If an excess demand for gold develops at the official price, then the central bank must "tighten" monetary policy.   If an excess supply of gold develops  at the official price, the central bank must "loosen" monetary policy.

Why require the central bank to actually buy and sell gold?  It is a simple rule that constrains the central bank to make the needed changes in monetary policy to keep the price of gold at its "official" level.   The macroeconomic consequence of the regime is that the equilibrium price level depends on the relative price of gold, which in turn depends on the supply and demand for gold.  Shifts in that equilibrium price level will be associated with shifts in spending on output, but in the long run, nominal GDP will equal potential output times the equilibrium price level.

Now, consider a multiple standard.   In place of gold, paper money is redeemable with a bundle of commodities.   It could be a fixed amount of gold plus a fixed amount of silver plus a fixed amount of copper plus a fixed amount of steel plus a fixed amount of aluminum.   A more inclusive bundle is possible as well.   A bushel of wheat plus a bushel of corn, plus a bushel of rice could be added.

With a multiple standard, commodity coins are either highly impractical or literally impossible.   Settlement of payments with bundles of commodities is difficult and costly.   Similarly, holding reserves made up of all of the various items in the bundle would be costly for central (or private) banks.

Some advocates of a multiple standard see holding large commodity reserves as a virtue.   However, consider the opposite extreme where reserves are minimal to nonexistent.   The central bank would be compelled to adjust monetary policy, presumably by buying or selling government bonds or other securities, such that the sum of the market prices of the items in the bundle totals to the "official" price.   If the net supply and demand conditions for the various items results in upward pressure on the price of the bundle, the central bank must tighten monetary policy.   If instead there is downward pressure on the total of the prices of the bundle items, then the central bank must loosen monetary policy.

What is the point of requiring the central bank to buy and sell the bundles?   It is a simple rule that compels the central bank to adjust its monetary policy so that the total price of the bundle remains fixed at the "official" price.    The macroeconomics of the regime would be that the price level would depend on the relative price of the bundle.   If relative prices of the items in the bundle are subject to independent variation, the more inclusive the bundle, the more stable the relative price of the bundle.   Of course, as the bundle approaches the makeup of output, then the price level becomes closer to depending on the price of the bundle relative to itself, which is fixed by definition.

How is it possible to overcome the cost of storing these commodities?   Extending the items included in the bundle is desirable, but there is a trade off with cost of storage.   Further, a substantial portion of output is made up of goods and services that cannot be stored at all.   How can they be included?

Indirect convertibility requires that the issuer of money, such as a central bank, buy and sell some "redemption medium" that has a current market value equal to the sum of the market prices of the items in the bundle of  goods that serves as medium of account.    I tend to favor some kind of security, such as T-bills, but it is possible to explain the system using gold as a redemption medium.

Using gold as redemption medium, the central bank would buy and sell gold that has a market value equal to the sum of the actual market prices of the items making up the bundle of goods and services that defines the dollar.   As before, what the central bank would actually do is use open market operations in government bonds or other securities to tighten monetary policy when the total price of the items in the bundle would otherwise tend to rise above its official price and loosen monetary policy when the total price of the items in the bundle would otherwise tend to fall below its official price.

Why require indirect convertibility?   It is a simple (well, maybe not so simple) rule that compels the central bank to make the appropriate changes in monetary policy.   Indirect convertibility is a substitute for direct convertibility.

How does indirect convertibility impose this constraint?   If the total of the market prices of the items in the bundle should actually deviate from target, the central bank would be obligated to buy or sell the redemption medium, here gold, at a price different from the market price.   Those trading with the central bank would make profit and the central bank would suffer financial losses.   Because there would be transactions costs for those redeeming and selling or buying and depositing gold, this creates a range for variation in the total price of the bundle.   To avoid ruinous financial losses, the central bank would be compelled to adjust monetary policy to keep the total price of the bundle within the range determined by transactions costs.

Indirect convertibility does not involve fixing the price of the redemption medium, gold in this example.   The price of gold is free to adjust according to supply and demand conditions in the gold market.   If the price of the bundle is on target, the central bank is obligated to buy and sell gold at the current market price, which is the same price that everyone receives on the market.   There is no particular reason to for anyone to trade gold with the central bank.   There would be nothing socially desirable about people buying or selling gold at the central bank.

Even if the price of the bundle deviates from target, the market price of gold isn't fixed.   The market price of gold can vary with the supply and demand for gold, though the central bank is providing arbitrage profits to those who trade gold with the central bank.

The market forces created by indirect convertibility are very powerful in terms of keeping the price of the bundle within a narrow range.   However, shifts in the relative supply and demand conditions of the bundle, particularly a narrow bundle, would require very sharp shifts in monetary policy that would result in perhaps very damaging shifts in nominal expenditure on output and on the broader price level.   These would be similar to supply shocks.

Unfortunately, expanding the bundle creates measurement problems.   The analysis above assumes continuous measurement.   If the total price of the bundle is measured only periodically, requiring the central bank to make redemptions based upon the last measurement until the subsequent measurement could be extremely disruptive.   This is especially true with monthly (or quarterly) measurements, but weekly or even daily measurements would hardly help.

Yeager suggested that perhaps the answer is to redeem now with some of the redemption medium, and then use the subsequent measurement of the price of the bundle to determine the additional amount of the redemption medium that must be provided to complete the transaction.     I took this idea and developed it such that the central banks (or private banks, really) buy and sell the redemption media at its current market price and then after the subsequent measurement of the actual market prices of the bundel items, the amount transacted would be adjusted according to any deviation of the total market price of the bundle from the target price.

The "adjustment" is equivalent to a futures contract.     If the total of the prices of items in the bundle is divided by the target price for the bundle, the result is an index number.   The goal is for the central bank to adjust monetary policy to keep the price index at 100.     Indirect convertibility using the subsequent measurement of the price index involves the central bank buying and selling the redemption medium at its market price along with a futures contract on the price index.   If the price index is above target, the central bank must pay those who purchased the redemption medium and a the futures contract.   If the price index is below target, the central bank must pay those who sold the redemption medium and a futures contract.

If those buying and selling the futures match, the central bank buys and sells equal amounts of the redemption medium and is hedged on the future contract.   If the price index comes in above or below target, the central bank subsequently transfers funds between those who bought redemption medium and those who sold it.

If, on the other hand, there is an expectation that the price index will be above 100, then there is an incentive to redeem money for gold (buy gold) in order to obtain a futures contract from the central bank.   If the price index does come in above target, the central bank would owe money to all of those who redeemed money.   The central bank would be given a financial incentive to avoid that consequence by tightening monetary policy before the price level rose, keeping it on target at 100.

If there is an expectation that the price index will be below 100, then there is an incentive to sell gold to the central bank in order to sell the futures contract.   If the price index does come in below 100, then the central bank would owe money  to all of those from whom it purchased the gold.   To avoid those losses, the central bank would need to implement an expansionary monetary policy.

The central bank would have a financial incentive to always adjust monetary policy to keep the price index on target.   If the change in the price index was a bolt from the blue, and no one expected it, then there would be no incentive to buy or sell gold and buy or sell a futures contract on the index.   There would be no financial consequences for the central bank.

If the deviation of the price index from 100 is so small that the payments are too small to cover transactions costs, then there is no incentive to trade the futures contract.   The incentives only come into play with significant and expected shifts in the price index.   The central bank is compelled by the threat of financial losses to tighten or loosen monetary policy to avoid any significant expected deviation of the price index from target.

Sumner pointed out that very next  measurement of the price index would be inappropriate.  That is because the redemptions would be occurring after some the prices used to calculate the index have already been measured.   This argument suggests that purchases and sales of the redemption medium in April should be adjusted according to any deviation of the price index from 100 in May.  This would be reported in early June.  

Since the actual point of the regime is to impose financial losses on the central bank for significant anticipated deviations of the price index from target, there is no reason to actually require that some redemption medium be purchased or sold.   The financial losses are solely from the futures contracts and it is to avoid those losses that the central bank uses ordinary open market operations to keep the expected value of the price index on target.   Trading gold or some other redemption medium is just an unnecessary third wheel.

Exactly which future measure of the price index should be used is not obvious.   Why not have the central bank buy and sell futures this month on the price index two or three months in the future rather than one month? 

And finally, the futures contracts don't have to be on a price index.   It is possible to use some other nominal macroeconomic magnitude--for example, an index calculated by deviations of nominal GDP from a target growth path.  

The rationale for the system is to impose a financial penalty on a central bank that fails to adjust its monetary policy enough to avoid a significant expected deviation of the value of some policy goal from target.   Those of us who believe that a nominal GDP level target is the best (or least bad) target, would propose that the penalty be for failing to adjust monetary policy to avoid a significant expected deviation of nominal GDP from its target growth path.

In my view, that is the purpose of index futures convertibility.   It is a substitute for direct convertibility of money with a single easily storable commodity like gold or silver.    Its benefit is that it constrains the central bank (or a private banking system if that can be managed) to stabilize expected spending on output rather than the price of gold.   It is better to stabilize the growth path of spending on output rather than some measure of the price level.   And it is better to stabilize the growth path of spending on output rather than have it fluctuate with the supply and demand conditions for gold.

Index futures convertibility necessarily has little connection with existing futures contracts which involve a changing price of the futures contract to reflect expectations of a changing price of the underlying commodity at the settlement date.   Further, it has little connection to the typical futures contract which involves a storable commodity (or financial asset) and so allows hedging.   The logic where futures prices drive spot prices by hedging and storage just does not apply.

The notion that there will be a futures contract on some macroeconomic statistic that the central bank is trying to stabilize, and the central bank will watch the price of that futures contract and vary its policy instrument settings to stabilize it, and particularly according to some mechanical rule, is fraught with difficulties.   But I have never conceived of index futures convertibility as being anything like that.